MASARYK UNIVERSITY
Faculty of Science
Habilitation Thesis
Analysis of biomacromolecular
structural fragments
Brno 2016 Radka Svobodov´a Vaˇrekov´a
To my grandmother, my parents and my daughter Radunka.
Acknowledgements
I would like to thank my past supervisors for their valuable advice, my colleagues
and co-authors for our fruitful work together and also my family for their love and
support. Last but not least, I thank God for his mercy and patience with my faults.
iii
Contents
Preface 1
1 Introduction 2
2 Analysis of biomacromolecular structural fragments 6
2.1 Validation MV, VDB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 Validation of annotation – validation analyses . . . . . . . . 7
2.1.3 Validation – procedure and software . . . . . . . . . . . . . . 8
2.1.4 Example: Validation of nipah G glycoprotein . . . . . . . . . 9
2.2 Description, detection and extraction PTQ, MO, MO2 . . . . . . . . . . 10
2.2.1 General biomacromolecular fragments PTQ . . . . . . . . . . 10
2.2.1.1 State of the art . . . . . . . . . . . . . . . . . . . . . 10
2.2.1.2 Description – molecular language PatternQuery . 11
2.2.1.3 Detection and extraction – procedure and software 11
2.2.1.4 Example: Detection of LecB sugar binding sites . . 12
2.2.2 Channels and pores MO, MO2 . . . . . . . . . . . . . . . . . . . 12
2.2.2.1 State of the art . . . . . . . . . . . . . . . . . . . . . 12
2.2.2.2 Channel detection – procedure and software . . . . 13
2.2.2.3 Example: Detection of channels in cytochrome P450 15
2.3 Comparison SB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.1 State of the Art . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.2 Fragment comparison – procedure and software . . . . . . . 17
2.3.3 Example: Comparison of Zn binding sites in zinc ﬁngers . . 18
2.4 Characterization EO, EB, EL, EPM, EAM, BAX, MO, MO2 . . . . . . . . . . . 19
2.4.1 Partial atomic charges . . . . . . . . . . . . . . . . . . . . . . 19
2.4.1.1 State of the art . . . . . . . . . . . . . . . . . . . . . 19
2.4.1.2 Parameterization of EEM EO, EB, EL . . . . . . . . . . 21
2.4.1.3 EEM charges – procedure and software EPM, EAM, EL 23
2.4.1.4 Example: Docking of glycerol into ubiquitin EAM . 24
2.4.2 Channel characteristics MO, MO2 . . . . . . . . . . . . . . . . . 25
2.4.2.1 State of the art . . . . . . . . . . . . . . . . . . . . . 25
2.4.2.2 Channel properties . . . . . . . . . . . . . . . . . . 26
2.4.2.3 Channel properties – procedure and software . . . 27
2.4.2.4 Example: Properties for known channels . . . . . . 27
iv
3 Selected applications 29
3.1 Validation: Quality of different molecular classes VDB . . . . . . . . 29
3.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.2 Data set preparation and methodology . . . . . . . . . . . . 29
3.1.3 Overall ligand validation results . . . . . . . . . . . . . . . . 30
3.1.4 Quality comparison of individual molecular classes . . . . . 31
3.1.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Charges in small molecules: Prediction of pKa
PQ, PE, PS . . . . . . . 32
3.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.2 Quantitative Structure-Property Relationship modeling . . . 33
3.2.3 Prediction of pKa using QM charges PO . . . . . . . . . . . . 34
3.2.4 Prediction of pKa using EEM charges PE . . . . . . . . . . . . 36
3.2.5 3D structure sources for pKa prediction using charges PS . . 38
3.2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3 Charges in proteins: BAX Activation BAX . . . . . . . . . . . . . . . 41
3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.2 Analysis of charge transfer within Bax activation . . . . . . 42
3.3.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4 Channels: Enzyme channels anatomy AN . . . . . . . . . . . . . . . 44
3.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.4.2 Data set preparation and methodology . . . . . . . . . . . . 45
3.4.3 Channel occurrence and geometrical properties . . . . . . . 46
3.4.4 Channel chemical properties . . . . . . . . . . . . . . . . . . 46
3.4.5 Channel physicochemical properties . . . . . . . . . . . . . . 47
3.4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4 Future prospects 50
5 Summary 51
Bibliography 53
List of publications included in the habilitation thesis 66
ValidatorDB: database of up-to-date validation results for ligands and
non-standard residues from the Protein Data Bank . . . . . . . . . . 68
PatternQuery: web application for fast detection of biomacromolecular
structural patterns in the entire Protein Data Bank . . . . . . . . . . 76
High-quality and universal empirical atomic charges for chemoinformatics
applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
How does the methodology of 3D Structure preparation inﬂuence the
quality of pKa prediction? . . . . . . . . . . . . . . . . . . . . . . . . 94
AtomicChargeCalculator: interactive web-based calculation of atomic
charges in large biomolecular complexes and drug-like molecules . 105
Anatomy of enzyme channels . . . . . . . . . . . . . . . . . . . . . . . . . 119
MotiveValidator: interactive web-based validation of ligand and residue
structure in biomolecular complexes . . . . . . . . . . . . . . . . . . 128
MOLE 2.0: advanced approach for analysis of biomacromolecular channels136
Predicting pKa values from EEM atomic charges . . . . . . . . . . . . . . 150
v
Rapid calculation of accurate atomic charges for proteins via the Electronegativity
Equalization Method . . . . . . . . . . . . . . . . . . . 166
Charge proﬁle analysis reveals that activation of proapoptotic regulators
Bax and Bak relies on charge transfer mediated allosteric regulation 178
MOLEonline 2.0: interactive web-based analysis of biomacromolecular
channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
SiteBinder: an improved approach for comparing multiple protein structural
motifs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Predicting pKa Values of substituted phenols from atomic charges: comparison
of different quantum mechanical methods and charge distribution
schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
Electronegativity Equalization Method: parameterization and validation
for large sets of organic, organohalogene and organometal molecule 228
Optimized and parallelized implementation of the Electronegativity Equalization
Method and the Atom-Bond Electronegativity Equalization
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
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Preface
This habilitation thesis is a compilation of scientiﬁc publications to which I contributed
as the ﬁrst author, the corresponding author, or as a co-author. The articles
were published between 2006 and 2015, and a list of them is given on page 66.
A common topic of all the publications is the analysis of biomacromolecular structural
fragments such as ligand and metal binding sites, channels and pores, and
supersecondary structure elements. Speciﬁcally, the articles focus on the development
of approaches for the validation, detection, extraction, comparison and
characterization of fragments, and also on the application of these approaches
for solving important biological questions. The accompanying text highlights the
author’s contribution to the ﬁeld of biomacromolecular structural fragment analyses,
and it also contains a brief introduction to the topic. Detailed information
on the developed approaches and their applications can be found in the enclosed
original publications.
1
1
Introduction
In recent years, the life science research community has strongly beneﬁted from
the fact that a vast amount of data is available about various types of molecules.
For example, we can obtain the complete human genome of a selected individual
in less than 14 days, nearly 90 million various small molecules are described
in freely accessible databases (e.g., Pubchem [1], ChEMBL [2], ZINC [3], DrugBank
[4]), more than 110 thousand biomacromolecular structures have been determined
and published (Protein Data Bank [5]). This richness of data has catalyzed
and strengthened the formation of so-called modern life sciences – life science specializations
focused on research utilizing some part of this data. The best known
modern life sciences are genomics, proteomics, metabolomics, systems biology,
bioinformatics, structural bioinformatics, and chemoinformatics. Although these
modern life sciences are relatively young, they have provided many key results
in basic and applied research – from understanding biomacromolecular functions
and mechanisms of their action to the classiﬁcation of types of disease or the rational
development of novel drugs (e.g. [6–12]).
An important and very interesting development in modern life sciences is
the interconnection of structural bioinformatics and chemoinformatics. Structural
bioinformatics focuses on researching three-dimensional (3D) biomacromolecular
structures – e.g., their prediction, comparison and characterization. Chemoinformatics
focuses on small organic molecules (primarily drugs or ligands) and
studies mainly their 3D structure generation, similarity searches, and predictions
of their properties or activities. Chemoinformatics and structural bioinformatics
are highly compatible, since we need to discover both biomacromolecules and
their targets – ligands. A powerful combination of structural bioinformatics and
chemoinformatics enables us to focus on key regions of a biomacromolecule –
biomacromolecular structural fragments such as ligand or metal binding sites,
channels, pores, or supersecondary structure motifs. Analyses of these fragments
can produce very beneﬁcial outputs such as discovering drug design patterns,
information for the classiﬁcation of biomacromolecules, understanding the relationship
between structure and function, and predicting their putative functions
(e.g. [11–20]). The interconnection of structural bioinformatics and chemoinformatics
can therefore bring useful insights into biology, biochemistry and biomolecular
chemistry.
2
Nowadays, when we would like to analyze the biomacromolecular structural
fragments, we are in both a great and a challenging situation, caused by the real
richness of the available data. I would like to demonstrate these two sides of
the coin with a small example. In 1990, there was just one 3D structure of a cytochrome
P450cam in Protein Data Bank (found using its UniProt [21] molecular
name ”p450-cam”). In 2000, 22 structures of these cytochromes were available
(with various substrates, including a few mutants). Nowadays, we have 120 such
cytochrome structures in Protein Data Bank. Therefore, twenty years ago, analyses
focused on some properties of cytochrome fragments (e.g., how cytochrome
active sites or the channels leading to them look in general) were purely science
ﬁction. Ten years ago, some modest analyses could be performed, but their statistical
signiﬁcance or the proper coverage of substrates were questionable. Today,
we have a supercritical volume of data and we can do really meaningful, useful
and reliable analyses. In parallel, the richness of the data introduces a signiﬁcant
problem. In 1990, the analysis of one structure could be done easily intuitively
and manually. About ten years ago, the manual analyses were theoretically still
applicable (if a researcher had enough students) or some basic methodologies implemented
in in-house scripts could be used. Currently, manual processing is
clearly nonsense and employing some basic methodologies meets with problems,
because they are not robust and general enough to handle a large and heterogeneous
set of samples. Therefore, before we can begin the highly interesting analyses
and before we can obtain some key results, we must ﬁrst focus on the methodologies
and software tools for performing analyses. Unfortunately, we cannot
just ﬁnd and obtain ready-to-use approaches for individual analyses of biomacromolecular
structural fragments. The reason for this is that these methodologies
are still under intensive development.
Our deep interest in biomacromolecular structural fragments and in parallel,
the lack of approaches for their realization motivated us to concentrate our work
on two interconnected goals. The ﬁrst was the development of methodologies
for the analysis of biomacromolecular structural fragments. The second was their
application in resolving important biological and chemical questions. Therefore
my habilitation thesis is also focused on these two topics.
Important steps within the analysis of protein structural fragments are their
validation, detection, extraction, comparison and characterization. The necessity
of structure validation became evident when some published structures were
found to contain serious errors [22–25]. Reliable and well-established approaches
for the validation of standard biomacromolecular building blocks (amino acids
and nucleotides) are now available [26–29]. The validation of ligands, which are
frequent components of biomacromolecular fragments and the main sources of
their errors [30], is a markedly more complex problem and its methodology is still
under development. We introduced an extended methodology for the validation
of ligand annotation, applicable for any ligands and non-standard residues [MV,
VDB].
An essential step in biomacromolecular structural fragment analysis is the collection
of all fragment samples. Therefore, the fragment should be ﬁrst described
via a proper molecular language, then detected within the structures and then extracted
from them. Several molecular languages for describing various molecular
structures were introduced [31–33] and also a few approaches were developed for
3
the extraction of specialized compounds [11,12,16,17,20,34]. Based on them, we
developed the molecular language PatternQuery [PTQ], which enables any structural
fragment to be determined, and a methodology for the rapid extraction of
fragments described this way from the Protein Data Bank. An important class
of biomacromolecular fragments are their channels and pores, since they provide
a substrate with access to an active site. Few methodologies for their extraction
have been published – Caver [35–37], MolAxis [38, 39], MOLEonline [MO] and
MOLE 2.0 [MO2]. The last two were developed by ourselves.
A substantial task within structural fragment analysis is also fragment comparison.
In general, when we compare similar 3D structures, we need to ﬁrst
pair corresponding atoms of the compared structures and then the structures are
superimposed based on this pairing. Many state-of-the-art approaches for comparing
organic molecules were developed, and they include implicit [40–44] or
sequence alignment-based pairing [45–47]. We created an approach employing
so-called combinatorial and subgraph matching pairing [SB], which is appropriate
for fragments.
The ﬁnal step in the process of structural fragment analysis is its characterization,
i.e. determining the fragment’s characteristic properties. Partial atomic
charges are one such property, providing information about the electron distribution
within a molecule. The most appropriate approach for their calculation is
quantum mechanics (QM), which is unfortunately very demanding in terms of
time and computational resources. A faster alternative to QM are empirical methods,
of which the Electronegativity Equalization Method (EEM) [48] is the most
popular and applicable. EEM has been signiﬁcantly improved in recent years [49–
53], and we also intensively participated in its development. Speciﬁcally, we published
EEM parameterization for organic molecules [EO], for biomacromolecules
[EB] and for ligands [EL]. In parallel, we developed a methodology for calculating
EEM charges in large biomacromolecules (a parallel approach [EPM] and an approximative
method [EAM]) and in ligands and drug-like molecules [EL]. Other
key characteristics of biomacromolecular structural fragments are channel properties.
While the channel radius and length were calculated by all current channel
detection tools, our approaches MOLEonline [MO] and MOLE 2.0 [MO2] provide
a rich set of chemical, geometrical and also physico-chemical channel properties.
The developed methodologies for the analysis of biomolecular structural fragments
enabled us to perform several interesting studies and in this way resolve
a few important biological and chemical questions. Speciﬁcally, we evaluated
the quality of structures for different molecular classes [VDB], we used charges
for pKa prediction [PQ,PE,PS] and for researching apoptotic protein Bax activation
[BAX], and we discovered the anatomy of enzyme channels [AN].
A quality evaluation of individual ligands or biomacromolecules can be straightforward
to obtain [MV]. But we lack the bigger picture -– information about the
quality of various molecular classes (e.g., drug molecules, organometals, carbohydrates).
Therefore, we performed such an analysis [VDB]. The best quality proved
to be drug molecules, probably because markedly more effort is expended on determining
their structure in biomacromolecular complexes. Carbohydrates and
polycyclic ligands exhibited problems in the chirality of their carbon atoms, as
expected. The most problematic ligands are organometals, exhibiting clear validation
problems in most validation criteria.
4
Partial atomic charges proved to correlate with the acid dissociation constant
pKa [54–57]. This constant is an important molecular property and its values are of
interest in chemical, biological, environmental and pharmaceutical research [58–
60]. At the same time, its measurement is highly demanding and its prediction
is still a challenge. Therefore, we focused our research on charge-based approaches
to pKa prediction. We demonstrated that QM charges are highly successful
descriptors for the prediction of pKa via Quantitative Structure-Property
Relationship (QSPR) models [61], but a proper charge calculation approach must
be used [PQ]. We later demonstrated that empirical charges calculated via EEM
are also applicable for pKa prediction [PE]. We then found that the pKa predicting
QSPR models are sensitive to the 3D structure generation methodology employed
for preparation of input molecular 3D structures. Therefore, we evaluated
which 3D structure sources are applicable [PS]. We discovered that a workﬂow for
the fast and accurate prediction of pKa can be as follows: The preparation of 3D
structures via the data- and knowledge-based approach (used in software tools
CORINA [62] and Omega [63]) with no further optimization, calculation of EEM
charges for these structures and then the EEM QSPR prediction of pKa. Such a
workﬂow can be directly used within the process of in silico drug design or incorporated
into other chemoinformatics applications.
Charges can also help us to understand the mechanisms of important biological
processes -– e.g., the activation of the apoptotic protein Bax [BAX]. Apoptosis is
a programmed cell death, and its proper regulation is essential for multi-cellular
organisms. Apoptosis includes Bax activation [64, 65], Bax oligomerization and
forming pores in the mitochondrial membrane. The Bax activation mechanism
is still unclear and it motivated us to investigate changes in the Bax charge proﬁle
upon activation. We found [BAX] that charge reorganizations after activator
binding mediate the exposure of the functional sites of Bax (i.e., the C-domain
and BH3 domain) and as a consequence activate Bax. The afﬁnity of the Bax Cdomain
for its binding groove is decreased due to the Arg94-mediated abrogation
of the Ser184-Asp98 interaction. We further identiﬁed a network for charge transfer,
which brings the activation information from the activation site, through the
hydrophobic core of Bax, to the distant functional sites of Bax. The network was
mediated by a hub of three residues on helix 5 of the hydrophobic core of Bax.
Channels play a key role in enzymes – proteins which catalyze reactions changing
substrates into products [66–77]. The reason for this is that the enzymatic active
site is often buried deep within their structure and connected to the outside
by a channel. Therefore, these channels inﬂuence the substrate preference of the
active site. An important biological question is what properties the enzyme channels
have. We performed analyses of the channels in more than 4,000 enzyme
structures [AN]. We identiﬁed that at least 64% of these enzymes contain on average
two channels longer than 15 ˚A leading to the catalytic site. The longest and
the most hydrophobic channels were found in oxidoreductases and the shortest
and the most hydrophilic channels in ligases. The composition of channel lining
residues differed from the average composition of enzyme structures as well as
from the composition of the protein surface. Speciﬁcally, aromatic, charged and
polar amino acids occur more frequently in channel walls. All of these ﬁndings
indicate that the active site access channels have a signiﬁcant biological function,
as they are involved in co-determining the enzyme’s substrate preferences.
5
2
Analysis of biomacromolecular
structural fragments
2.1 Validation MV, VDB
2.1.1 State of the Art
The validation of biomacromolecular structures obtained by NMR and X-ray crystallography
has become a very important topic, because some published structures
have been found to contain serious errors [22–25]. The ﬁrst step in the
validation of biomacromolecules and their complexes is checking the standard
building blocks (residues), namely standard amino acids and nucleotides. The
usual methodology is to evaluate the speciﬁc properties of all of these standard
residues (e.g., electron density, atom clashes, bond lengths, bond angles, torsion
angles). These approaches are embedded into common validation software tools
such as OOPS [29], WHAT CHECK [26], PROCHECK [27], PROCHECK-NMR
[78], AQUA [78] and MolProbity [28].
The next key step is the validation of ligands and non-standard residues. This
step can be performed in a similar manner as for the standard residues (with focus
on electron density and atom clashes). Such a methodology is implemented in
several validation software packages: ValLigURL [79], Mogul [80], Coot [81] and
PHENIX [82].
A different methodology for validating ligands was developed later – the validation
of annotation. The goal of this approach is to evaluate if the ligand or
non-standard residue is denoted (annotated) correctly, i.e., if its structure corresponds
to the 3-letter code it was assigned in the PDB ﬁle format. Speciﬁcally, the
topology and stereochemistry of the validated molecule are compared to those
of a correct molecule (reference molecule, model), and any differences found are
reported. The ﬁrst proposal of such an approach was published by L¨utteke et al.
and implemented in Pdb-care [83]. It contained basic validation analyses and it
was purely focused only on carbohydrates. The demand for more universal and
deeper ligand validation analyses and also the end of the availability of Pdb-care
motivated us to accept the challenge and focus on the development of ligand validation
methodologies based on the validation of annotation.
6
Speciﬁcally, we developed a rich set of validation analyses, which covers the
main issues observed in the topology (2D structure) and geometry (3D structure)
of ligands and which are important for their correct annotation [MV, VDB].
These analyses can be performed on any ligand from the Protein Data Bank. In
parallel we also developed the software tools MotiveValidator [MV] and ValidatorDB
[VDB] to facilitate of the analyses. MotiveValidator is a tool that enables
individual ligand or sets of ligands to be validated and introduces several advanced
validation analyses. ValidatorDB provides a database of weekly updated
validation results for all ligands from the Protein Data Bank and introduces further
useful validation analyses.
2.1.2 Validation of annotation – validation analyses
Validation analyses can be classiﬁed into three categories, namely Completeness,
Chirality and Advanced analyses (Figure 2.1) [VDB].
The Completeness analyses attempt to ﬁnd which atoms are missing (Figure
2.1 B), whether these atoms are part of rings (Figure 2.1 C), or the structure
is degenerate, i.e., the molecule contains very severe errors (Figure 2.1 D). These
severe errors may refer to residues overlapping in the 3D space, or atoms which
are disconnected from the rest of the structure.
The Chirality analyses are only performed on complete structures, and aim to
evaluate the chirality of each atom in the validated molecule. We distinguish between
several types of chirality errors: on carbon atoms (C chirality, Figure 2.1 E),
on metal atoms (Metal chirality, Figure 2.1 F), on atoms with 4 substituents in
one plane (Planar chirality, Figure 2.1 G), on atoms connected to at least one substituent
by a higher order bond (High order chirality, Figure 2.1 H), and the remaining
chirality issues (Other chirality).
The Advanced analyses are focused on issues which are not actual chemical
problems, but which can complicate further processing and exploration of the
data, and thus should be noted. The Substitution analysis (Figure 2.1 I) reports the
replacement of an atom with an atom of a different chemical element. The Foreign
atom analysis (Figure 2.1 J) detects atoms which originate from the neighborhood
of the validated molecule (i.e., having different PDB residue ID than the majority
of the validated molecule), and generally marks sites of inter-molecular linkage.
The Different naming analysis (Figure 2.1 K) identiﬁes atoms whose name in PDB
format is different from the standard convention for the validated molecule. The
Zero RMSD analysis reports molecules whose structure is identical (root mean
square deviation = 0 ˚A ) to the model. The Alternate conformations analysis detects
the occurrence of alternate conformations in the validated PDB entry.
Basic validation analyses (i.e., missing atoms and wrong chirality) were published
by L¨utteke et al. [83]. We introduced the detection of missing rings, substitutions,
different atom naming and foreign atoms [MV]. Afterwards, we presented
a classiﬁcation of chirality errors and also extended the set of advanced
validation analyses (i.e., zero RMSD and Alternate conformation) [VDB].
7
Completenessanalyses
Complete structure
correct chirality
A
Incomplete structure
missing atom
B
Incomplete structure
missing ring
C
Incomplete structure
degenerate motif
D
Complete structure
correct chirality
Wrong chirality
C chirality error
Wrong chirality
Metal chirality error
Wrong chirality
Planar chirality error
Wrong chirality
High order error
Advancedanalyses
Complete structure
substitution
I
Complete structure
foreign atom
J
Complete structure
different name
L
SIA SIA SIA SIA
A
Chiralityanalyses
O1 instead of O6
Complete structure
correct chirality
Complete structure
correct chirality
Complete structure
correct chirality
Complete structure
correct chirality
FE G H
SIA AVC HEM CMP
SIA
AVCSIA HEM CMP
SIA SIA SIA
Figure 2.1: Examples of results provided by different validation analyses. ValidatorDB classiﬁes
results into three main categories (Completeness, Chirality, Advanced), each referring to several
related analyses.
2.1.3 Validation – procedure and software
The ligand is validated based on its annotation (i.e., the 3-letter code of the residue
in the PDB ﬁle). The ligand itself with its immediate vicinity (2 neighbouring
atoms) are taken as an input for validation. The model (reference molecule for
8
validation) is taken from the wwPDB CCD database [84] and has the same annotation.
The validation proceeds by identifying the maximum common subgraph
between the input motif and the model. The validated molecule and the model are
then superimposed via Sitebinder [SB] in such a way that their root mean square
deviation (RMSD) is minimal. The superimposition provides a pairing (bijection)
between atoms in the validated molecule and corresponding (chemically equivalent)
atoms in the model. This bijection enables various properties of each atom
in the validated molecule to be compared, with those of the chemically equivalent
atom from the model. All the validation analyses are based on this comparison of
atom properties (presence, chirality, element symbol, PDB name, etc.). A scheme
of the validation procedure is depicted in [MV].
The above-mentioned procedure is incorporated into two software tools – MotiveValidator
[MV] and ValidatorDB [VDB]. MotiveValidator is a web application,
which enables the user to validate individual ligands or their sets. It can
be found at http://ncbr.muni.cz/MotiveValidator. ValidatorDB is a database
which summarizes the validation results for all ligands found in the Protein Data
Bank. It is updated weekly based on updates to the Protein Data Bank and can be
found at http://ncbr.muni.cz/ValidatorDB.
2.1.4 Example: Validation of nipah G attachment glycoprotein
complexed with ephrin-B3
Nipah virus infection may lead to severe respiratory disease and fatal encephalitis
in humans. The Nipah virus relies on the Nipah G attachment glycoprotein for
host cell recognition. The crystal structure of the glycoprotein complexed with
its receptor ephrin-B3 (PDB ID: 3D12 [85]) contains 30 instances of 11 different
carbohydrates, each with one ring and ﬁve chiral atoms.
Figure 2.2: Validation of all carbohydrate ligands in Nipah G attachment glycoprotein and its
receptor ephrin-B3 (PDB ID: 3D12). 13 out of 30 ligands displayed incorrect chirality of 1 to 5
atoms.
9
We validated all carbohydrate structures in this biomacromolecular complex
using MotiveValidator [MV]. The validation showed that 13 of these ligands had
incorrect chirality (see Figure 2.2). In the few cases with GLC or NGA ligands,
all 5 chiral atoms exhibited incorrect chirality. Manual inspection of the structure
showed further discrepancies in the ligand part (see details in [MV]).
2.2 Description, detection and extraction PTQ, MO, MO2
2.2.1 General biomacromolecular fragments PTQ
2.2.1.1 State of the art
When we need to analyze biomacromolecular structural fragments, it is ﬁrst necessary
to ﬁnd and obtain individual samples of the fragment among the available
structures. In general, such a fragment (also called a pattern) can be any set
of atoms – e.g., a protein backbone, ligands or metals together with their binding
sites or surroundings, speciﬁc amino acid or nucleotide sequences, atoms or
residues satisfying given criteria (distance, composition, intramolecular connectivity),
etc. A key step is to describe the fragment in a manner that is readable
to a computer, and in this way develop a query for detecting the fragment. The
fragments can be described based on their 1D structure (sequence), 2D structure
(topology) or 3D structure (geometry) or via some combination of all of these as-
pects.
This description of the fragment requires a molecular language general enough
to record all the possible properties of the fragment. At the same time, the language
needs to be simple and transparent enough to be usable by the wider research
community.
To date, several languages for the description of molecular structure have been
designed. One of the most used languages is SMARTS (SMILES arbitrary target
speciﬁcations language) [31]. It is an extension of the SMILES linear notation
(used to describe the 2D structure of a molecule), that uses wild cards (i.e., expressions
that can match multiple elements) for atoms and bonds. This enables queries
to be speciﬁed where only partial information about the structure of the molecule
is provided. Other languages describing molecular structures are for example
MQL (molecular query language) [32] and SLN (Sybyl line notation) [33, 86]. In
parallel, a few software tools were developed to enable the extraction of some
structural patterns [11,12,16,17,20,34]. Unfortunately, these tools are designed to
operate either on a low number of structures, or their functionality is focused on
very speciﬁc and narrow applications.
Because we had a strong need to automatically process (and therefore also automatically
detect) the fragments, we focused on the development of an applicable
molecular language. Namely, we developed the language PatternQuery [PTQ],
which enables the robust and straightforward description of biomacromolecular
structural fragments. We also developed a methodology and software – the PatternQuery
web application [PTQ], which detects all samples of the fragment in
Protein Data Bank based on its description in the PatternQuery language.
10
Figure 2.3: The query recognizes the binding pocket of any residue containing a pyranose moiety
in the envelope glycoprotein gp160 from Human immunodeﬁciency virus 1 in complex with
Homo sapiens immunoglobulins (PDB ID: 3U7Y). A) First, the query identiﬁes a pyranose moiety
(a ring composed of 5 carbons and an oxygen atom). B) Then, all residues which include this pattern
in their structure are identiﬁed. C) Finally, all the residues that are at most 4 ˚A from any of
the pyranose-containing residues are detected as well.
2.2.1.2 Description – molecular language PatternQuery
PatternQuery [PTQ] is a molecular language based on the Python programming
language. This molecular language describes biomacromolecular structural fragments
using the nature and relationship between atoms, residues, and other structural
elements. The individual fragment descriptions in the language (co called
queries) deﬁne the composition, topology, connectivity, and geometry of a fragment.
Therefore, the PatternQuery language enables us to operate at the 1D, 2D
and also 3D structure level. PatternQuery contains 110 keywords, examples of
several PatternQuery keywords are given below:
• Atoms(X) returns all atoms with the element symbol X
• Residues(R1, R2) returns all residues with the 3-letter code R1 or R2
• ConnectedAtoms(F, r) returns all atoms within distance r from fragment F
• Authors(F) returns the authors of the structure containing fragment F
• Weight(F) returns the molecular weight of fragment F
The queries can be also combined into more complex ones. Figure 2.3 gives an
example of a query that identiﬁes and extracts a fragment made up of a residue
containing a pyranose moiety, together with its immediate surroundings.
2.2.1.3 Detection and extraction – procedure and software
The PatternQuery language describes a fragment in such a way that it can be
easily translated into a set of rules. In parallel, our methodology for ﬁnding
fragments represents a biomacromolecular structure as a molecular graph, where
atoms are vertexes and bonds are edges. Searching for a fragment is therefore
realized as the detection of sets of atoms which meet the criteria deﬁned in the
PatternQuery language description.
This methodology is implemented in PatternQuery server [PTQ] – an interactive
web application for ﬁnding and obtaining a fragment from the whole Protein
Data Bank. Depending on the complexity of the deﬁned queries and the amount
11
of data set entries, running the queries may take from a few seconds, up to approximately
one hour (for the whole Protein Data Bank). The application PatternQuery
is available at http://ncbr.muni.cz/PatternQuery.
2.2.1.4 Example: Detection of LecB sugar binding sites
Pseudomonas aeruginosa is an opportunistic pathogen associated with a number
of chronic infections. This pathogen forms a bioﬁlm, enabling it to survive both
the response of the host immune system, and antibiotic treatment [87]. One of
the cornerstones of bioﬁlm formation is the presence of sugar-binding proteins
on the outer cell membrane - LecA (PA-IL) and LecB (PA-IIL). Their inhibition is
considered to be a promising approach for anti-pseudomonadal treatment [88].
We employed PatternQuery to discover sugar binding sites of similar geometry
to the tetrameric LecB entry in the PDB. Speciﬁcally, we searched for 2 calcium
ions at most 4 ˚A apart, and all the residues directly interacting with either of
these ions. Furthermore, only the molecular fragments containing a residue with
a furan or pyran ring were preserved. The complete query which identiﬁes such
fragments is given in [PTQ]. The initial analysis of the PDB archive revealed 355
different fragments originating from 231 PDB entries. However, the majority of
the sugar moieties originated from nucleotides. To ﬁlter them out, a simple ﬁlter
was employed, which gave 108 distinct fragments originating from 36 PDB entries
of 7 different organisms. The majority of them originated from P. aeruginosa,
however other pathogens such as Ralstonia solanacearum, Burkholderia cenocepacia,
or Chromobacterium violaceum were identiﬁed among the organisms of origin. The
sugar-binding domain in 87 fragments is composed of 3x Asp, 2x Asn and Glu
and Gly residues, which is the binding site referred to as the sugar binding motif
in the literature [89] for a total of 24 PDB entries from 3 organisms. In 12 further
fragments a glycine residue was not present due to the fact that the structure
stored in the PDB is only the asymmetric unit, rather than the expected biological
unit, which is a tetramer. Finally, the remaining 9 fragments originated from 6 different
pectate lyase (EC: 4.2.2.2) structures and exhibited a different binding motif
to the LecB protein. Details on the analysis can be found in [PTQ]. Information
about the structural similarity of the P. A aeruginosa LecB sugar binding site with
sugar binding sites in R. solanacearum, B. cenocepacia and C. violaceum fully agrees
with the ﬁndings published by Mitchell et al. [90].
2.2.2 Channels and pores MO, MO2
2.2.2.1 State of the art
A channel (or tunnel) is a pathway connecting a point inside the biomacromolecule
(e.g., an active site) to an exterior one. A pore is a pathway that passes through
the biomacromolecule from one point on the surface to another. Channels play
signiﬁcant roles in many biologically relevant systems. For example, the internal
pores of ion channel proteins maintain a highly selective ionic balance between
the cell interior and exterior [91–95], photosystem II channels are involved in photosynthesis
[96,97], ribosomal polypeptide exit channels allow nascent peptides to
leave the ribosome during translation [34], and active site access/egress channels
12
enable the substrate/product to enter/leave the occluded active sites of various
enzymes (e.g., cytochrome P450 [75,98–102], acetylcholinesterase [103–105], etc.).
Information about the nature of active site access paths can also be utilized in
biotechnology applications aimed at designing more effective and selective enzymes
[106–108]. Therefore, the identiﬁcation and characterization of channels
are fundamental to understanding numerous biologically relevant processes and
serve as a starting point for rational drug design, protein engineering and biotechnological
applications.
Over the last few years, numerous computational approaches have been developed
for the detection and characterization of empty spaces in biomacromolecules,
particularly in proteins [109]. The main strategies used in the developed algorithms
can be grouped into four classes [110]. The ﬁrst class is comprised of
grid-based methods, which project biomacromolecular structures onto a 3D grid,
process the void grid voxels and connect them into pockets or tunnels. These
methods are used in numerous software tools, such as POCKET [111], 3V [112],
LIGSITE [113,114], dxTuber [115], HOLLOW [116], CHUNNEL [117], and CAVER
1.x [35]. Sphere-ﬁlling methods belong to the second class. These methods carpet
biomacromolecules with spheres layer by layer. A cluster of carpeting spheres
is considered a pocket. This method is implemented in SURFNET [118] and
PASS [119]. The third class involves slice and optimization methods. These methods
split a biomacromolecular structure into slices along a starting vector deﬁned
by the user and then optimization methods are used to determine the largest
sphere. These approaches are implemented in the software HOLE [120] and PoreWalker
[121]. The fourth class represents methods utilizing Voronoi diagrams, in
which the shortest path is searched for from a starting point to the biomacromolecular
surface. This approach was used in the previous version of MOLE 1.x [106]
and it is also utilized in other software tools, e.g., MolAxis [38,39], CAVER 2.0 [36]
and CAVER 3.0 [37].
In our work, we introduced a marked improvement and enrichment of the
current channel detection methodology, based on Voronoi diagram utilization and
found in the software MOLE. This software was originally developed by our research
group and it is one of the most used and best known software tools for the
detection and characterization of channels and pores. Our improved methodology
was published in two steps – the ﬁrst approach was part of the MOLEonline
web service [MO] and further improvements were introduced as a part of the
MOLE 2.0 software tool [MO2].
2.2.2.2 Channel detection – procedure and software
The algorithm for ﬁnding channels implemented in MOLE (version 2.0 and higher)
involves seven steps: i) computation of the Delaunay triangulation/Voronoi diagram
of the atomic centers, ii) construction of the molecular surface, iii) identiﬁcation
of cavities, iv) identiﬁcation of possible channel start points, v) identiﬁcation
of possible channel end points, vi) localization of channels, and vii) ﬁltering of the
localized channels (see Figure 2.4).
13
Figure 2.4: Scheme showing the steps involved in the channel calculation algorithm, illustrated
for cytochrome P450 3A4 (PDB ID: 1TQN).
Step i: Computing the Delaunay triangulation/Voronoi diagram In the ﬁrst step,
the Delaunay triangulation of the atomic centers is computed. The Voronoi diagram
is then constructed as the dual of the Delaunay triangulation.
Steps ii and iii: Approximating the molecular surface and identifying cavities
The molecular surface is approximated by the iterative removal of boundary
tetrahedrons from the outermost layers (i.e., tetrahedrons found at the interface
between the molecule and the external environment). Boundary tetrahedrons produced
by the triangulation are removed in this step if they are sufﬁciently large
to ﬁt a sphere with a given probe radius. The remaining tetrahedrons form one
or more connected components. We call the components that contain at least one
tetrahedron on the molecular surface cavity diagrams.
Steps iv and v: Identifying possible start and end points of channels
The approach includes two ways to specify potential channel start and end
points:
• Computed: Start and end points are deﬁned as the centers of the deepest
tetrahedrons in each cavity. The depth of the tetrahedron is deﬁned as the
number of Voronoi edges from the closest boundary tetrahedron.
• User-deﬁned: Speciﬁed by a user deﬁned 3D point. Next, cavities that have
at least one tetrahedron within a deﬁned distance from the user-speciﬁed
point are found. Finally, for each such cavity, the start point is selected as
the circumsphere center of the tetrahedron closest to the original point. Potential
channel end points are placed in the centers of particular boundary
tetrahedrons in such a way that the distance between the two end points is
at least the cover radius. This is achieved by picking the largest boundary
tetrahedron and marking it as an exit, then removing all boundary tetrahedrons
within the cover radius. This process is repeated until all non-exit
boundary tetrahedrons are removed.
14
Step vi: Computing channels
Once the potential start and end points have been identiﬁed, channels are computed
as the shortest paths between all pairs of start and end points in the same
cavity diagram. To achieve this, Dijkstra’s algorithm is used. At this stage, each
channel is represented by a sequence of tetrahedrons. The next step is to approximate
the channel centerline by a natural cubic spline of the circumsphere centers
of the tetrahedrons. Additionally, a ”radius spline” is computed that determines
the centerline distance to the closest atom van der Waals sphere.
Step vii: Filtering of channels The above-described steps usually generate a
large number of channels. However, many of these channels are either too narrow
(i.e., have a bottleneck with a small radius) to be considered relevant or are
duplicated (i.e., too similar to each other). To obtain the most relevant channels,
the methodology contains a ﬁltering of too narrow and too similar channels.
This methodology is implemented in MOLEonline [MO] – an interactive web
application for ﬁnding channels and pores. In parallel, its implementation is also
available in MOLE 2.0 [MO2] – a standalone software package focused on the detection
and characterization of channels and pores. Both these tools are available
at http://ncbr.muni.cz/mole.
2.2.2.3 Example: Detection of channels in cytochrome P450
Figure 2.5: Results of channel analysis of Cytochrome P450 3A4 (CYP3A4). Three channels
found from a user-speciﬁed starting point (calculation started from Glu 308 and Thr 309 according
to the CSA]) are shown – the solvent channel (in blue), the channel 2a (in dark red) and the channel
2e (in light red).
Microsomal Cytochrome P450 (CYP) enzymes are important for the metabolism
of many endogenous compounds and xenobiotics [122,123]. CYPs share a buried
active site [124], which is connected to the outside environment by various access/egress
channels [102]. These channels are responsible for substrate passage
15
to and product release from the active site, and they are considered to be involved
in the substrate preferences of CYP, which has been shown to vary considerably
among CYP enzymes [75,100].
Figure 2.5 shows all the channels connecting the active site of an enzyme CYP
3A4 (PDB ID: 1TQN) with the exterior (detected via MOLEonline). The topranked
channel found by MOLEonline (blue in Figure 2.5) is the solvent channel
(as described in [102]). The solvent channel is 10 ˚A long and its bottleneck
is 1.41 ˚A wide. These ﬁndings are consistent with previous data, which have
identiﬁed the solvent channel as the main channel responsible for active site solvation
[125]. Other two channels are 2x family channels (as described in [102]),
which are considered to be involved in hydrophobic substrate binding. Their position
and shape fully agree with published information [100,126].
2.3 Comparison SB
2.3.1 State of the Art
Comparing biomacromolecular structural fragments is a necessary task during
the analysis of these fragments. It enables e.g. multiple fragments to be processed
as one sample or to classify fragments according their similarity. In addition,
knowledge concerning fragment similarity can help us to understand the relationship
between a protein’s structure and function, to classify biomacromolecules, to
identify evolutionary relationships between proteins, and to obtain patterns for
drug discovery [11–20].
The comparison of 3D structures is a complex topic that can be divided into
several subtopics. We distinguish between methods that compare compounds
with identical (or very similar) 2D structure, as opposed to methods dealing with
compounds for which the 2D structure differs signiﬁcantly. In our work, we were
mainly focused on a comparison of molecules with identical (or very similar) 2D
structures (also called superimposition or superposition), because it is very helpful
in processing biomacromolecular fragments. The superimposition consists of
two interdependent stages [SB]. First, it is necessary to ﬁnd the correspondence
(atom pairing) between the atoms coming from different structures. In the second
step, the sets of paired atoms (3D points) are ﬁtted together as tightly as possible
by a geometrical transformation (optimal ﬁtting). There are several heuristics and
algorithms to obtain an atom pairing.
Implicit pairing associates atoms with the same index or position (i.e., pairing
the i-th atom of the ﬁrst molecule to the i-th atom of the second molecule). Many
state-of-the-art programs that offer the superimposition of organic molecules (e.g.
Chimera [40], VMD [41], Gromacs [42], gOpenMol [43], Pymol [44]) use implicit
pairing.
Employing sequence alignment is an improvement on the implicit pairing approach.
First, the sequence alignment is performed by a selected algorithm (e.g.,
Needleman and Wunsch alignment [127], ICM ZEGA alignment [128] etc.). Afterwards,
the atoms from the aligned residues are paired using an implicit pairing.
This approach is only applicable for the superimposition of proteins or protein
sequences with a reasonable degree of sequence similarity. Several drug design
16
A B
Figure 2.6: A) Implicit pairing between residues PHE 83 (blue) and PHE 91 (orange) from the
PDB entry 2WH6, and the superimposition calculated by the program VMD, which uses this pairing.
B) The best possible pairing between PHE 83 (blue) and PHE 81 (orange) from 2WH6 and
the superimposition calculated by our program SiteBinder, which is able to ﬁnd this pairing. The
differences compared to the implicit pairing are indicated with red arrows. In both A) and B),
atoms are denoted by their number in the residue, while their PDB name is in brackets.
packages (e.g., MOE [45], Discovery Studio [46], ICM [47], etc.) implement this
approach.
The systematic (combinatorial) approach ﬁnds all possible pairings and is therefore
very robust, but in parallel it can be nontrivially time-consuming.
Subgraph matching, which was originally developed for processing molecules
with different 2D structures, can also be used to ﬁnd a relevant pairing. This
approach identiﬁes the largest possible atom sets that can be superimposed.
When an atom pairing has been found, the paired 3D points are ﬁtted by performing
a geometrical transformation. The transformation can be found via an
iterative approach [129], via a closed form solution that utilizes rotation matrices
[130] or by the application of a quaternion algebra [131–133], which is currently
the most frequently used solution.
The comparison of fragments has several speciﬁcs. For example, the order
of atoms in the fragments can be different, therefore the implicit atom pairing
can neither be used for fragments nor for residues. Figure 2.6 demonstrates how
sensitive a superimposition is to the choice of atom pairing.
The next challenge in fragment superimposition is the fact that a comparison
of many fragments simultaneously (e.g. several thousands) is required and often
also a common pattern needs to be detected. This motivated us to develop
a methodology tailored to fragment superimposition and capable of handling
its difﬁculties. The methodology is implemented in the web application SiteBinder
[SB].
2.3.2 Fragment comparison – procedure and software
Superimposition of two fragments: Our methodology [SB] provides two superimposition
approaches – a combinatorial approach and a subgraph matching
approach.
The combinatorial approach ﬁrst generates a set of all chemically meaningful
atom pairings. These pairings are generated in such a way, that ﬁrst the atoms in
both fragments are divided into subsets according their properties. Speciﬁcally,
the subsets can be created according to a residue name, a residue identiﬁer and
17
an element symbol. Afterwards, all pairings between fragments which connect
atoms from the same subsets are generated. Then for each pairing, the optimal ﬁt
is performed using a state-of-the-art quaternion algebra approach [134]. Finally,
the pairing which provides the closest ﬁt is selected, and the ﬁt calculated using
this pairing is taken as the result. This approach can only superimpose fragments
containing the same number of atoms for each element symbol.
The subgraph matching approach ﬁrst detects the largest subgraph of the two
fragments. Afterwards, it generates the atom pairings based on the subgraph. For
all the pairings, the optimal ﬁt is calculated again using the quaternion algebra
approach. The best ﬁt is then taken as the result.
Superimposition of multiple fragments: We used a multiple superimposition
approach published by Wang et al. [135], adapted it to biomacromolecular
fragments and combined it with our algorithm for the superimposition of two
fragments. Our multiple superimposition approach works in two steps. First,
each fragment is superimposed onto the ﬁrst one. Afterwards, we calculate an
average fragment as the arithmetic average of the x, y and z coordinates of the
corresponding atoms. Next, all the fragments are superimposed onto the average
fragment. The new coordinates of all these superimposed fragments are used as
an input to the next iteration of the multiple superimposition approach. The iterative
superimposition process ends when a further iteration is not able to improve
the ﬁt.
2.3.3 Example: Comparison of Zn binding sites in zinc
ﬁngers
Cys2His2 zinc ﬁngers are one of the most common structural motifs in eukaryotes
- each ﬁnger recognizes three to four base pairs of DNA. There is also evidence
that some Cys2His2 zinc ﬁngers bind RNA and that others may participate in
protein-protein interactions. Individual ﬁngers contain approximately 30 amino
acids, and the hallmark of the motif is the presence of two cysteines and two
histidines that serve as zinc ligands. It can be deﬁned as the pattern X2-CYS-X2-
4-CYS-X12-HIS-X3-5-HIS, where X represents any amino acid residue. We used
SiteBinder to determine whether the center of the zinc ﬁnger motif (i.e., two CYS,
two HIS and a Zn atom) has a conserved geometry. First, we collected all zinc
ﬁngers from the Protein Data Bank. Speciﬁcally, we found 329 zinc ﬁngers from
205 different Protein Data Bank structures. Afterwards, we performed four superimpositions
for our set of zinc ﬁnger central motifs. These procedures differed in
the number of atoms selected for superimposition (displayed in red in Figure 2.7).
The results showed that the part of the motif which closely surrounds Zn has a
conserved structure and the conformation of more distant parts of CYS and HIS
may differ. We then focused on a special group of zinc ﬁnger Cys2His2 motifs,
namely those known to bind RNA. Their superimposition showed that the motifs
coming from the PDB entry 1ZU1 are markedly different than those in the other
investigated RNA binding proteins. This is probably explained by the fact that
one of the two HIS residues faces the binding site with the opposite face of the
imidazole ring (see Figure in [SB]). This structural dissimilarity correlates with a
18
functional difference. Speciﬁcally, the 1ZU1 zinc-ﬁnger motif has evolved to bind
double-stranded RNA [136].
A B
C D
Figure 2.7: Superimposition of 329 zinc ﬁnger central motifs. A) 9 superimposed atoms, RMSD
0.501 ˚A , B) 15 superimposed atoms, RMSD 0.527 ˚A , C) 19 superimposed atoms, RMSD 0.599 ˚A ,
D) 33 superimposed atoms, RMSD 0.840 ˚A . Atoms used in the superimposition procedure are in
red. For ease of visual interpretation, only the ﬁrst 80 motifs are displayed.
2.4 Characterization EO, EB, EL, EPM, EAM, BAX, MO, MO2
2.4.1 Partial atomic charges
2.4.1.1 State of the art
Partial atomic charges are real numbers describing the distribution of electron
density in a molecule, thus providing clues to the chemical behaviour of the molecules.
The concept of charges began to be used in physical chemistry and organic
chemistry. Afterwards, partial atomic charges were adopted by computational
chemistry and molecular modelling, where they are used to calculate electrostatic
interactions, describe the reactivity of the molecule etc. Speciﬁcally, they are applied
in molecular dynamics, docking, conformational searches, binding site pre-
19
dictions etc. Recently, partial atomic charges also became popular in chemoinformatics
and bioinformatics, as they proved to be informative descriptors for
QSAR and QSPR modelling [PQ, PE, PS] [54, 56, 137–140] and for other applications
[141–143]; they can be utilized in pharmacophore design [144–146], virtual
screening [147–149], similarity searches [150–152], molecular structure comparison
[153–155] etc.
Partial atomic charges cannot be determined experimentally or derived straightforwardly
from the results of quantum mechanics (QM), and many different methods
have been developed for their calculation. The most common method for
charge calculation is an application of the QM approach and afterwards the utilization
of a charge calculation scheme. Charge calculation schemes can use orbitalbased
population analysis, wave-function-dependent physical observables or the
reproduction of charge-dependent observables. Examples of orbital-based population
analyses are Mulliken population analysis (MPA) [156, 157], L¨owdin population
analysis [158] and Natural population analysis (NPA) [159, 160]. Wavefunction-dependent
physical observables are applied in the atoms-in-molecules
(AIM) approach [161,162], Hirshfeld population analysis [163–165], CHELPG [166]
and Merz-Singh-Kollman (MK) [167, 168] method. The reproduction of chargedependent
observables is embedded in the CM1, CM2, CM3, CM4, and CM5 approaches
[169,170].
Unfortunately, QM charge calculation approaches are very time-consuming. A
markedly faster alternative is to employ empirical charge calculation approaches,
which can also provide highly accurate charges. These approaches can be divided
into conformationally-independent, which are based on 2D structure (e.g.,
Gasteiger’s and Marsili’s PEOE [171,172], GDAC [173], KCM [174], DENR [175])
and conformationally-dependent, calculated from the 3D structure (e.g., EEM [48],
QEq [176] or SQE [177,178]). Conformationally-dependent charges are considered
to be more suitable for the characterization of biomacromolecules and their fragments.
The reason is that these charges contain extensive information not only
about the chemical surroundings of atoms, i.e., its topology (2D structure based
charges), but also the geometry and “chemical quality” of the surroundings. Such
information is missing, for example, in force ﬁeld charges which use averaged
atomic charges from large sets of structures. Therefore we focused purely on this
category of atomic charges.
EEM (electronegativity equalization method) is the most frequently used conformationally-dependent
empirical charge calculation approach. It calculates charges
using the following system of linear equations:








B1
κ
R1,2
· · · κ
R1,N
−1
κ
R2,1
B2 · · · κ
R2,N
−1
...
...
...
...
...
κ
RN,1
κ
RN,2
· · · BN −1
1 1 · · · 1 0








·







q1
q2
...
qN
¯χ







=







−A1
−A2
...
−AN
Q







(2.1)
where qi is the charge of atom i; Ri,j is the distance between atoms i and j; Q is the
total charge of the molecule; N is the number of atoms in the molecule; ¯χ is the
molecular electronegativity, and Ai, Bi and are empirical parameters. EEM is not
only a rapid charge calculation approach, but it can also provide highly accurate
20
charges, i.e., they can mimic the QM charges for which EEM has been parameterized.
Therefore, many EEM parameter sets for various QM charge calculation
approaches were published later or recently [50, 51, 53, 179, 180]. Also, we participated
in the EEM parameterization process – we published a parameterization
for organic molecules [EO], for biomacromolecules [EB] and for ligands [EL].
In parallel, a few freely available software tools also include an EEM charge
calculation method [181,182]. We also contributed to this ﬁeld, speciﬁcally we developed
a methodology for calculating of EEM charges in large biomacromolecules
– ﬁrst a parallel approach [EPM] and then an approximative method [EAM]. We
also created an OpenBabel patch for calculating the EEM charges in ligands and
drug-like molecules [EL].
2.4.1.2 Parameterization of EEM EO, EB, EL
EEM parameterization for organic molecules We ﬁrst focused on EEM parameterization
more than ten years ago. Our goal was to provide EEM parameters for
organic, organohalogen and organometal molecules. For this reason, we developed
the following EEM parameterization procedure:
• Selection of set of molecules for parametrization.
• Calculation of QM atomic charges for all molecules in the selected set (via
Gaussian).
• Calculation of average electronegativity of molecule:
¯χ = N
N
∑
i=1
1
x0
i
−1
(2.2)
• Calculation of x and y pairs for each atom:
x = qi (2.3)
y = χi − κ
N
∑j=1 (j=i)
qj
Ri,j
(2.4)
Note: This is calculated for all values of in a deﬁned set.
• Division of x and y pairs into sets according to the atom that the pair belongs
to.
• Calculation of parameters A and B for each set of x and y pairs.
• Finding the optimal κ value.
The methodology enabled us to perform parameterizations based on really
large sets of organic molecules. Speciﬁcally, we did EEM parameterization on 12
training sets selected from a database of predicted 3D structures (NCI DIS) and
from a database of crystallographic structures (CSD), where each set contained
21
2,000 to 6,000 molecules. The results of this parameterization conﬁrmed that the
number of molecules in the training set is very important for the quality of the
parameters. One result of our EEM parameterization was improved EEM parameters
(based on HF/STO-3G/MPA QM charges) for elements that were already
parameterized, speciﬁcally: C, O, N, H, S, F and Cl. We also calculated new parameters
for elements not yet parameterized, speciﬁcally for Br, I, Fe and Zn. The
results of this parameterization are summarized in the article [EO].
EEM parameterization for biomacromolecules We then focused on EEM parameterization
for biomacromolecules. Speciﬁcally, we prepared EEM parameters
for proteins containing calcium and no other metals nor any ligands. The proteins
itself are too large to perform QM charge calculations on them. Therefore, the
inputs for our EEM parameterization were protein fragments. These fragments
included the Ca atom and its surroundings. Therefore, we adapted the parameterization
procedure in the appropriate way:
• Selection of a set of proteins for parameterization.
• Preparation of their fragments.
• Calculation of QM atomic charges for all fragments in the selected set (via
Gaussian).
• Common EEM parameterization procedure (the same as for organic molecules).
This procedure enabled us to perform EEM parametrization for large protein
fragments as input structures. We calibrated the EEM parameter sets using atomic
charges computed by three population analyses (MPA, NPA, iterative Hirshfeld),
at the Hartree-Fock level with two basis sets (6-31G*, 6-31G**) and in two environments
(gas phase, implicit solvent). Thus, we produced 24 sets of EEM parameters.
Afterwards, we did an external validation of these EEM parameters on two
reference proteins (insulin and ubiquitin) and we found, that all EEM parameter
sets reproduce QM charges very accurately. The results of this parameterization
are summarized in the article [EB].
EEM parameterization for ligands We recently found, that even though several
EEM parameter sets have been published for organic molecules, none of
them were rich enough to cover common drug-like molecules, ligands and consequently
also biomacromolecular fragments. The reason for this was that the
available parameters only focused on a very limited part of the chemical space.
Speciﬁcally, they contained only parameters a for few elements, and even for these
elements only some bond orders were available. This strongly limits the applications
of EEM in fragment characterization and also its usage in chemoinformatics
and bioinformatics.
For this reason, we took our EEM parameterization methodology for organic
molecules [EO], improved its efﬁcacy (developing the parameterization tool NEEMP
[183]) and employed it to obtain universal and accurate EEM parameters for druglike
molecules and ligands. In this way we prepared six EEM parameter sets.
They enable the user to calculate EEM charges in a quality comparable to quantum
mechanics (QM) charges based on common charge calculation schemes (i.e.,
22
MPA, NPA and AIM) and a robust QM approach (HF/6-311G, B3LYP/6-311G).
The calculated EEM parameters exhibited very good quality on a training set and
also on a test set. They were applicable for at least 95% of molecules in key drug
databases (Drugbank, ChEMBL, Pubchem and ZINC) compared to less than 60%
of the molecules from these databases for which the other EEM parameters can be
used. The results of this parameterization are summarized in the article [EL].
2.4.1.3 EEM charges – procedure and software EPM, EAM, EL
Optimized and parallelized EEM charge calculation method (EEM SOLVER)
When we started our research in the ﬁeld of EEM atomic charges and their applications,
we found that even though the EEM method is published, there is
no available software tool for implementing it. This motivated us to prepare
such a tool. Speciﬁcally, we developed the software EEM SOLVER, which enables
the user to calculate EEM charges based on the inputted EEM parameters,
which he/she provides. EEM SOLVER is a command line application and has
two versions – a serial version, which is able to calculate EEM charges in small organic
molecules, and a parallel version which can be also used for large biomacromolecules.
The serial version includes this straightforward methodology:
• Filling the EEM matrix
• Transforming the matrix into row echelon form via Gaussian elimination
• Solving the equation system
The parallel version replaces the Gaussian elimination (the most complex part
of the method) with the parallel algorithm WIRS [184] and implemented this algorithm
within the PVM environment [185].
We also demonstrated the accuracy and performance of EEM SOLVER with
several examples. The parallel version was even applicable for molecules with
more than 1,000 atoms. These results are summarized in the article [EPM] and
the software EEM SOLVER is available here: http://ncbr.muni.cz/~svobodova/
eem_abeem/
EEM charges for large biomolecular complexes and drug-like molecules (ACC)
Recently, the necessity to process much larger biomacromolecules and also a community
demand for web-based software forced us to provide a new software solution
for the calculation of EEM charges. Speciﬁcally, we developed the web
application Atomic Charge Calculator (ACC). ACC embeds all published EEM
parameters and also enables the utilization of user-provided EEM parameters.
ACC can perform charge calculations for large sets of organic molecules (e.g., ten
thousands of molecules or more). In parallel, ACC is also able to calculate EEM
charges on really large biomacromolecular systems (e.g., close to a hundred thousand
atoms). ACC processes small molecules using the same methodology as
EEM SOLVER.
In parallel, it offers two new approaches for EEM calculation on large biomacromolecules
– EEM Cutoff and EEM Cover. These approaches work by splitting the
EEM matrix into multiple smaller matrices. With the EEM Cutoff approach, for
23
each atom in the molecule, ACC generates a fragment made up of all atoms within
a cutoff radius R of the original atom. Thus, for a molecule containing N atoms,
the EEM Cutoff approach solves N smaller EEM matrices describing a set of N
overlapping fragments from the original molecule. This markedly reduces the
complexity and time demands of the algorithm. EEM Cover provides another
streamlining of the calculations. It also splits the EEM matrix into smaller matrices,
but it only generates fragments for a subset of atoms in the molecule. Thereore,
the number of EEM matrices that need to be solved is reduced by at least 50%
compared to EEM Cutoff, while maintaining high accuracy. Both the EEM Cutoff
and EEM Cover method are approximative approaches, but their accuracy is very
high and in fact comparable to standard EEM.
We demonstrated the performance and applicability of ACC on three case
studies – a set of organic molecules, a set of antimicrobial peptides and a large
proteosome (more than 80,000 atoms). These results are summarized in the article
[EAM] and the software EEM SOLVER is available here: http://ncbr.muni.cz/
ACC
EEM charges for ligands and drug-like molecules (OpenBabel patch) The EEM
method was also implemented in the software tool OpenBabel. A weak point of
this implementation was that it only allowed one set of EEM parameters to be
used (namely, EEM parameters published by Bultnick et al. [50], based on QM
charge calculation approach B3LYP/6-31G*/MPA). These parameters only cover
a few elements (i.e., C, O, N, H, F). Unfortunately, OpenBabel replaced the EEM
parameters for missing elements with the EEM parameters for some other atom
types. This nonstandard approximation caused inaccuracies in the results. For
this reason, we provided an OpenBabel patch which introduces our EEM parameters
published in [EL]. Closely after its release, the developers of OpenBabel incorporated
our solution directly into OpenBabel.
2.4.1.4 Example: Docking of glycerol into ubiquitin based on
diﬀerent charges EAM
To show the applicability of EEM charges in proteins, we performed the common
docking calculation of glycerol into ubiquitin. Speciﬁcally, we used the same
ubiquitin molecule which was employed for the external validation of the EEM
parameters for proteins. Glycerol was chosen as a potential ligand because it has
been found to stabilize the native state of ubiquitin [186]. The ligand’s initial conformation
was taken from the coordinates of the ideal glycerol model available in
Ligand Expo [84] and contained 5 rotatable bonds.
In this experiment, we compared the docking results obtained in the ideal case
(therefore via using accurate QM charges) with the results obtained via various
empirical charges. The QM charges were calculated by HF/6-31G*/MPA. The
empirical charges were the EEM charges (calculated by our parameters mimicking
HF/6-31G*/MPA and published in [EB]), the Gasteiger-Marsili charges and the
AMBER ff94 charges. The results of the docking are depicted in Figure 2.8.
The ﬁgure shows that the docking results obtained using QM charges are well
reproduced via the EEM charges given by the above-mentioned EEM parameters.
The EEM binding pose differs by 0.07 kcal/mol and an RMSD of 0.131 ˚A from the
24
Figure 2.8: Docking of glycerol into ubiquitin via: A) HF/6-31G*/MPA QM charges: estimated
binding energy −9.64 kcal/mol. B) HF/6-31G*/MPA mimicking EEM charges: estimated binding
energy −9.71 kcal/mol, RMSD 0.132 ˚A compared to the QM pose. C) Gasteiger-Marsili charges:
estimated binding energy -8.65 kcal/mol, RMSD 3.244 ˚A compared to the QM pose. D) AMBER
ff94 charges: estimated binding energy −8.7 kcal/mol, RMSD 3.235 ˚A compared to the QM pose.
binding pose given using QM charges. For comparison, using Gasteiger-Marsili
or AMBER ff9469 charges on ubiquitin produces different binding poses. Speciﬁcally,
the binding pose given by Gasteiger-Marsili charges differs from that given
by QM charges by 0.99 kcal/mol and an RMSD of 3.244 ˚A . The binding pose
given by AMBER ff94 charges differs by 1.57 kcal/mol, and an RMSD of 3.235 ˚A .
2.4.2 Channel characteristics MO, MO2
2.4.2.1 State of the art
Closely connected to channel detection discovery is research in the ﬁeld of channel
characterization, i.e., the calculation of channel properties. Channel properties can
be divided into three classes – geometrical (length, radius, bottleneck radius, etc.),
chemical (lining residues of the channel, their neighborhoods etc.), and physicochemical
(e.g., polarity, charge, hydropathy). These properties are essential for
understanding the channel’s chemical and biological role. Based on them we can
evaluate which compound (how large, positively or negatively charged, polar or
nonpolar) can pass through the channel and how easy or difﬁcult it will be from
the energetic point of view. Therefore the channel’s properties are a clue to the
substrate speciﬁcity of a channel.
Basic chemical and geometrical properties (lining residues, channel length and
radius) are automatically provided as a side product of all the channel detection
methodologies. Therefore even the initial versions of channel detection software
(MOLE 1.0 [106], Caver 1.0 [35], MolAxis [38, 39]) returned them as additional
data about the detected channels. The computation of more sophisticated geo-
25
metrical properties (bottleneck radius, local minima radius etc.) was included in
channel calculation approaches later, and is provided by recent versions of channel
discovery tools [37]. Obtaining the physicochemical properties of the channel
is relatively nontrivial. Therefore, despite their high usefulness, channel physicochemical
properties only started to become available a few years ago. Speciﬁcally,
they were introduced by the software tool MOLEonline [MO] and are also provided
by MOLE 2.0 [MO2] .
We contributed to this ﬁeld by developing the methodologies for calculating
physicochemical and advanced geometrical properties. These methodologies are
incorporated in the software tools MOLEonline [MO] and MOLE 2.0 [MO2].
2.4.2.2 Channel properties
A channel can be viewed as a void volume inside the biomacromolecular structure,
and it can be described using the arrangement of residues which surround
this empty volume. Highly interesting parts of the channel are its local narrowings,
which are referred to as local minima. The global minimum of the channel
is then referred to as the bottleneck.
There are three recognized types of channel properties – geometrical, chemical
and physicochemical. The chemical properties of the channel are focused on
the residues which surround the channel. The best known chemical property is
the so-called lining residues, which describes the residues which are found in
the channel walls. These chemical properties also include local minima residues,
bottleneck residues and various derived criteria such as the second layer of the
channel (residues directly adjacent to the lining residues) etc.
The geometrical properties of the channel describe its geometry characteristics.
Basic geometrical properties are channel length and the radius of the channel at
a speciﬁc point. Important points for measuring the radius are the bottleneck
and other local minima. Also the 3D position of the centerline (line composed of
points in the center of the channel) and a proﬁle of the channel are widely used
geometrical properties.
The most complex properties are the physicochemical properties. Nowadays,
channel discovery methodologies only provide values for a few of them, i.e., hydropathy,
polarity, mutability and charge. Hydrophobicity and hydrophilicity are
two extremes of a spectrum, commonly referred to as hydropathy, and describe
the tendency of a molecule to interact with water [187]. Polarity is the property of
a molecule given by the separation of electric charge, leading to the molecule having
electric poles. The mutability (or relative mutability) quantiﬁes the tendency
of an amino acid to be substituted (mutated) in a protein’s structure. Substitution
with similar amino acids generally retains protein function, while substitution
with amino acids with different properties may affect the protein’s structure
or function. Relative mutability is high for easily substitutable amino acids (e.g.,
small polar residues) and low for amino acids which play a signiﬁcant role in the
protein structure (e.g., amino-acids with substrate binding or catalytic activity).
Charge describes the localization of charged residues in the channel.
26
2.4.2.3 Channel properties – procedure and software
Our channel characterization methodology ﬁrst computes channel lining residues
and a channel centerline. The chemical and geometrical properties of the channel
are calculated in a straightforward manner by the application of linear algebra
algorithms.
A calculation of physicochemical properties is performed in the following way:
the properties are calculated based on tabulated values for unique residues surrounding
the channel (article [MO2] contains information about these tabulated
values). Speciﬁcally, the property values for all lining amino acids, which have
a side chain oriented towards the channel, are summarized and then averaged.
The calculation of individual properties contains specialized steps. Hydropathy
is computed using the Kyte-Doolittle scale [187] and when the amino acid
has its main chains oriented towards the channel, tabulated hydropathy values
for glycine (Gly) are used. With polarity, the value for asparagine (Asn) is used
for amino acids with the main chain oriented towards the channel. Amino acid
residues that have their main chains lining the channel are not considered when
computing mutability. Charge is calculated by a different procedure – as the
sum of the charges of individual amino acid side chains. We use the charge
(protonation or deprotonation) at physiological pH, therefore lysine and arginine
are positively charged, whereas aspartic and glutamic acids are negatively
charged. Despite the protonation state of histidine being dependent on its microenvironment,
we treat all histidines as positively charged. This simpliﬁcation only
produces a slight inaccuracy and enables us to perform the calculation faster. This
methodology is implemented in the web application MOLEonline [MO] and in
the software package MOLE 2.0 [MO2]. Both these tools are available at http:
//ncbr.muni.cz/mole.
2.4.2.4 Example: Physicochemical properties for known channels
We evaluated the physicochemical properties calculated by MOLE 2.0 for several
biomacromolecules containing biologically important channels/pores with
known functionality and known functions.
Gramicidin D (PDB ID: 1GRM) is known to form a polar pore in membranes
(Figure 2.9 A) [188], which agrees with the physico-chemical properties identiﬁed
using MOLE 2.0.
In the cytochrome c oxidase (PDB ID: 1M56), MOLE 2.0 identiﬁed two channels
with different polarities (Figure 2.9 B), which may be involved in the transfer
process required for the proper functioning of this enzyme [189].
For the nicotinic acetylcholine receptor (PDB ID: 2BG9), MOLE 2.0 computed
the central pore (Figure 2.9 C) lined with 18 negatively charged amino acids. This
could explain the experimentally observed selectivity for cation permeation [190].
Afterwards, we analyzed carbonic anhydrase (PDB ID: 3EYX), a biomacromolecule
which can utilize the inorganic carbon sources CO2 and HCO−
3 [191].
MOLE 2.0 predicted that the channel is highly polar (Figure 2.9 D), in agreement
with expectations.
These results demonstrate that physicochemical properties may provide useful
information about the nature of the channel and its biological function.
27
A B
DC
Figure 2.9: Comparison of known properties of biologically important channels/pores and their
polarity calculated with MOLE 2.0. A) gramicidin D, B) cytochrome c oxidase, C) nicotinic acetylcholine
receptor, D) carbonic anhydrase. The nonpolar channels are in blue and the polar channels
in red.
28
3
Selected applications
3.1 Validation: Evaluation of quality for different
classes of molecules VDB
3.1.1 Introduction
It is a well-known fact that the validation of biomacromolecular structures is an
important issue for the life sciences community [22–25]. Several studies showed
that ligands are the most problematic and corrupted parts of biomacromolecules
[30]. Thanks to current software tools [26–29], we can evaluate the quality of any
individual ligand in a biomacromolecular structure. Moreover, thanks to complete
validation information for the ligands from the Protein Data Bank [VDB],
we can see a summary of the quality status for all instances of one ligand (e.g., all
samples of α-D-mannose) in the Protein Data Bank. Therefore, we can compare
whether a particular ligand (i.e., all its instances on average) has a higher or lower
quality than another. Or we can recognize ligands with a low or high quality.
This is very helpful, but we are still missing the bigger picture – information
about the quality of various molecular classes (e.g., drug molecules, organometals,
sugars). Namely, how strongly do the classes of molecules differ in quality?
Which classes of molecules are more problematic from the quality point of view
and therefore will require more of our attention? And in contrast, which classes
of molecules have good quality and we can trust their structures? Additionally,
are some types of validation errors common for some classes of molecules? We focused
on these questions in our work. Speciﬁcally, we selected several important
classes of molecules and evaluated their quality.
3.1.2 Data set preparation and methodology
In our analysis, we focused on six classes of molecules, which are important from
the scientiﬁc point of view and which are in parallel markedly chemically different.
Speciﬁcally, we selected a class of experimental drugs and a class of approved
drugs, because drugs are one of the most frequent targets of research. Afterwards,
29
we chose a class of carbohydrates, because they are known as molecules containing
a lot of errors. Interestingly, their structural errors were so alarming that the
ﬁrst ligand validation tool was focused speciﬁcally on carbohydrates [83]. Next,
we selected mannose derivatives – a well-deﬁned subclass of carbohydrates – to
see how ﬂuctuating quality is inside the carbohydrate class. Then, we also selected
a further class that includes highly biologically important molecules (hormones,
metabolites etc.) and which can potentially contain more validation issues
– polycyclic molecules. Last but not least, we added the class of organometals –
a group of molecules highly interesting from the application point of view. The
formal deﬁnition of the individual classes is the following:
• Experimental drugs: Described in DrugBank [4] as experimental drugs, i.e.,
have been shown to bind speciﬁc proteins in mammals, bacteria, viruses,
fungi, or parasites.
• Approved drugs: Described in DrugBank as approved drugs, i.e., have received
approval in at least one country.
• Carbohydrates: Contain the pyran or furan ring. Molecules with P (e.g.,
ATP) were excluded, as their quality is inﬂuenced more by the occurrence of
phosphate derivatives than by the sugar part.
• Mannose derivatives: A subclass of carbohydrates, i.e., all carbohydrates
derived from mannose.
• Polycyclic molecules: Contain 3 or more conjugated rings. The molecules
with metals were excluded, as their quality is inﬂuenced more by the presence
of the metal than by their polycyclic structure.
• Organometals: Contain a metal atom.
For each class of molecules, we collected all their member ligands from the
wwPDB Chemical Compound Dictionary [84]. Afterwards, for each member ligand,
we extracted all their instances from the Protein Data Bank, validated them
and averaged the validation results for all instances belonging to the same molecular
class. In this way, we obtained validation results for all six analyzed molecular
classes. In parallel, we also calculated the overall ligand validation results
(i.e., the averaged validation results for all ligands from the Protein Data Bank).
Finally, we compared the validation results for individual classes and the overall
ligand validation results.
3.1.3 Overall ligand validation results
The overall ligand validation results (from August 10th 2014, see Table 3.1) showed
that about 9% of ligands are incomplete, of which about 6% are missing at least
one atom and 2.6% are missing rings. Chirality problems occur in less than 8%
of the remaining validated ligands. The frequency of basic chirality errors is even
lower – only 2.4% of molecules exhibit chirality errors at a carbon atom, and 1.4%
at a metal atom. Other chirality issues are generally reported more frequently -–
i.e., 4.3% of molecules have the wrong High order chirality and 1.1% the wrong
30
Planar chirality. Therefore, about 83% of validated molecules are complete and
have the correct chirality. This statement is slightly more optimistic than previous
estimates, which are based on the ﬁt to the electron density and 3D structure of
the ligands, and place the expected percentage of erroneous molecules between
20 and 30% [83,192].
Table 3.1: Summarization of validation results for individual molecular classes and comparison
with the overall validation results for all ligands in the Protein Data Bank (from August 10th 2014).
!
! All!ligands! Polycyclic!
Carbo1
hydrates!
Mannose!
derivates!
Organo1
metals!
Experi1
mental!
drugs!
Approved!
drugs!
Number!of!PDB!entries!
analyzed!
102364' 3568' 8752' 1534' 5216' 15307' 958'
Number!of!validated!
molecules!!
238153' 6804' 57302' 6341' 22600' 37450' 1934'
Number!of!models!used!
as!reference!
17674' 1370' 913' 53' 331' 3399' 185'
Incomplete!! 8.9%' 6.7%' 5.9%' 3.5%' 18.0%' 6.1%' 3.2%'
Missing!only!atoms! 5.9%' 3.1%' 4.2%' 3.0%' 6.0%' 5.0%' 0.9%'
Missing!rings! 2.6%' 3.0%' 1.5%' 0.1%' 10.7%' 0.6%' 2.0%'
Degenerate! 0.5%' 0.6%' 0.2%' 0.4%' 1.4%' 0.5%' 0.3%'
Wrong!chirality! 7.9%' 5.5%' 4.0%' 7.6%' 16.5%' 2.1%' 2.8%'
Wrong!C!chirality! 2.4%' 3.5%' 4.0%' 7.4%' 2.5%' 1.7%' 2.8%'
Wrong!Metal!chirality! 1.4%' 0.0%' 0.0%' 0.0%' 14.3%' 0.0%' 0.0%'
Wrong!High!order!
chirality!
4.3%' 1.9%' 0.0%' 0.2%' 0.0%' 0.4%' 0.0%'
Wrong!Planar!chirality! 1.1%' 0.0%' 0.0%' 0.0%' 10.5%' 0.1%' 0.8%'
Complete! 91.1%! 93.3%! 94.1%! 96.5%! 82.1%! 93.9%! 96.8%!
Complete!+!Correct!
chirality!
83.0%! 87.6%! 90.1%! 88.9%! 64.3%! 91.8%! 93.9%!
'
Legend:!The'color'code'refers'to'the'relative'difference'between'the'results'of'each'case'study'and'the'
PDBDwide'average'for'all'ligands.''Specifically:!
>'2'times'better,'>'30%'better,'>'30%'worse,'>'2'times'worse'
'
3.1.4 Quality comparison of individual molecular classes
Validation results for individual molecular classes are summarized in Table 3.1.
The validation results for experimental drugs demonstrated, that the quality of
their structures is clearly much higher than the statistics for all ligands.
For approved drugs, i.e., drugs already on the market, the situation is even
better. About 95% of these molecules are complete and have the correct chirality,
a consequence of the fact, that markedly more effort is expended on determining
their structure in biomacromolecular complexes.
Compared to the statistics for all ligands, carbohydrate molecules have overall
a higher quality (higher percentage of molecules with complete structure and
correct chirality). Nonetheless, they exhibit more errors in C chirality, probably
because they generally contain more chiral atoms.
Mannose derivatives play an important role in cell-cell recognition, a biological
function which relies heavily on chirality. Therefore they must have a characteristic
structure (determined by chirality) and are also strongly predisposed to
have C chirality errors. We found that the percentage of errors in C chirality is
over 3 times higher for mannose derivatives than the PDB-wide evaluation for all
ligands.
31
Polycyclic molecules exhibit similar trends to carbohydrate molecules, since
their structure is also ring-based. They also exhibit more errors in C chirality
than the average, probably due to their more complicated, carbon-based scaffolds.
Interestingly, they contain less C chirality errors than carbohydrates, conﬁrming
carbohydrates to be highly problematic from the quality point of view.
Organometals seem to have a low quality in general, showing that many challenges
remain in the ﬁeld of organometal structure determination.
3.1.5 Conclusions
The analysis of the quality of all ligands in the Protein Data Bank showed that 8%
of ligands are incomplete and a further 9% of ligands have chirality errors. Therefore,
more than 80% of ligand structures are correct. Experimental and approved
drugs were found to be molecular classes with a markedly higher quality than
average ligands. As expected, carbohydrates proved to be problematic from the
quality point of view, since they have a markedly higher percentage of C chirality
errors. This problem is further accented for mannose derivatives. Polycyclic ligands
gave similar results to carbohydrates, only with slightly lower percentage of
C chirality. The most problematic ligands are organometals, exhibiting outstanding
validation problems in most of the validation criteria.
3.2 Charges in small molecules: Prediction
of pKa
PQ, PE, PS
3.2.1 Introduction
The acid dissociation constant, Ka, and its negative logarithm pKa, are important
molecular properties and their values are of interest in chemical, biological,
environmental and pharmaceutical research [58–60]. pKa values have found applications
in many areas, such as the evaluation and optimization of candidate
drug molecules [193–195], ADME proﬁling [196,197], pharmacokinetics [58], understanding
protein-ligand interactions [59,198], etc. Moreover, the key physicochemical
properties such as lipophilicity, solubility, and permeability are all pKa
dependent. For these reasons, pKa values are important for virtual screening.
Furthermore, pKa is often used as a descriptor for QSAR models. Unfortunately,
experimental pKa values are usually unavailable even for compounds from the
chemical catalogues. In addition to that, obtaining experimental pKa values for
newly designed molecules (i.e., molecules existing only as a sketch on paper) is a
long-term project, because ﬁrst the synthetic pathway must be discovered. Therefore,
both the research community and pharmaceutical companies are interested
in the development of reliable and fast methods for pKa prediction.
Several approaches for pKa prediction have been developed [198–201], speciﬁcally
LFER (Linear Free Energy Relationships) methods [202,203], database methods,
decision tree methods [204], ab initio quantum mechanical calculations [205,
206], QSPR (Quantitative Structure-Property Relationship) modelling [56,137,207]
32
or ANN (artiﬁcial neural networks) methods [208]. However, pKa value prediction
remains a challenge for the research community.
An application of partial atomic charges for calculating the relative acidity or
reactivity of organic compounds is a known concept in organic chemistry. The
reason for this is that the partial atomic charges concept enables the prediction
of relative acidity or reactivity by estimating the extent of charge delocalization
based on molecular structure information. Therefore, the correlation between
pKa and relevant atomic charges calculated by different ab initio or semiempirical
approaches has been analyzed. For example, Gross et al. [54] calculated QM
charges via different population analyses and studied their correlation with pKa
for substituted phenols and anilines. Similarly, Kreye et al. [55] compared the
correlations of three different QM charge types (calculated via various levels of
theory) for substituted phenols. Dixon et al. calculated pKa from σ and π partial
charges [56], Citra [57] used partial charges and bond order, Xing et al. [209]
charges and polarizabilities, Soriano et al. [210] charges and frontier orbital energy
and Yangjeh [211] combined charges, polarizability, molecular weight, hydrogenbond
accepting capability and partial-charge weighted topological electronic descriptors.
The above-mentioned studies demonstrated that charges are very powerful
descriptors for pKa modelling and they demonstrate a linear dependency on
pKa. This indicates that partial atomic charges are very promising descriptors for
QSPR models focused on pKa prediction.
In our work, we continue to research pKa prediction methods. Speciﬁcally, we
focused on charge-based QSPR models for pKa prediction. Our ﬁrst publication
in this ﬁeld analysed the inﬂuence of QM theory level, basis set and population
analysis on the accuracy of QSPR models employing QM charges [PQ]. The second
publication answered the question of whether accurate but computationally
demanding QM charges can be replaced with markedly rapidly obtainable empirical
charges [PE]. Speciﬁcally, we used the empirical method EEM (Electronegativity
Equalization Method) – an approach mimicking QM charges, for which it was
parameterized. EEM is very fast and accurate and moreover, we have published
several EEM parameter sets [EO, EP, EL] and a few software tools for EEM calculation
[EPM, EAM, EL]. Our third pKa related publication ﬁlled in the ﬁnal piece
of the puzzle. Namely, it discusses how the 3D structure generation methodology
inﬂuences the accuracy of charge-based QSPR models for pKa prediction [PS]. All
three of our articles together therefore describe a way to quickly and precisely
predict pKa for newly designed molecules.
3.2.2 Quantitative Structure-Property Relationship mod-
eling
QSPR (Quantitative Structure-Property Relationship) models [61] calculate a molecular
property as a function of descriptors – values, which are computed directly
from the molecular structure. The relationship between a property and its descriptors
is predominantly linear and has the following form:
property = param1 · descr1 + param2 · descr2 + · · · + paramn · descrn + paramn+1
(3.1)
33
where descr1, descr2, ..., descrn are the descriptors mentioned above; param1,
param2, ..., paramn+1 are parameters of the QSPR model and n is the number of
descriptors in the model. The parameters are calculated based on experimental
values of the property and multiple linear regression (MLR) is the most common
parameterization method.
The quality of QSPR models, i.e. the correlation between the experimental
property and the property calculated by the model, is evaluated using so-called
quality criteria of the QSPR model [61]. The most frequently used quality criteria
are the squared Pearson correlation coefﬁcient (R2), root mean square error
(RMSE), average absolute pKa error ( ¯∆), standard deviation of the estimation (s)
and Fisher’s statistics of the regression (F).
3.2.3 Prediction of pKa using QM charges PO
Introduction. QM charges are the most accurate partial atomic charges obtainable.
Therefore they are the best choice for understanding the correlation between
charge descriptors and pKa. For this reason, we used them to design our ﬁrst
charge-based QSPR models and to recognize which charge descriptors we should
use in these models. QM charges can be calculated via several theory levels, basis
sets and charge calculation schemes. Different QM charge calculation approaches
(i.e. combinations of QM theory level, basis set and charge calculation scheme)
are appropriate for different applications. Therefore we also evaluated, which
QM charge calculation approaches are suitable for pKa prediction.
Methods. For our research, we used a dataset containing 124 phenol molecules.
The phenols were selected, because they are frequently used to evaluate QSPR
models. Their 3D structures, which are necessary for QM charge calculation, were
obtained from the DTP NCI database [212]. Experimental pKa values, required for
the parameterization of QSPR models, were taken from the Physprop database
[213].
We analyzed QM charges calculated via ﬁve theory levels. The ﬁrst two were
the Hartree–Fock (HF) method and second-order Møller–Plesset (MP2) perturbation
theory, which includes more sophisticated approximations of the Hamiltonian
than HF. The other three were density functional theory methods with BLYP,
BP86 and B3LYP functionals. BLYP is a gradient-corrected functional and is denoted
according to its authors (Becke, Lee, Yang and Parr). BP86 (Becke Perdew
1986) is similar to BLYP, but uses an older correlation functional (Perdew86). B3LYP
(Becke, three-parameter, Lee-Yang-Parr) is a hybrid functional constructed as a
linear combination of the HF and BLYP functionals. In parallel, we used three
basis sets (the simple basis set STO-3G and the more advanced basis sets 6-31G*
and 6-311G) and ﬁve charge calculation schemes – natural population analysis
(NPA), Mulliken charges (MPA), L¨owdin charges, Hirshfeld charges, and MerzSingh-Kollman
charges ﬁtted to the electrostatic potential (MK). Therefore, we
evaluated 75 (5*3*5) different QM charge calculation approaches.
In parallel, we tested various charge descriptors expressing charges close to the
phenolic OH group (which includes the dissociating hydrogen atom). Speciﬁcally,
we tested these descriptors: The atomic charge of the hydrogen atom from the
phenolic OH group (qH), the charge on the oxygen atom (qO), the charge on the
34
Table 3.2: Squared Pearson coefﬁcients (R2) between calculated and experimental pKa .
R2
for the basis set 6-31G* R2
for the basis set 6-311G
Theory
level
Charge calculation scheme
Theory
level
Charge calculation scheme
MK Hir. Löw. MPA NPA MK Hir. Löw. MPA NPA
BLYP 0.813 0.886 0.959 0.953 0.959 BLYP 0.826 0.868 0.926 0.932 0.96
BP86 0.813 0.89 0.959 0.954 0.959 BP86 0.825 0.874 0.931 0.939 0.959
B3LYP 0.808 0.897 0.963 0.959 0.961 B3LYP 0.822 0.882 0.937 0.938 0.962
HF 0.788 0.908 0.966 0.966 0.963 HF 0.811 0.907 0.95 0.945 0.961
MP2 0.788 0.912 0.966 0.966 0.964 MP2 0.812 0.91 0.951 0.945 0.961
R2
for the basis set STO-3G Legend
Theory
level
Charge calculation scheme excellent R2
RMSE Δ
MK Hir. Löw. MPA NPA excellent 0.95 – 0.97 0.4 – 0.5 0.32 – 0.38
BLYP 0.786 0.886 0.879 0.896 0.877 very good 0.92 – 0.95 0.5 – 0.63 0.38 – 0.51
BP86 0.787 0.882 0.878 0.896 0.876 good 0.9 – 0.92 0.63 – 0.7 0.51 – 0.54
B3LYP 0.817 0.902 0.895 0.904 0.894 acceptable 0.85 – 0.9 0.7 – 0.8 0.54 – 0.64
HF 0.867 0.928 0.92 0.92 0.92 weak 0.8 – 0.85 0.8 – 0.97 0.71 – 0.73
MP2 0.869 0.929 0.921 0.922 0.921 very weak < 0.8 > 0.97 > 0.73
!
!
!
carbon atom binding the OH group (qC1) and charges on all the other carbons
from the benzene ring.
Results. The best correlation with experimental pKa values were given by the
descriptors qH, qO and qC1, the other descriptors only gave a weak correlation.
Therefore, we utilized the following pKa predicting QSPR model:
pKa = paramH · qH + paramO · qO + paramC1 · qC1 + constant (3.2)
where paramH, paramO, paramC1 and constant are the parameters of the QSPR
model. For each evaluated QM charge calculation approach, we parameterized an
individual QSPR model (therefore we had 75 QM QSPR models). The parameterization
of the QSPR models was performed via multiple linear regression (MLR).
Afterwards, we utilized these QSPR models for pKa prediction, compared the predicted
and the experimental pKa values and calculated quality criteria (R2, RMSE,
¯∆) for all of them. The values of the most common quality criterion (R2) are summarized
in Table 3.2. Based on these results, we evaluated which QM theory level,
basis set and charge calculation scheme are applicable for pKa prediction.
In general, the results showed us that QM QSPR models provide a successful
approach for pKa prediction. Speciﬁcally, more than 25% of the models had
excellent quality (R2 >0.95) and more than half exhibited very good quality (R2
>0.9). All ﬁve examined theory levels are applicable for pKa prediction. The best
QSPR models are provided by MP2 and HF and their accuracy is comparable. The
most appropriate basis set is 6-31G*, the results for the 6-311G basis set are slightly
weaker. Surprisingly, the charges calculated via the simple basis set STO-3G also
provide acceptable QSPR models. The selection of the charge calculation scheme
had the strongest inﬂuence on the accuracy of the QM QSPR model. Mulliken,
Natural and L¨owdin population analyses with all levels of theory and basis sets
35
provide charges that are appropriate for pKa prediction. Hirshfeld population
analysis is also usable, when a proper theory level is selected. In the contrast, MK
charges are not applicable for pKa prediction via QSPR models, because all the
models based on these charges gave a weak quality.
3.2.4 Prediction of pKa using EEM charges PE
Introduction. Although QM charges provide accurate pKa predicting QSPR models,
these charges have one big limitation – their calculation is very time-consuming.
Therefore, QM QSPR models cannot be used for pKa prediction with a large set
of molecules. At the same time molecules with molecules with a large number of
atoms cannot be treated with QM QSPR models, or at least the prediction is highly
time-consuming. For these reasons, QM QSPR models cannot be used in virtual
screening or drug design, and also their applicability in chemionformatics is limited.
A markedly faster alternative to QM charges is the use of EEM charges (i.e.,
charges calculated by the Electronegativity Equalization Method). EEM charges
have a comparable accuracy to QM charges, for which they were parameterized.
These facts motivated us to focus on EEM QSPR models. Speciﬁcally, our goal
was to design successful EEM QSPR models and to evaluate the inﬂuence of EEM
parameter set selection on their accuracy.
Methods. The analyses of EEM QSPR models were performed on a data set containing
74 phenol molecules. The robustness and the applicability of the models
was afterwards illustrated using a data set with 80 carboxylic acids. The 3D structures
of the molecules were taken from DTP NCI and their pKa values originated
from Physprop. For our research, we used all EEM parameters published to date.
Speciﬁcally, we found 18 different EEM parameter sets, published in 8 different articles
[EO] [48,50–53,179,180] and reﬂecting 8 different QM charge calculation approaches.
Two of them contain charge calculation schemes which were not evaluated
in [PQ] – namely AIM (atoms in molecules) [161,162], and CHELPG [166].
Basic information about the EEM parameters and corresponding QM parameters
used are in Table 3.3 and more details can be found in the article [PE]. We needed
to compare the EEM QSPR models with the corresponding QM QSPR models.
Therefore we calculated not only EEM charges, but also the corresponding QM
charges and we prepared both EEM QSPR models and the corresponding QM
QSPR models.
Even though EEM charges are able to mimic the QM charges for which they
were parameterized, it is clear that they cannot fully maintain the accuracy of
QM charges. Therefore in our work we also focused on improving the QSPR
models to compensate for this effect. Speciﬁcally, we took inspiration from the
article of Dixon et al. [56] and introduced two further pKa correlating descriptors –
charge on the phenoxide O− from the dissociated molecule (qOD), and the charge
on the carbon atom binding this oxygen (qC1D). For this reason, we evaluated
not only the three descriptor QSPR (3d QSPR) models mentioned in [PQ] (see
equation 3.2 in page 35), but also the extended ﬁve descriptor QSPR (5d QSPR)
models. This means that we worked with 36 (2*18) EEM QSPR models and 16
(2*8) QM QSPR models. All the QSPR models were parameterized by MLR and
afterwards we utilized them for pKa prediction, compared the predicted and the
36
experimental pKa and calculated their quality criteria (R2, RMSE, ¯∆). Values of R2
are summarized in Table 3.3.
Table 3.3: Basic information about EEM parameters (ﬁrst three columns) and R2 for correlation
of experimental pKa and pKa predicted via EEM QSPR model based on these EEM parameters.
3d EEM 5d EEM 3d QM 5d QM
HF/STO-3G MPA Svob2007_cbeg2 0.8671 0.9179
Svob2007_cmet2 0.8663 0.9189
Svob2007_chal2 0.8737 0.9203
Svob2007_hm2 0.8671 0.9179
Baek1991 0.9099 0.9195
Mort1986 0.8860 0.9142
HF/6-31G* MK Jir2008_hf 0.8696 0.9154 0.8394 0.8864
B3LYP/6-31G* MPA Chavez2006 0.8910 0.9192
Bult2002_mul 0.8876 0.9158
NPA Ouy2009 0.8731 0.9094
Ouy2009_elem 0.8727 0.9132
Ouy2009_elemF 0.8848 0.8866
Bult2002_npa 0.9044 0.9180
Hir. Bult2002_hir 0.8415 0.9050 0.9122 0.9477
MK Jir2008_mk 0.8696 0.9148
Bult2002_mk 0.8639 0.9131
Chel. Bult2002_che 0.8695 0.9057 0.8528 0.9087
AIM Bult2004_aim 0.8646 0.9017 0.9609 0.9677
Legend
excellent
excellent
very good
good
acceptable
weak
QM theory level
+ basis set
Charge
calc.
scheme
EEM parameter
set name
0.9501
0.9670
0.71 – 0.73
0.9588
0.8447
0.9646
0.9723
0.9679
0.8960
0.8 – 0.85
0.7 – 0.8
0.8 – 0.97
0.9 – 0.92 0.63 – 0.7
0.95 – 0.97
0.92 – 0.95
0.4 – 0.5
0.5 – 0.63
0.32 – 0.38
R2
of QSPR model
0.38 – 0.51
0.51 – 0.54
0.54 – 0.640.85 – 0.9
R
2
RMSE
Δ
Δ
Results. As we expected, QM QSPR models exhibited similar behavior to what
we had seen in [PQ]. Speciﬁcally, the QM QSPR models based on Mulliken or Natural
population analyses were very accurate, models based on Hirshfeld population
analysis were acceptable and models employing MK charges again proved
to be weak. The CHELPG charges provide comparable results to MK, because
they are based on a similar approach. A new ﬁnding was that QM QSPR models
based on AIM charges are also very accurate. The introduction of new descriptors
brought about an improvement to QM QSPR models, especially when the original
3d QM QSPR models were weaker.
37
EEM QSPR models performed worse than QM QSPR models, but they still
gave an acceptable accuracy. In particular 5d EEM QSPR models demonstrated
very good quality criteria. An interesting and pleasant fact is that EEM QSPR
models are not as sensitive to the choice of EEM parameter set.
When we prepared similar QSPR models for carboxylic acids, these models
gave comparable trends and accuracy, and therefore illustrated the robustness and
transferability of this pKa prediction approach.
3.2.5 3D structure sources for pKa prediction using
charges PS
Introduction. A necessary input for pKa prediction using charge-based QSPR
models is the 3D structure of the molecule. The experimental 3D structures were
only measured for a limited set of molecules. On the other hand, when we design
a molecule (or a set of molecules for virtual screening), obtaining its (their)
experimental structure is a long-term project, because we ﬁrst need to synthetize
the molecule or ﬁnd some other source of it. The markedly faster and in reality
the only applicable way, to obtain the 3D structure of these molecules is to generate
the structure automatically. There are a few methodologies for preparing
3D structures and they are implemented in several software tools. Speciﬁcally,
the 3D structure can be created via a data- and knowledge-based approach (used
in CORINA [62], OpenBabel [182] and Omega [63]), distance geometry approach
(Balloon [181], RDKit [214]) or other approaches (Frog2 [215]); e.g, Frog2 ﬁrst generates
a graph of rings and acyclic elements, and afterwards performs a Monte
Carlo search. Some of the software tools were used to prepare the 3D structures
stored in well-known databases. For example, CORINA was employed in the
preparation of DTP NCI database [212] and Omega was used to prepare Pubchem
database [1]. An important question is which methodology and software tool can
be used to obtain proper 3D structures. This means 3D structures applicable for
accurate pKa prediction via our QM and EEM QSPR models. A primary goal of
our work was to answer this question.
Methods. We performed our analyses on three data sets: 60 phenols, 82 carboxylic
acids and 48 anilines. Additionally, we tested our results on an independent
test set containing 53 phenol molecules. For all of these molecules, we obtained
experimental pKa values from the Physprop database. Afterwards, for each
molecule, we obtained its 3D structure from 6 different sources: From the DTP
NCI and Pubchem databases and via the software tools Balloon, Frog2, OpenBabel
and RDKit. Furthermore, for each of these 3D structures we performed three
types of optimization: none, QM (B3LYP/6-31G*) and MM (MMFF94). Additionally,
we also performed an optimization via the MM force ﬁeld UFF (Universal
Force Field) for structures prepared with RDkit, because it was recommended
by RDKit’s developers. For each 3D structure, we calculated QM charges via 4
QM charge calculation approaches (i.e., HF/STO-3G/MPA, B3LYP/6-31G*/MPA,
B3LYP/6-31G*/NPA, and B3LYP/6-31G*/AIM) and EEM charges via corresponding
parameters. These charge calculation approaches were selected, because they
provided high-quality QSPR models [PQ, PE]. Afterwards, we prepared QM and
38
Table 3.4: R2 describing correlation between calculated and experimental pKa for QM QSPR
models.
Class of
molecules
Charge
calculation
approach
HF,
STO-3G,
MPA
B3LYP,
6-31G*,
MPA
B3LYP,
6-31G*,
NPA
B3LYP,
6-31G*,
AIM
HF,
STO-3G,
MPA
B3LYP,
6-31G*,
MPA
B3LYP,
6-31G*,
NPA
B3LYP,
6-31G*,
AIM
HF,
STO-3G,
MPA
B3LYP,
6-31G*,
MPA
B3LYP,
6-31G*,
NPA
B3LYP,
6-31G*,
AIM
none 0.896 0.939 0.908 0.904 0.823 0.720 0.819 0.846 0.836 0.903 0.912 0.805 0.859
MM 0.917 0.881 0.933 0.891 0.867 0.587 0.805 0.843 0.874 0.953 0.927 0.921 0.867
QM 0.915 0.871 0.901 0.856 0.890 0.618 0.824 0.807 0.948 0.967 0.933 0.921 0.871
none 0.894 0.912 0.906 0.891 0.896 0.876 0.876 0.884 0.934 0.911 0.924 0.916 0.902
MM 0.967 0.931 0.907 0.938 0.907 0.830 0.903 0.922 0.958 0.973 0.965 0.926 0.927
QM 0.969 0.963 0.953 0.939 0.917 0.853 0.906 0.917 0.875 0.973 0.911 0.853 0.919
none 0.947 0.971 0.960 0.973 0.931 0.891 0.911 0.910 0.951 0.970 0.966 0.903 0.940
MM 0.958 0.963 0.959 0.936 0.938 0.889 0.929 0.922 0.954 0.955 0.967 0.914 0.940
QM 0.891 0.935 0.861 0.902 0.925 0.854 0.903 0.921 0.942 0.959 0.937 0.892 0.910
none 0.955 0.961 0.957 0.963 0.869 0.658 0.845 0.876 0.952 0.973 0.966 0.930 0.909
MM 0.961 0.965 0.959 0.961 0.863 0.665 0.841 0.875 0.958 0.975 0.967 0.927 0.910
QM 0.955 0.957 0.956 0.936 0.845 0.674 0.804 0.827 0.874 0.974 0.928 0.880 0.884
none 0.960 0.950 0.935 0.900 0.909 0.873 0.891 0.907 0.938 0.939 0.921 0.937 0.922
MM 0.963 0.911 0.927 0.864 0.916 0.885 0.892 0.916 0.942 0.979 0.966 0.916 0.923
QM 0.943 0.936 0.922 0.886 0.901 0.871 0.896 0.908 0.934 0.974 0.885 0.828 0.907
none 0.782 0.895 0.796 0.882 0.780 0.723 0.804 0.817 0.853 0.816 0.851 0.796 0.816
MM-UFF 0.947 0.961 0.941 0.934 0.894 0.821 0.842 0.860 0.965 0.979 0.973 0.980 0.925
MM 0.931 0.909 0.934 0.950 0.902 0.750 0.797 0.862 0.959 0.976 0.967 0.927 0.905
QM 0.935 0.944 0.933 0.922 0.861 0.696 0.814 0.855 0.940 0.964 0.927 0.908 0.892
0.931 0.934 0.924 0.917 0.886 0.776 0.858 0.878 0.926 0.953 0.936 0.899
R2
≥ 0.7 R2
< 0.7Legend R2
≥ 0.95 R2
≥ 0.9 R2
≥ 0.866 R2
≥ 0.833 R2
≥ 0.8
PubChem
RDKit
Average
Source+Optimization
Balloon
Frog2
NCI
OpenBabel
R2
Phenols Carboxylic acids Anilines
Average
Table 3.5: R2 describing correlation between calculated and experimental pKa for EEM QSPR
models.
Class of
molecules
Charge
calculation
approach
EEM:
HF,
STO-3G,
MPA
EEM:
B3LYP,
6-31G*,
MPA
EEM:
B3LYP,
6-31G*,
NPA
EEM:
B3LYP,
6-31G*,
AIM
EEM:
HF,
STO-3G,
MPA
EEM:
B3LYP,
6-31G*,
MPA
EEM:
B3LYP,
6-31G*,
NPA
EEM:
B3LYP,
6-31G*,
AIM
EEM:
HF,
STO-3G,
MPA
EEM:
B3LYP,
6-31G*,
MPA
EEM:
B3LYP,
6-31G*,
NPA
EEM:
B3LYP,
6-31G*,
AIM
none 0.873 0.904 0.903 0.888 0.832 0.924 0.888 0.853 0.806 0.847 0.826 0.870 0.868
MM 0.852 0.906 0.907 0.885 0.800 0.917 0.883 0.837 0.867 0.845 0.855 0.880 0.870
QM 0.869 0.908 0.906 0.890 0.772 0.917 0.889 0.851 0.953 0.930 0.908 0.945 0.895
none 0.907 0.897 0.898 0.858 0.832 0.875 0.831 0.870 0.894 0.879 0.904 0.887 0.878
MM 0.918 0.906 0.917 0.868 0.859 0.888 0.860 0.848 0.863 0.857 0.852 0.902 0.878
QM 0.921 0.907 0.918 0.869 0.841 0.898 0.866 0.874 0.939 0.926 0.907 0.939 0.900
none 0.906 0.906 0.899 0.890 0.875 0.926 0.891 0.879 0.870 0.852 0.839 0.882 0.884
MM 0.891 0.926 0.926 0.916 0.860 0.920 0.888 0.829 0.844 0.834 0.848 0.889 0.881
QM 0.896 0.924 0.925 0.912 0.821 0.923 0.884 0.834 0.921 0.884 0.869 0.920 0.893
none 0.900 0.920 0.912 0.908 0.830 0.898 0.848 0.826 0.860 0.849 0.851 0.899 0.875
MM 0.900 0.919 0.911 0.907 0.827 0.903 0.849 0.835 0.858 0.851 0.857 0.897 0.876
QM 0.896 0.917 0.911 0.904 0.807 0.911 0.856 0.851 0.946 0.935 0.939 0.934 0.901
none 0.896 0.918 0.913 0.902 0.888 0.891 0.866 0.873 0.874 0.881 0.874 0.907 0.890
MM 0.887 0.917 0.915 0.899 0.874 0.902 0.876 0.871 0.886 0.852 0.872 0.900 0.888
QM 0.898 0.921 0.925 0.899 0.825 0.923 0.894 0.892 0.890 0.905 0.867 0.927 0.897
none 0.894 0.907 0.904 0.885 0.836 0.932 0.889 0.874 0.832 0.842 0.840 0.857 0.874
MM-UFF 0.923 0.917 0.912 0.895 0.801 0.919 0.866 0.844 0.838 0.845 0.843 0.875 0.873
MM 0.899 0.908 0.902 0.892 0.823 0.907 0.871 0.852 0.846 0.852 0.854 0.897 0.875
QM 0.909 0.919 0.916 0.895 0.753 0.915 0.881 0.851 0.933 0.892 0.869 0.923 0.888
0.897 0.913 0.911 0.893 0.829 0.910 0.872 0.855 0.880 0.871 0.867 0.902
R2
≥ 0.833
PubChem
RDKit
Average
Legend R2
≥ 0.95 R2
≥ 0.9 R2
≥ 0.866 R2
≥ 0.8 R2
≥ 0.7
NCI
OpenBabel
Source+Optimization
Balloon
Frog2
R2
Phenols Carboxylic acids Anilines
Average
39
EEM QSPR models for each combination of molecular type, 3D structure source,
optimization, and charge calculation approach. Speciﬁcally, we used the extended
QSPR models [PE], i.e., QSPR models also including descriptors from dissociated
forms of molecules (phenols, carboxylic acids) or associated forms of molecules
(anilines). Finally, we predicted pKa via these QSPR models, compared the results
with experimental pKa values, calculated the quality criteria for the models
(R2, RMSE, ¯∆) and evaluated the models. R2 values are summarized in Tables 3.4
and 3.5.
Results. QM QSPR models proved to be highly accurate for all four types of
QM charge calculation approach, as in [PQ, PE]. EEM QSPR models performed
less well than QM QSPR models, but provided acceptable results, as in [PE].
Interestingly, the type of molecule also inﬂuences the accuracy of QSPR models.
Speciﬁcally, these models are weaker (but still acceptable) for carboxylic acids.
A reason for this could be that the carboxyl group bound some arbitrary chemical
scaffold. In contrast, the –OH group of phenols and –NH2 group of anilines have
the same, conserved neighborhood – the phenolic ring, which additionally allows
a higher de-localization of electrons.
A major message of our work is, that an appropriate selection of 3D structure
source and optimization method is essential for the QSPR modeling of pKa. The
3D structures from the DTP NCI and Pubchem databases, i.e. structures generated
by CORINA and Omega, respectively, exhibited the best performance. These
3D structures provided very accurate QSPR models for all the tested molecular
classes and charge calculation approaches, and they do not require optimization.
Frog2 also performed very well for all of the tested molecular classes and charge
calculation approaches. Other 3D structure sources can be used, but they are not
so robust, and an unfortunate combination of molecular class and charge calculation
approach can lead to weak QSPR models. Additionally, these structures
generally need to be optimized in order to produce high-quality QSPR models.
Speciﬁcally, the best approach is to apply MM optimization to 3D structures used
with QM QSPR models, and QM optimization to 3D structures used with EEM
QSPR models.
3.2.6 Conclusions
We showed that QM charges are very successful descriptors for the prediction of
pKa via QSPR models. The accuracy of the prediction is strongly inﬂuenced by
the selection of the charge calculation scheme. Proper charge calculation schemes
were MPA, NPA and AIM.
We later demonstrated that empirical charges calculated via EEM are also applicable
for pKa prediction. The EEM charges should be parameterized based on a
proper QM charge calculation scheme. Because EEM charges are less precise than
QM charges, EEM QSPR models have to contain more descriptors.
We then found that the pKa predicting QSPR models are sensitive to the source
of molecular 3D structure. The most appropriate 3D structure sources are CORINA
and Omega and moreover, the 3D structures generated by these software
tools do not require further optimization.
40
Therefore, a workﬂow for the rapid and accurate prediction of pKa can be as
follows: The preparation of 3D structures by CORINA or Omega with no further
optimization, the calculation of EEM charges for these structures and then
the EEM QSPR calculation of pKa. Such a workﬂow can be used directly within
the process of in silico drug design or incorporated into other chemoinformatics
applications.
3.3 Charges in proteins: BAX Activation BAX
3.3.1 Introduction
Apoptosis is a programmed cell death and is fundamental for development, growth
and homeostasis in multi-cellular organisms. Malfunctions in the apoptosis machinery
are known to be involved in cancer, autoimmune diseases, neurodegenerative
disorders etc. An important process within apoptosis is mitochondrial
outer membrane permeabilization. This permeabilization allows the release of
apoptotic proteins from the mitochondrial inter-membrane space, which causes
the activation of cell death proteases. Afterwards, the proteases cleave the cell’s
cytoskeleton and genetic material. This permeabilization is executed by the Bcl-
2 family proteins Bak and Bax, which are activated during apoptosis and then
oligomerize and form pores in the mitochondrial membrane [216–219]. Bak and
Bax oligomerisation is controlled by a set of further Bcl-2 proteins [220–223]. The
activation of Bak and Bax is performed via a subclass of apoptotic Bcl-2 proteins
such as Bim and Bid [224–226]. The activation steps required for Bax oligomerization
were extensively investigated [227–231]. They include Bax translocation
from the cytosol to the mitochondrial membrane, and changes in Bax conformation.
Conformational changes of Bax include the exposure of its C-domain, insertion
in this C-domain into the membrane, and exposure of the Bax BH3 domain,
one of four homology domains of Bcl-2 proteins. In inactive Bax [229], the Cdomain
is tightly bound inside a hydrophobic pocket, denoted the ‘BH groove’
(Figure 3.1 A). This tight binding increases the solubility of Bax and keeps Bax in
the cytosol, when apoptosis is not required. Gavathiotis et al. [231] synthesized
a helix mimicking the BH3 domain of the activator Bim (denoted Bim-SAHB, because
it is a Bim-stabilized α-helix of Bcl-2 domains) and they also resolved a
structure of Bim-SAHB activated Bax via NMR (Figure 3.1 B). Interestingly, the
suggested Bax activation site and the Bax C-domain are separated by over 25 ˚A.
Additionally, the binding of Bim-SAHB to Bax is weak and transient, and neither
signiﬁcant disturbances in the helical packing, nor covalent modiﬁcations have
been observed in Bax upon activation. Therefore the mechanism by which the
binding of Bim-SHAB into the Bax activation site involves a C-domain and causes
its exposure still remains unclear [64,65].
Charge transfer was discovered to be signiﬁcant in many biomolecular interactions
[232–234]. Therefore we investigated the role of charge transfer during
Bax activation. For this analysis, we utilized partial atomic charges calculated via
the Electronegativity Equalization Method (EEM) [48] and EEM parameters for
biomacromolecules [EB].
41
A B
Figure 3.1: A) A structure of inactive Bax (PDB ID: 1F16), with its BH3 domain (cyan), the Cdomain
(yellow) and loop 1–2 (pink). The rest of the protein is in gray. B) A structure of Bax
activated by Bim-SAHB (PDB ID: 2K7W), where Bim-SAHB is shown in purple, other domains
have the same coloring as in inactive Bax, and the rest of the protein is in orange.
3.3.2 Analysis of charge transfer within Bax activa-
tion
The analysis of the charge transfer was performed on 3D structures obtained from
the Protein Data Bank – the inactive Bax structure had the PDB ID 1F16 and active
Bax in complex with the activator peptide Bim-SAHB had the PDB ID 2K7W. We
computed EEM atomic charges on both structures using an EEM parameter set
for biomacromolecules, which was based on the HF/6-31G*/MPA quantum mechanical
charge calculation approach [EB]. Afterwards, we calculated the absolute
charge transfer per residue and we used this value as a metric for evaluating the
overall charge transfer within the Bax. Speciﬁcally, we concentrated on residues
with a high value of absolute charge transfer. At the same time, we took into
account published information about residues which play an important role in
Bax activation (e.g., which mutation inﬂuences the activation) [229,235]. Based on
this information, we analysed the correlation between the high absolute charge
transfer value of a residue and its reported inﬂuence on Bax activation.
Experimental evidence suggests that in inactive Bax, the C-terminal helix is
bound tightly to its hydrophobic pocket (BH-groove). During activation, this
binding becomes destabilized. Consequently, the C-domain vacates the BH-groove
and inserts into the mitochondrial outer membrane. Mutagenesis studies showed
a critical interaction between residues Ser184 and Asp98 at the C-domain-BHgroove
interface, whose abrogation can immediately activate Bax [229, 235]. We
therefore focused on the changes in charge density distribution in the vicinity of
this interaction. Our calculations did not report any change in the charge proﬁle
of Ser184. But they showed that Arg94 becomes more positive after activation.
This can lead to the recruitment of Asp98, the abrogation of the Asp98-Ser184 interaction,
and ultimately the destabilization of the C-domain (see Figure 3.2). This
demonstrates that the binding of Bim-SAHB to Bax can activate Bax by destabilizing
the interaction between the Bax C-domain and its binding groove.
42
A B
Figure 3.2: A) In inactive Bax, Asp98 interacts with Ser184, which keeps the C-domain in its
binding pocket. B) In active Bax, the now more positively charged Arg94 interacts with Asp98,
which no longer contributes to the stabilization of the Bax C-domain in its BH-groove.
Figure 3.3: Top view of helix 5, showing the organization of residues Trp107, Arg109 and Lys119
inside the hydrophobic core of Bax and also the location of other residues with a high charge
transfer. Residues with markedly positive or negative charge transfer upon activation are in blue
or red, respectively.
A further uncertainty in Bax activation is the way the BH-groove is inﬂuenced
by the binding of Bim-SAHB to Bax, because the Bax activation site and the Bax
C-domain are separated by over 25 ˚A. The residues which exhibited a high charge
transfer provided a clue to the way the activation information proceeds through
the protein. Foremost, signiﬁcant changes in the net residue charges were found
at the Bax activation site, the BH3-domain (required for oligomerization) and the
C-domain (required for membrane insertion). Since these are all functional sites
of Bax, these changes could expected. At the same time, George et al. [235] found
that a triple alanine mutant at residues 63–65 (on the BH3 domain of Bax) prevented
Bax oligomerisation and apoptotic activity, which fully correlates with the
high charge transfer we found on residues 64 and 65 upon Bax activation. However,
in addition to the expected changes, our method surprisingly also identiﬁed
signiﬁcant charge transfer on the central helix, inside the hydrophobic core of
Bax (residues Trp107, Arg109 and Lys119 on helix 5). The presence of signiﬁcant
charge transfer in a predominantly hydrophobic environment suggests that helix
43
5 acts as a hub which collects and distributes charge density. This idea is also supported
by the spatial organization of residues Trp107, Arg109 and Lys119 inside
the hydrophobic core (Figure 3.3), suggesting that the interaction at the Bax activation
site is transmitted via a network of charges from the activation site, through
the protein core, to the C- and BH3-domains.
3.3.3 Conclusions
We investigated the changes in the Bax charge proﬁle upon activation via a functional
peptide of its natural activator protein, Bim. We found that charge reorganizations
after activator binding mediate the exposure of the functional sites of Bax
(i.e., C-domain and BH3 domain) and consequently activate Bax. The afﬁnity of
the Bax C-domain for its binding groove is decreased due to the Arg94-mediated
abrogation of the Ser184-Asp98 interaction. We further identiﬁed a network for
charge transfer, which brings the activation information from the activation site,
through the hydrophobic core of Bax, to the distant functional sites of Bax. The
network was mediated by a hub of three residues on helix 5 of the hydrophobic
core of Bax. Our results suggest that allostery mediated by charge transfer is
responsible for the activation of Bax.
3.4 Channels: Enzyme channels anatomy AN
3.4.1 Introduction
Enzymes are proteins which catalyze reactions that change substrates into products.
The enzymatic reactions occur in active sites of the enzymes. Based on the
type of chemical reaction which enzymes catalyze, they can be categorized into
six enzymatic classes, each marked by its Enzyme Commision (EC) number [236].
Therefore, we use the following enzymatic classes: oxidoreductases (EC1), transferases
(EC2), hydrolases (EC3), lyases (EC4), isomerases (EC5), and ligases (EC6).
Thanks to the many analyses of enzymatic reactions, we now have a better
understanding of how active site chemistry works [237–240] and which amino
acids are present in the sites [241]. However, relatively little is known about how
the substrates enter the active sites and how the respective products leave them.
Some active sites are located on the surface of the protein, in clefts or pockets,
other enzymes have active sites deeply buried inside. These buried active sites
are connected to the outside by one or more channels. These channels therefore
allow the passage of substrates and products to/from the active site [66–77]. It
has been shown that mutations in the access channels to enzyme active sites can
alter the substrate preferences of enzymes, and may be utilized in the rational
design of enzymes [107, 242]. Despite the channels themselves being intensively
studied in recent years, there was no in-depth analysis of enzyme channels. For
this reason, we focused on performing such an analysis. Our goal was ﬁrst to
recognize, whether the channels are a general property of the majority of enzyme
structures and how often they are present. Afterwards, we studied the geometrical
properties of the channel, such as their length. Then, we focused on channel’s
chemical properties and we analyzed their lining residues, bottleneck residues,
44
residue composition within their parts etc. Last but not least, we concentrated on
the channel’s physicochemical properties.
3.4.2 Data set preparation and methodology
For performing the channel analyses, we ﬁrst prepared a dataset of enzyme structures.
Speciﬁcally, we selected all the enzymes whose active sites were annotated
in the Catalytic Site Atlas (CSA) [243] and whose structures were available in the
Protein Data Bank [244]. Afterwards, we removed the low quality structures (with
a resolution higher than 2.5 ˚A) and structures sharing at least 90% sequence identity.
In this way we obtained a data set containing 4,306 enzymes.
Figure 3.4: Channel parts, depicted on a channel pyridoxal-5’-phosphate-dependent acyl-CoA
transferase (PDB ID 3KKI). Active site amino acids (present in the internal part of the channel)
are shown in green, amino acids in the middle part forming the wall of a local minimum (channel
narrowing) are in yellow, and amino acids in the external part lining the bottleneck are in blue.
Internal, middle and external parts are colored orange, red and magenta, respectively.
For all the enzymes from the data set, we calculated channels via MOLE 2.0
software [MO2] and the starting point of the channels was the active site. MOLE 2.0
was also used for calculating the channel’s geometrical, chemical and physicochemical
properties. For the needs of the analysis, the channel was divided into
particular parts – external, middle, and internal (depicted in Figure 3.4). Important
areas of the channel are also their local minima (narrowings of the channel)
and global minimum (bottleneck of the channel) – see Figure 3.4.
45
3.4.3 Channel occurrence and geometrical properties
We found that 64% of the enzymes contained channels at least one 15 ˚A long
channel and more than 87% contain channels at least 5 ˚A long. However, the
short channels may correspond to the paths of active sites located in biomacromolecular
pockets, therefore in our study we focused purely on channels longer
than 15 ˚A. Channel occurrence varies among the enzymatic classes. The highest
percentage (77.8%) of enzymes with channels longer than 15 ˚A was identiﬁed in
oxidoreductases, while the lowest percentage (51.8%) applied to hydrolases. The
average number of channels in an enzyme was two.
The median channel length was 27.7 ˚A, 40% of channels were 15–30 ˚A long
and 10% of enzymes contained channels longer than 50 ˚A. Surprisingly, we found
that the number of long channels does not correlate with protein size. The median
length of channels in the enzymatic classes was comparable (see Figure 3.5) – oxidoreductases
have a median channel length slightly longer (by about 2 ˚A) than
other enzymes, whereas transferases and ligases have a shorter average channel
length (also by about 2 ˚A). An interesting ﬁnding was that the channel length only
exhibited a low correlation with the enzyme atom count.
Figure 3.5: Average channel length in individual enzymatic classes in comparison with the
overall average channel length.
3.4.4 Channel chemical properties
We calculated the frequencies of amino acids in deﬁned regions of a channel (e.g.,
lining residues, external, middle and internal part, bottleneck, local minima) and
compared this frequency with the frequency of these amino acids in the whole enzyme
structure. Speciﬁcally, we calculated the ratio of the amino acid frequency
in the deﬁned region to its frequency in the whole enzyme. This comparison provided
us with direct information about the preference or exclusion of an amino
acid (or a group of amino acids) from some regions. The results of this analysis
are visualized in Figure 3.6.
The rather bulky and aromatic amino acids (His, Tyr, Trp, Arg), occur over
1.25 times more frequently in the channel lining residues than in the whole enzyme.
Additionally, other amino acids (Asn, Phe, Asp, Thr, Met, Ser) also exhibit
a slightly higher frequency in the channel lining residues than in the rest of the
46
protein. On the other hand, nonpolar aliphatic amino acids (Pro, Gly, Ile, Leu,
Ala, and Val) are signiﬁcantly less common in channel lining residues.
The channel bottlenecks reﬂect the composition of lining residues, but they
contain signiﬁcantly more cysteine (Cys), histidine (His) and tyrosine (Tyr) residues
than usual and much fewer small aliphatic amino acids (Pro, Gly and Ala). As
histidine (His) and cysteine (Cys) have unique binding properties, it is possible to
hypothesize that these binding properties might provide a gate-keeping activity
at the channel bottlenecks.
The frequencies of amino acids in active sites, on the protein surface and inside
the protein, or in general channels, are markedly different from both the average
protein amino acid composition and the composition of the lining residues.
The active sites contain signiﬁcantly more amino acids that could be part of a
catalytic cycle (His, Asp, Cys, Glu, Arg, Tyr, Lys) enabling proton and electron
shufﬂing and covalent bond reorganization. Conversely, the frequency of less
reactive amino acids (Trp, Thr, Gln, Phe) or amino acids with nonreactive sidechains
(Met, Ala, Pro, Ile, Val, Leu) is lower in the active sites. These results are
in perfect agreement with data published by Holliday and coworkers [245]. On
the other hand, the surface regions contain mainly charged (Lys, Arg, Glu, Asp)
and polar residues (Asn, Gln), which facilitate contact with the polar water environment.
Also, the surface has a higher than average frequency of prolines (Pro),
as these helix-breaker amino acids are common in turns in the protein structures
and rigidify the protein fold.
Channel-lining residues are not uniformly distributed along the length of the
channel. Internal parts of the channel tend to contain more aromatic residues (His,
Trp, Tyr) together with cysteine (Cys).
These trends are similar to the catalytic site propensities. The frequencies of
amino acids in the middle regions of the channels correspond to the frequencies
in the entire channel with the exception of glycine (Gly) and aromatic amino acids
(Trp, Tyr, Phe), which are present more frequently. We may hypothesize that the
higher frequency of glycine (Gly) in the middle channel parts is because it facilitates
ﬂexibility, which may be important for substrate/product channeling between
the active site and protein surface [101] , whereas aromatic amino acids can
serve as gate-keepers. External parts of the channel bear more charged residues
than any other part (Arg, Lys, Glu, Asp) together with proline (Pro) and glutamine
(Gln). The analysis of amino acids leading to active sites, divided according to the
six enzymatic groups, shows that amino acid channel propensities correspond
to overall channel propensities. However, some differences were identiﬁed (see
[AN] for details). The main ﬁndings were that channels in oxidoreductases have
signiﬁcantly lower frequencies of charged lining amino acids but higher frequencies
of aliphatic lining amino acids. On the other hand, channels in ligases contain
fewer cysteine, aromatic and aliphatic amino acids and more charged amino acids
and glycine.
3.4.5 Channel physicochemical properties
We ﬁrst focused on channel hydropathy. The average channel hydropathy is
−0.92 (the hydropathy of amino acids varies from the −4.5 of Arg to the 4.5 of Ile).
47
Figure 3.6: Enhancement of amino acid frequency in different parts of the enzyme structure.
Amino acids that are found more often than average in different regions of an enzyme’s structure.
The distribution plots of hydropathy (Figure 3.7) also indicate that hydrophilic
channels are preferred to hydrophobic ones.
We then analyzed channel polarity. We found that the average channel polarity
is 16.5 (the polarity varies between 52.0 for highly polar amino acids and 0.0 for
nonpolar amino acids). This indicates that the channels are relatively polar.
Taking all this information into account we may conclude that the average
channel has a slightly negative hydropathy and higher polarity. However highly
hydrophobic and nonpolar, as well as highly hydrophilic and polar, channels were
also detected.
We also analyzed the presence of charged amino acid side chains (Asp, Glu,
His, Lys and Arg) in channel walls. On average the channel walls are lined
with two negative and two positive side chains, resulting in sum neutral channel
walls. Despite this, we also identiﬁed channels with signiﬁcant extreme physicochemical
properties (see [AN]).
We also found that enzymatic classes differ in their average physico-chemical
properties (Figure 3.7): oxidoreductases (EC1) exhibit the most hydrophobic as
well as the least polar channels among the enzyme classes, while ligases (EC6),
and to some extent also isomerases (EC5), lyases (EC4) and hydrolases (EC3), exhibit
the most hydrophilic as well as the most polar channels. In parallel, we
identiﬁed that some physico-chemical features differ across the three parts of the
channel: internal, middle and external. The polarity of the middle part is always
lower than the polarity of both the internal and external parts, respectively. The
lower polarity of the middle part of the channel is also reﬂected in its signiﬁcantly
more hydrophobic behaviour. The charged residues occur mainly in the external
parts of enzyme channels, while the internal and middle part contain more
aromatic residues.
48
Figure 3.7: Average channel length in individual enzymatic classes in comparison with the
overall average channel length.
3.4.6 Conclusions
To summarize, we analyzed channels in 4,306 enzyme structures from the Protein
Data Bank, which are annotated in the Catalytic Site Atlas. We identiﬁed that
at least 64% of these enzymes contain on average two channels longer than 15
˚A leading to the catalytic site. Consequently, we can anticipate that these enzymes
contain buried active sites. The longest and the most hydrophobic channels were
found in oxidoreductases, while the smallest number of channels were detected
in hydrolases and the shortest and the most hydrophilic channels in ligases. The
composition of channel lining residues differs from the average composition of
enzyme structures as well as from the composition of the protein surface. Hydrophobic
aliphatic amino acids, which are the most common amino acids found
in protein cores, occur in channel walls less frequently, whereas aromatic, charged
and polar amino acids occur more frequently in channel walls. All these ﬁndings
indicate that the active site access channels have a signiﬁcant biological function
as they are involved in co-determining the enzyme’s substrate preferences.
49
4
Future prospects
In the ﬁeld of biomacromolecular structural fragments analysis, a lot of effort is
still invested in the development and improvement of their methodologies. Some
analyses merely require an extension of current approaches (e.g., validation, channel
detection), others need marked improvements (e.g., accurate calculation of
channel physicochemical properties) and many new types of analyses are still
under development. A current trend in the performance of structural fragment
analyses is the precalculation of their results for available structures and providing
these results to the user directly. Another important activity is the integration
of key analyses directly into the databases of biomacromolecular structures (e.g.,
Protein Data Bank). This activity is connected with the need to markedly streamline
the analyses and enable their rapid execution on the complete database.
A straightforward application of structural fragment analyses is the prediction
of fragment (or biomacromolecule) properties such as acid dissociation constants,
activities, partition coefﬁcients etc. Another important utilization is research focused
on common aspects or features of selected structural fragments – for example,
the typical charge distribution of cytochrome channels, standard amino acid
surroundings of a fucose-binding site, etc. This knowledge provides us with a clue
to understanding their chemical interactions and some insight into their biological
role. Furthermore, based on this information, we can predict the occurrence of individual
structural fragments. A highly interesting and at the same time a highly
challenging application is the study of the mechanisms and effects connected with
certain chemical actions (e.g., the activation of a particular biomacromolecule, the
binding of a particular ligand). Last but not least, there are even greater possibilities
associated with the analysis of biomacromolecular structural fragments
— its application may enable us to predict the inﬂuences of individual structural
changes within fragments (e.g., the inﬂuence of a certain point mutation, a ligand
modiﬁcation or an atom substitution).
50
5
Summary
Biomacromolecules (e.g, proteins, nucleic acids, polysaccharides) are essential biological
entities, since they are responsible for building cell components and ensuring
their functionality. The biomacromolecule is a large object containing several
thousand atoms. Different parts (fragments) of them play diverse roles – e.g.,
they create an active site, bind a certain ligand or metal, form a channel or a pore,
or are responsible for the proper shape of the molecule. The research of these
fragments (especially biologically important fragments) can provide very useful
results such as discovering drug design patterns, information for the classiﬁcation
of biomacromolecules, understanding the relationship between their structure
and function, discovering their putative functions etc. A key property of
these fragments is their three-dimensional structure. At the same time, a vast
amount of biomacromolecular structural data is currently available. We can beneﬁt
from these resources and focus on analyses of biomacromolecular structural
fragments.
In my habilitation thesis, I describe key steps of this analysis – the validation,
detection, extraction, comparison and characterization of biomacromolecular
structural fragments – and methodologies for their realization. I also summarize
here my contribution to the development of these approaches. Afterwards, I
focus on particular applications of selected analyses: a quality comparison of different
molecular classes, the prediction of acid dissociation constants using partial
atomic charges, understanding apoptosis protein activation based on partial
atomic charges and the discovery of enzyme channel anatomy.
51
Appendix
52
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List of publications included in the
habilitation thesis
[VDB] Sehnal, D., Svobodov´a Vaˇrekov´a, R., Pravda, L., Ionescu, C.-M., Geidl, S., Horsk´y, V.,
Jaiswal, D., Wimmerov´a, M. and Koˇca, J. (2015) ValidatorDB: database of up-to-date validation
results for ligands and non-standard residues from the Protein Data Bank. Nucleic
Acids Res., 43, D369–D375. IF: 9.112 (2014); Authorship: First
[PTQ] Sehnal, D., Pravda, L., Svobodov´a Vaˇrekov´a, R., Ionescu, C.-M. and Koˇca, J. (2015) PatternQuery:
web application for fast detection of biomacromolecular structural patterns
in the entire Protein Data Bank. Nucleic Acids Res., 43, W383–W388. IF: 9.112 (2014);
Authorship: Co-author
[EL] Geidl, S., Bouchal, T., Raˇcek, T., Svobodov´a Vaˇrekov´a, R., Hejret, V., Kˇrenek, A., Abagyan,
R. and Koˇca, J. (2015) High-quality and universal empirical atomic charges for chemoinformatics
applications. J. Cheminform., 7, 59. IF: 4.547 (2014); Authorship: Corresponding
[PS] Geidl, S., Svobodov´a Vaˇrekov´a, R., Bendov´a, V., Petrusek, L., Ionescu, C.-M., Jurka, Z.,
Abagyan, R. and Koˇca, J. (2015) How does the methodology of 3D structure preparation
inﬂuence the quality of pKa prediction? J. Chem. Inf. Model., 55, 1088–1097. IF: 3.738
(2014); Authorship: Corresponding
[EAM] Ionescu, C.-M., Sehnal, D., Falginella, F.L., Pant, P., Pravda, L., Bouchal, T., Svobodov´a
Vaˇrekov´a, R., Geidl, S. and Koˇca, J. (2015) AtomicChargeCalculator: interactive webbased
calculation of atomic charges in large biomolecular complexes and drug-like
molecules. J. Cheminform., 7, 50. IF: 4.547 (2014); Authorship: Co-author
[AN] Pravda, L., Berka, K., Svobodov´a Vaˇrekov´a, R., Sehnal, D., Ban´aˇs, P., Laskowski, R.A.,
Koˇca, J. and Otyepka, M. (2014) Anatomy of enzyme channels. BMC Bioinformatics, 15,
379. IF: 2.576; Authorship: Co-author
[MV] Svobodov´a Vaˇrekov´a, R., Jaiswal, D., Sehnal, D., Ionescu, C.-M., Geidl, S., Pravda, L.,
Horsk´y, V., Wimmerova, M. and Koˇca, J. (2014) MotiveValidator: interactive web-based
validation of ligand and residue structure in biomolecular complexes. Nucleic Acids Res.,
42, W227–W233. IF: 9.112; Authorship: First
[MO2] Sehnal, D., Svobodov´a Vaˇrekov´a, R., Berka, K., Pravda, L., Navr´atilov´a, V., Ban´aˇs, P.,
Ionescu, C.-M., Otyepka, M. and Koˇca, J. (2013) MOLE 2.0: advanced approach for analysis
of biomacromolecular channels. J. Cheminform., 5, 39. IF: 4.540; Authorship: Co-author
[PE] Svobodov´a Vaˇrekov´a, R., Geidl, S., Ionescu, C.-M., Skˇrehota, O., Bouchal, T., Sehnal, D.,
Abagyan, R. and Koˇca, J. (2013) Predicting pKa values from EEM atomic charges. J. Cheminform.,
5, 18. IF: 4.540; Authorship: First
66
[EB] Ionescu, C.-M., Geidl, S., Svobodov´a Vaˇrekov´a, R. and Koˇca, J. (2013) Rapid calculation
of accurate atomic charges for proteins via the Electronegativity Equalization Method. J.
Chem. Inf. Model., 53, 2548–2558. IF: 4.068; Authorship: Corresponding
[BAX] Ionescu, C.-M., Svobodov´a Vaˇrekov´a, R., Prehn, J.H.M., Huber, H.J. and Koˇca,J. (2012)
Charge proﬁle analysis reveals that activation of pro-apoptotic regulators Bax and Bak
relies on charge transfer mediated allosteric regulation. PLoS Comput. Biol., 8, e1002565.
IF: 4.867; Authorship: Co-author
[MO] Berka, K., Han´ak, O., Sehnal, D., Ban´aˇs, P., Navratilov´a, V., Jaiswal, D., Ionescu, C.-M.,
Svobodov´a Vaˇrekov´a, R., Koˇca, J. and Otyepka, M. (2012) MOLEonline 2.0: interactive
web-based analysis of biomacromolecular channels. Nucleic Acids Res., 40, W222–W227.
IF: 8.278; Authorship: Co-author
[SB] Sehnal, D., Svobodov´a Vaˇrekov´a, R., Huber, H.J., Geidl, S., Ionescu, C.-M., Wimmerov´a,
M. and Koˇca, J. (2012) SiteBinder: an improved approach for comparing multiple protein
structural motifs. J. Chem. Inf. Model., 52, 343–359. IF: 4.304; Authorship: Corresponding
[PQ] Svobodov´a Vaˇrekov´a, R., Geidl, S., Ionescu, C.-M., Skˇrehota, O., Kudera, M., Sehnal, D.,
Bouchal, T., Abagyan, R., Huber, H.J. and Koˇca, J. (2011) Predicting values of substituted
phenols from atomic charges: comparison of different quantum mechanical methods and
charge distribution schemes. J. Chem. Inf. Model., 51, 1795–1806. IF: 4.675; Authorship:
First
[EO] Svobodov´a Vaˇrekov´a, R., Jirouˇskov´a, Z., Vanˇek, J., Suchomel, S. and Koˇca, J. (2007) Electronegativity
Equalization Method: parameterization and validation for large sets of organic,
organohalogene and organometal molecule. Int. J. Mol. Sci., 8, 572–582. IF: 0.750;
Authorship: First
[EPM] Svobodov´a Vaˇrekov´a, R. and Koˇca, J. (2006) Optimized and parallelized implementation
of the Electronegativity Equalization Method and the Atom-Bond Electronegativity
Equalization Method. J. Comput. Chem., 27, 396–405. IF: 4.893; Authorship: First
67
ValidatorDB: database of up-to-date
validation results for ligands and
non-standard residues from the Protein Data
Bank
68
Published online 11 November 2014 Nucleic Acids Research, 2015, Vol. 43, Database issue D369–D375
doi: 10.1093/nar/gku1118
ValidatorDB: database of up-to-date validation results
for ligands and non-standard residues from the
Protein Data Bank
David Sehnal1,2,3,†
, Radka Svobodov´a Vaˇrekov´a1,2,†
, Luk´aˇs Pravda1,2
, Crina-Maria Ionescu1
,
Stanislav Geidl1,2
, Vladim´ır Horsk´y3
, Deepti Jaiswal1
, Michaela Wimmerov´a1,2
and
Jaroslav Koˇca1,2,*
1
CEITEC––Central European Institute of Technology, Masaryk University Brno, Kamenice 5, 625 00 Brno, Czech
Republic, 2
National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kotl´aˇrsk´a 2, 611 37
Brno, Czech Republic and 3
Faculty of Informatics, Masaryk University Brno, Botanick´a 68a, 602 00 Brno, Czech
Republic
Received August 29, 2014; Revised October 24, 2014; Accepted October 24, 2014
ABSTRACT
Following the discovery of serious errors in the structure
of biomacromolecules, structure validation has
become a key topic of research, especially for ligands
and non-standard residues. ValidatorDB (freely
available at http://ncbr.muni.cz/ValidatorDB) offers a
new step in this direction, in the form of a database
of validation results for all ligands and non-standard
residues from the Protein Data Bank (all molecules
with seven or more heavy atoms). Model molecules
from the wwPDB Chemical Component Dictionary
are used as reference during validation. ValidatorDB
covers the main aspects of validation of annotation,
and additionally introduces several useful validation
analyses. The most signiﬁcant is the classiﬁcation
of chirality errors, allowing the user to distinguish
between serious issues and minor inconsistencies.
Other such analyses are able to report,
for example, completely erroneous ligands, alternate
conformations or complete identity with the model
molecules. All results are systematically classiﬁed
into categories, and statistical evaluations are performed.
In addition to detailed validation reports for
each molecule, ValidatorDB provides summaries of
the validation results for the entire PDB, for sets of
molecules sharing the same annotation (three-letter
code) or the same PDB entry, and for user-deﬁned
selections of annotations or PDB entries.
INTRODUCTION
Validation of biomacromolecular structures has become a
very important topic, because some published structures
have been found to contain serious errors (1–4). The first
step in the validation of biomacromolecules and their complexes
is checking the standard building blocks, namely,
standard amino acids and nucleotides. The usual procedure
is to evaluate specific properties of each residue (e.g. electron
density, atom clashes, bond lengths, bond angles, torsion
angles, etc.). Various software tools have been developed
to perform such analyses, e.g. WHAT CHECK (5),
PROCHECK (6), MolProbity (7) and OOPS (8).
The next key step is the validation of ligands and nonstandard
residues in biomacromolecular structures, which
can be performed in a similar manner as for standard
residues (focus on electron density, atom clashes, etc.). An
example of software specialized on this type of validation
is ValLigURL (9). This approach was also added to several
software tools focused on the validation of standard
residues (Mogul (10), Coot (11), PHENIX (12)).
A different ligand validation approach, which can be
denoted as validation of annotation, was developed later.
The goal of this approach is to evaluate if the ligand or
non-standard residue is annotated correctly (i.e. if its structure
corresponds to the three-letter code it was assigned in
the Protein Data Bank (PDB) file format). Specifically, the
topology and stereochemistry of the validated molecule are
compared to those of a reference molecule (model), and
any differences found are reported. The first software tool
implementing this methodology has been pdb-care (13), a
tool specialized on carbohydrates. The next step has been
MotiveValidator (14), which allows validation of all ligands
and residues, performs basic validation analyses and reports
*To whom correspondence should be addressed. Tel: +420 54949 4947; Fax: +420 54949 2556; Email: Jaroslav.Koca@ceitec.muni.cz
†
The authors wish it to be known that, in their opinion, the first two authors should be regarded as Joint First Authors.
C The Author(s) 2014. Published by Oxford University Press on behalf of Nucleic Acids Research.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by-nc/4.0/), which
permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact
journals.permissions@oup.com
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D370 Nucleic Acids Research, 2015, Vol. 43, Database issue
basic warnings (substitutions, foreign atoms, different naming).
Because this approach is relatively young, the available
tools cover only some of its key topics, leaving many aspects
to be explored or improved.
At the same time, with the exponential increase in the
size of structural databases, the concept of storing precomputed
validation results is becoming increasingly attractive.
The first step in this direction was achieved by the
PDBREPORT database (5), which is a collection of the outputs
from the WHAT CHECK program. Afterward, the
PDB REDO database (15) of validation results for existing
PDB entries was published. Recently, wwPDB included
validation reports (16) providing detailed validation results
for individual PDB entries directly into their pages.
In our work, we address all challenges described above.
We first developed and implemented an improved approach
for the validation of annotation, which we subsequently
applied to validate all ligands and non-standard residues
in the PDB. We then collected all results and built the
database ValidatorDB, which offers several advantages over
currently available tools (ValLigURL, pdb-care, Motive-
Validator):
r ValidatorDB is a database of precomputed validation results
for all ligands and non-standard residues in the PDB
(except small molecules having fewer than seven heavy
atoms).
r ValidatorDB provides summaries of the validation results
for the entire PDB, for sets of molecules sharing the
same annotation or the same PDB entry, and for userdefined
selections of annotations or PDB entries.
r ValidatorDB provides a systematic insight into validation
results. The validation analyses are classified into
three main categories (Completeness, Chirality and Advanced),
each containing several related analyses.
r ValidatorDB classifies the types of chirality errors, enabling
the user to distinguish between serious chirality
issues and minor inconsistencies.
r ValidatorDB performs novel analyses and can report
completely erroneous ligands, alternate conformations,
identity with the model molecules, etc. Such analyses can
provide information valuable for further data processing.
ValidatorDB obtains correct structures of ligands and
non-standard residues from the wwPDB Chemical Components
Dictionary (wwPDB CCD) (17), which it uses as reference
molecules (models) during validation. ValidatorDB
is updated weekly, and is freely available via the Internet at:
http://ncbr.muni.cz/ValidatorDB.
VALIDATION ANALYSES
As ValidatorDB implements the approach of validation of
annotation, each validated molecule is compared against a
model with the same annotation from wwPDB CCD. The
validation analyses performed by ValidatorDB cover the
main issues which have been observed in the topology (2D
structure) and geometry (3D structure) of ligands and nonstandard
residues, and which are important for their correct
annotation. These validation analyses, along with their
respective results, can be classified into three categories,
namely, Completeness, Chirality and Advanced analyses
(Figure 1). If no issues are found during these analyses, the
molecule is marked as having complete structure and correct
chirality (Figure 1a).
The Completeness analyses attempt to find which atoms
are missing (Figure 1b), whether these atoms are part of
rings (Figure 1c) or the structure is degenerate, i.e. the
molecule contains very severe errors (Figure 1d). These severe
errors may refer to residues overlapping in the 3D
space, or atoms which are disconnected from the rest of
the structure. Validated molecules exhibiting an error in at
least one of the Completeness analyses are denoted as incomplete,
whereas the remaining molecules are reported as
complete.
The Chirality analyses are performed only on complete
structures, and aim to evaluate the chirality of each atom
in the validated molecule. We distinguish between several
types of chirality errors: on carbon atoms (C chirality, Figure
1e), on metal atoms (Metal chirality, Figure 1f), on
atoms with four substituents in one plane (Planar chirality,
Figure 1g), on atoms connected to at least one substituent
by a bond of higher order (High-order chirality, Figure 1h)
and the remaining chirality issues (Other chirality). If no issues
are detected during the chirality analyses, the validated
molecule is marked as having Correct chirality, whereas the
remaining molecules are marked as having Wrong chirality.
Some types of chirality errors do not constitute real issues,
but are artifacts of the automated chirality-determination
procedure (i.e. planar chirality and high-order chirality).
Therefore, if the validated molecule is found to have these
chirality errors, but no other type of chirality issues, the
molecule is marked as having ‘Correct chirality (tolerant)’.
The Advanced analyses are focused on issues which are
not real chemical problems, but which can complicate further
processing and exploration of data, and thus should be
noted. When issues are found during an advanced analysis,
a warning is reported: Substitution, Foreign atom, Different
naming, Zero root mean square deviation (RMSD)
or Alternate conformations. The Substitution analysis (Figure
1i) reports the replacement of some atom by an atom
of a different chemical element. The Foreign atom analysis
(Figure 1j) detects atoms which originate from the
neighborhood of the validated molecule (i.e. having different
PDB residue ID than the majority of the validated
molecule), and generally marks sites of intermolecular linkage.
The Different naming analysis (Figure 1k) identifies
atoms whose name in PDB format are different than the
standard convention for the validated molecule. The Zero
RMSD analysis reports molecules whose structure is identical
(RMSD = 0 ˚A) to the model from wwPDB CCD. The
Alternate conformation analysis informs about the occurrence
of alternate conformations in the validated PDB en-
try.
DATA PREPARATION
Validation procedure for a single molecule
The starting information characterizing the investigated
molecule consists of a PDB residue ID, annotation and
PDB ID. According to this information, the input motif is
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Nucleic Acids Research, 2015, Vol. 43, Database issue D371
Figure 1. Examples of results provided by different validation analyses. ValidatorDB classifies results into three main categories (Completeness, Chirality,
Advanced), each referring to several related analyses. Information about the source of the particular molecules displayed here is given in Supplemental
Table S3.
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D372 Nucleic Acids Research, 2015, Vol. 43, Database issue
extracted from the PDB entry under investigation. The input
motif contains all atoms with the given PDB residue
ID, along with their surroundings (atoms within two bonds
from any atom of the investigated molecule). The annotation
of the molecule is used to identify a suitable model from
wwPDB CCD, which then serves as the correct reference
structure. The validation proceeds by identifying the maximum
common subgraph between the input motif and the
model. The atoms of the input motif which belong to this
common subgraph make up the validated molecule, which
can thus be reliably identified in the PDB entry under investigation.
The validated molecule and the model are then
superimposed (18) in such a way that their RMSD is minimal.
The superimposition provides a pairing (bijection) between
atoms in the validated molecule and the corresponding
(chemically equivalent) atoms in the model. This bijection
allows comparing various properties of each atom in
the validated molecule with those of the chemically equivalent
atom from the model. All the validation analyses are
based on this comparison of atom properties (presence, chirality,
element symbol, PDB name, etc.). Other unusual aspects
encountered during validation are reported as processing
warnings (e.g. which conformer was validated if several
conformers were present). A scheme of the validation
procedure is depicted in Supplemental Figure S1.
Generation of validation data for all ligands and non-standard
residues in the entire Protein Data Bank
The latest versions of the PDB and wwPDB CCD are downloaded
once a week, and the following steps ensue.
Obtaining a set of models for validation. Select all models
from wwPDB CCD which contain at least seven heavy
atoms, excluding the five standard nucleotides and their
common deoxy- forms, the 20 standard amino acids and
selenomethionine (MSE). ValidatorDB does not focus on
the standard building blocks of biomacromolecules because
many tools already cover these. Additionally, MSE is also
excluded from validation due to its extremely high occurrence
in the PDB (markedly higher than other ligands and
non-standard residues) and high incidence of circumstantial
inclusion in biomacromolecules (to aid X-ray crystallography
experiments).
Obtaining validation results for all ligands and non-standard
residues in a single PDB entry. For a PDB entry with a
given PDB ID, identify the PDB residue IDs of all molecules
sharing the annotation with any model obtained in the previous
step. Using the procedure described in the first step,
detect all validated molecules (via PDB residue ID and corresponding
annotation) and compare them to the appropriate
models. Collect the validation results for all molecules
validated in this PDB entry, and summarize the results of
each validation analysis.
Obtaining PDB-wide validation results for each ligand or
non-standard residue. For each set of molecules sharing
the same annotation, collect validation results from all PDB
entries and summarize the results of each validation analy-
sis.
Obtaining a validation overview for the entire PDB. Collect
and summarize the results of all types of validation analyses
for all validated molecules, irrespective of annotation or
PDB entry.
While the algorithm we use for data preparation is generally
applicable, highly automated and produces results
with straightforward interpretation, it does have limitations.
These limitations are described in detail in the Supplementary
Material.
DATABASE ORGANIZATION
ValidatorDB provides the user with direct access to a wide
range of validation reports, where the results of the validation
analyses are organized on several levels. Specifically:
r Validation report for a particular molecule or a set of
molecules (accessible via Search → Molecule Identifier),
depicted in Figure 2.
r Validation report for a particular PDB entry or a set of
PDB entries (accessible via Search → PDB Entry).
r Validation report for a particular annotation or a set of
annotations (accessible via Search → Molecule Annota-
tion).
r Table with validation results for all PDB entries (accessible
via Details by PDB Entry).
r Table with validation results for all annotations (accessible
via Details by Molecule).
r Graph with results of all validation analyses for the entire
PDB (accessible via Overview).
A description of the ValidatorDB user interface is provided
in the ValidatorDB Wiki Manual.
RESULTS AND DISCUSSION
Validation results for the entire PDB
One of the advantages of ValidatorDB is that it can provide
a straightforward overview of the quality of ligands
and non-standard residues in the entire Protein Data Bank.
The results in Supplemental Table S1 show that currently
the PDB (10 August 2014) contains about 9% incomplete
ligands and non-standard residues, out of which about 6%
miss at least one atom and 2.6% miss rings. Chirality problems
occur in less than 8% of the validated molecules. The
frequency of basic chirality errors is even lower––only 2.4%
of molecules exhibit chirality errors on a carbon atom, and
1.4% on a metal atom. Other chirality issues are generally
reported more frequently––i.e. 4.3% of molecules have
wrong High-order chirality plus 1.1% wrong Planar chirality,
but the majority of these are very probably artifacts
(as mentioned in the section Validation Analyses). Therefore,
about 83% of validated molecules are complete and
have correct chirality. This statement is slightly more optimistic
than previous estimations, which are based on the
fit to electron density and 3D structure of the ligands and
place the expected percentage of erroneous molecules between
20 and 30% (19,20). The situation appears even better
if we exclude the chirality errors reported during the Planar
and High-order chirality analyses. Specifically, about 88%
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Nucleic Acids Research, 2015, Vol. 43, Database issue D373
Figure 2. Detailed validation report for the saccharide MAN 957 from PDB entry 1E4M. The structure is complete, but exhibits a chirality error on atom
C5. Additionally, the warning of foreign atom at position O1 indicates that this molecule is part of an oligosaccharide chain.
of molecules are complete and have correct chirality for all
carbon and metal atoms.
On the other hand, the issues found by the Advanced
analyses occur more frequently than completeness and chirality
errors. More than 20% of the validated molecules contain
substitutions, and about 35% have at least one atom
formally located in the neighbor residue. Additionally, 38%
contain atoms which are not named in agreement with
the standard PDB atom naming convention. Overall, the
validation was carried out uneventfully for about 30% of
the molecules. While the results of the Advanced analyses
have no bearing over the chemical soundness of the validated
molecules, they indicate that further, especially automated
processing of these structures can be very problematic.
Therefore, it is indeed useful to validate the structure of
ligands or non-standard residues of interest before performing
further investigations, especially where a high degree of
automation is involved.
Samples
To show the functionality of ValidatorDB and also the importance
of such validation analyses, we selected a few interesting
samples and included them in the ValidatorDB web
page.
Case studies
One important question is how the quality of the structures
varies for different classes of molecules. We have thus
designed and conducted several case studies to show how
ValidatorDB can answer such questions. We selected the
molecules according to a combination of features related
to chemical structure, biological function, area of application,
availability, etc. The following classes were defined as
subsets of models from wwPDB CCD:
r Polycyclic molecules: contain three or more conjugated
rings. The molecules containing metals were excluded, as
their quality is influenced more by the presence of the
metal than by their polycyclic structure.
r Carbohydrates: contain the pyran or furan ring.
Molecules containing P (e.g. ATP) were excluded, as
their quality is influenced more by the occurrence of
phosphate derivatives than by the sugar part.
r Mannose derivatives: subclass of carbohydrates.
r Organometals: contain a metal atom.
r Experimental drugs: described in DrugBank (21) as experimental
drugs, i.e. have been shown to bind specific
proteins in mammals, bacteria, viruses, fungi or parasites.
r Approved drugs: described in DrugBank as approved
drugs, i.e. have received approval in at least one country.
A list of the annotations of the molecules from each class
can be found in the Supplementary Material. Summaries of
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D374 Nucleic Acids Research, 2015, Vol. 43, Database issue
the validation results for each class are given in Supplemental
Table S2.
Compared to the PDB-wide statistics for all ligands and
non-standard residues (see above), polycyclic molecules
have overall higher quality (higher percentage of molecules
with complete structure and correct chirality). Nonetheless,
they exhibit more errors in C chirality, probably due to their
more complicated, carbon-based scaffolds. Carbohydrate
molecules show similar trends as polycyclic molecules, since
their structure is also ring-based. However, they exhibit a
higher rate of errors in C chirality, a consequence of the
fact that they generally contain more chiral atoms. Mannose
derivatives play an important role in cell–cell recognition,
a biological function which relies heavily on chirality.
Therefore, they must have a characteristic structure (determined
by chirality) and are also strongly predisposed to
have C chirality errors. We found that the percentage of errors
in C chirality is over three times higher for mannose
derivatives than the PDB-wide evaluation for all ligands and
non-standard residues.
Organometals seem to have overall lower quality. Part of
the errors is artifacts of our validation algorithm, as such
molecules can have very complicated scaffolds (see algorithm
limitations in the Supplementary Material). However,
the majority of the reported errors are significant, proving
that many challenges remain in the field of structure determination
for organometals.
On the other hand, the overall quality of the structure
of experimental drugs is clearly much higher than the PDBwide
statistics for all ligands and non-standard residues. For
approved drugs, i.e. drugs already on the market, the situation
is even better. About 95% of these molecules are complete
and have correct chirality, a consequence of the fact
that markedly more effort is expended in the determination
of their structure in biomacromolecular complexes.
CONCLUSIONS
In this article we introduced ValidatorDB, a database of upto-date
validation results for all ligands and non-standard
residues from the Protein Data Bank (all molecules with
seven or more heavy atoms). The validation of annotation
approach implemented here employs correct reference
molecules in the form of models from the wwPDB CCD.
ValidatorDB offers analyses which cover the main aspects
of validation of annotation, by systematically evaluating the
completeness, chirality and other features of the validated
molecules. ValidatorDB is the only validation tool able to
report several types of chirality errors, which allows distinguishing
between serious chirality issues and formal inconsistencies.
ValidatorDB can further report completely erroneous
ligands, alternate conformations, identity with the
model, etc. The validation results are organized systematically,
from detailed reports for single molecules, to a PDBwide
general summary, and fully customized reports. All results
are available in interactive graphical and tabular form
via the web interface, and can be readily downloaded in convenient
formats.
SUPPLEMENTARY DATA
Supplementary Data are available at NAR Online.
FUNDING
This work was funded by the Ministry of Education,
Youth and Sports of the Czech Republic [LH13055],
the CEITEC - Central European Institute of Technology
[CZ.1.05/1.1.00/02.0068] from the European Regional
Development Fund, the “Capacities” specific program
[286154] and by INBIOR [CZ.1.07/2.3.00/20.0042] from
the European Social Fund and the state budget of the
Czech Republic. Additional support was provided by the
project “Employment of Newly Graduated Doctors of Science
for Scientific Excellence” [CZ.1.07/2.3.00/30.0009] cofinanced
from the European Social Fund and the state budget
of the Czech Republic. Funding for open access charge:
European Social Fund and the State Budget of the Czech
Republic [CZ.1.07/2.3.00/20.0042].
Conflict of interest statement. None declared.
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PatternQuery: web application for fast
detection of biomacromolecular structural
patterns in the entire Protein Data Bank
76
Nucleic Acids Research, 2015 1
doi: 10.1093/nar/gkv561
PatternQuery: web application for fast detection of
biomacromolecular structural patterns in the entire
Protein Data Bank
David Sehnal1,2,3,†
, Luk´aˇs Pravda1,2,†
, Radka Svobodov´a Vaˇrekov´a1,2
, Crina-Maria Ionescu1
and Jaroslav Koˇca1,2,*
1
CEITEC - Central European Institute of Technology, Masaryk University Brno, Kamenice 5, 625 00 Brno, Czech
Republic, 2
National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kotl´aˇrsk´a 2, 611 37
Brno, Czech Republic and 3
Faculty of Informatics, Masaryk University Brno, Botanick´a 68a, 602 00 Brno, Czech
Republic
Received March 13, 2015; Revised May 01, 2015; Accepted May 17, 2015
ABSTRACT
Well deﬁned biomacromolecular patterns such as
binding sites, catalytic sites, speciﬁc protein or nucleic
acid sequences, etc. precisely modulate many
important biological phenomena. We introduce PatternQuery,
a web-based application designed for detection
and fast extraction of such patterns. The application
uses a unique query language with Pythonlike
syntax to deﬁne the patterns that will be extracted
from datasets provided by the user, or from
the entire Protein Data Bank (PDB). Moreover, the
database-wide search can be restricted using a variety
of criteria, such as PDB ID, resolution, and organism
of origin, to provide only relevant data. The
extraction generally takes a few seconds for several
hundreds of entries, up to approximately one
hour for the whole PDB. The detected patterns are
made available for download to enable further processing,
as well as presented in a clear tabular and
graphical form directly in the browser. The unique
design of the language and the provided service
could pave the way towards novel PDB-wide analyses,
which were either difﬁcult or unfeasible in the
past. The application is available free of charge at
http://ncbr.muni.cz/PatternQuery.
INTRODUCTION
In the past years an overwhelming volume of biomacromolecular
structures have been deposited in the worldwide
deposition system Protein Data Bank (PDB) (1). The
amount of data which was available 20 years ago is nowadays
released every week, and this rapid pace is maintained.
Small high-resolution protein structures are deposited, as
well as extensive ribosomes or viral capsids. The whole
scientific community can benefit from this abundance of
biomacromolecular structures, being enabled to carry out
experiments and analyses which were not feasible before (2–
4). Such richness of 3D data accents the immense need for
structural bioinformatics tools and services to help in reasoning
out a variety of structural properties, which often go
hand in hand with biological function.
Presently, various computational tools and frameworks
exist for the definition of molecular (sub)structure, such as
SMILES (5), MQL (6), or SLN (7), which are mainly focused
on small organic compounds. There are also tools
that enable the definition and analysis of more general structural
patterns, some of which rely on an internal molecular
language (8–14). A structural pattern can, in principle,
be any part of a biomacromolecule, i.e. protein backbone,
ligands or metals together with their binding sites or
surroundings, specific amino acids or nucleotide sequences,
and sets of atoms or residues satisfying given criteria (distance,
composition, intramolecular connectivity, etc.). Nevertheless,
these tools are designed to operate either on
a low number of structures, or their functionality is focused
on very specific and narrow applications. Furthermore,
some of the most popular services and databases use
structure information for defining or inferring structurefunction
relationships (15,16). Even critical interaction sites
are defined at the primary and secondary structure level
(17,18), mainly because of the large structural variation of
biomacromolecules. Ultimately, to our knowledge, there is
no tool available for the general and systematic description
and extraction of 3D structural patterns from biomacromolecules
tailored for the mining of structural databases.
In this article, we address the general philosophy of describing
3D structural patterns, and present an approach
*To whom correspondence should be addressed. Tel: +420 54949 4947; Fax: +420 54949 2556; Email: Jaroslav.Koca@ceitec.muni.cz
†
These authors contributed equally to the paper as first authors.
C The Author(s) 2015. Published by Oxford University Press on behalf of Nucleic Acids Research.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by-nc/4.0/), which
permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact
journals.permissions@oup.com
Nucleic Acids Research Advance Access published May 26, 2015
byguestonFebruary21,2016http://nar.oxfordjournals.org/Downloadedfrom
2 Nucleic Acids Research, 2015
Figure 1. The query recognizes the binding pocket of any residue containing a pyranose moiety in the envelope glycoprotein gp160 from Human immunodeficiency
virus 1 in complex with Homo sapiens immunoglobulins (3u7y). One of the recognized patterns is highlighted in the box. (A) First, the query
identifies a pyranose moiety (a ring composed of 5 carbons and an oxygen atom). (B) Then, all residues which include this pattern in their structure are
identified. (C) Finally, all the residues that are at most 4 ˚A from any of the pyranose containing residues are detected as well. This ensures all the potential
coordination partners are recognized properly. The molecules were visualized using PyMOL.
for their effective identification and extraction from individual
biomacromolecules, as well as from the PDB archive.
This approach is implemented as the user-friendly web service
PatternQuery (PQ). The service is built on a simple
yet powerful language for the description of any molecular
structural patterns based on the nature and relationship
between atoms, residues and other structural elements. The
unique design of PQ allows the user to simultaneously operate
at the primary, secondary and tertiary level of biomacromolecular
structure.
The results provided by PQ can serve as a source of input
data in further analyses, such as structural and functional
assignment of uncharacterized proteins, analysis of newly
determined structures, comparative structural analysis, design
and engineering of novel functional sites, etc.
DESCRIPTION OF THE TOOL
PatternQuery is an interactive web application for the
optimal definition of biomacromolecular structural patterns,
followed by their fast detection and extraction
from the entire PDB or user defined datasets. These patterns
are described by unique expressions based on the
Python programming language, which are designed to define
biomacromolecular structural patterns based on the
nature and relationship between atoms, residues and other
structural elements. These expressions define the composition,
topology, connectivity, and 3D structure of a pattern.
By composing these expressions into a query, 3D structural
patterns can be identified inside biomacromolecules. Figure
1 gives the PQ query example that identifies and extracts a
3D pattern made up of a residue containing a pyranose moiety,
together with its immediate surroundings.
The PatternQuery application can be used in two modes.
The PQ Explorer mode (Figure 2) is useful for real-time
investigation of smaller datasets (either user-uploaded or
a small subset of the PDB), and tuning the queries prior
to searching the whole PDB. The PQ Service mode (Supplementary
Figure S1) is optimized for querying the entire
PDB archive. Finally, a command-line version of the PQ
application is available for processing in-house databases of
3D biomacromolecular structure data.
The PQ web pages contain several interactive guides,
which explain the features and give an easy walkthrough the
application, along with plenty of tips. Rich documentation
is provided as well, in the form of a Wiki user manual with
many examples.
PatternQuery workflow
The procedure of using the PatternQuery application involves
four steps: (i) query definition; (ii) input data specification;
(iii) running the PQ query; (iv) visualization and
analysis of retrieved patterns.
(i) Query definition
First, it is necessary to build a query that optimally
describes the structural pattern(s) of interest. The PatternQuery
language is well documented, and its usage
is richly illustrated on many examples and several case
studies. Detailed knowledge of the language is not required,
since the integrated high performance coding editor
(ACE, http://ace.c9.io) provides syntax suggestions
and relevant query examples. Multiple queries can be defined
for a single run.
(ii) Input data specification
Second, the queried data has to be specified. Small subsets
of the PDB, or the user’s own datasets can be queried
in the PQ Explorer mode. Large custom databases can be
queried using the command line version of PatternQuery.
In the PQ Service mode, the default queried dataset is a
weekly updated mirror of the latest release of the PDB
stored in the PDBx/mmCIF file format. Alternatively, a
subset of the PDB can be specified based on a list of PDB
entry IDs, or on various metadata criteria. By specifying
a subset of the PDB as input, it is ensured that only patterns
from relevant structures are retrieved, and the query
can be executed in a more time efficient manner. For
example one may restrict the search only to biomacromolecules
including a DNA chain from Homo sapiens,
determined by X-ray diffraction of resolution better than
2 ˚A and published in the past 3 years.
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Nucleic Acids Research, 2015 3
Optionally, all the patterns identified while running PQ
may be subjected to the structural validation of annotation
(19). During this process, which is briefly described
in the supplementary materials in the section SI Structure
Validation, all ligands and non-standard residues larger
than six heavy atoms are inspected for their completeness
and chirality correctness. Possible discrepancies or structural
inconsistencies are highlighted. This may aid further
processing of the results by discarding low-quality
patterns.
(iii) Running the PQ query
After setup, the specified data set is queried with all the
defined PQ expressions. This process involves generating
the structure’s internal representation, together with
proper bond identification based on the intramolecular
atomic distances, and then attempting to match the
PQ query with any suitable substructure. The theoretical
framework behind this process is given in the supplementary
materials (Theoretical Background section).
Depending on the complexity of the defined queries and
the number of dataset entries, running the queries may
take from a few seconds (for a few hundred small to
medium-sized entries), up to approximately one hour for
100 000 PDB entries. Most types of queries have O(N) or
O(N log N) time complexity (where N is the number of
atoms in the structure), meaning that doubling the number
of structures being processed will roughly double the
running time. A benchmark of the application is available
in the supplementary materials (section Performance
Overview).
(iv) Visualization and analysis of retrieved patterns
The PQ results consist of structure files with the patterns,
and statistics about their origin and composition. All the
results are made available for inspection or download under
a unique web address for at least a month, in both the
PQ Explorer and PQ Service modes.
The PatternQuery output provides a straightforward and
rich report in both tabular and graphical form, including
summary and detailed information about each pattern identified.
The summary includes the number of detected patterns
and PDB entries that the patterns were extracted from,
together with possible errors and warnings, often caused by
discrepancies either in the biomacromolecular structure, or
in the file format. The detailed report provides a pattern
view, focused on each individual pattern identified, and a
PDB entry view, focused on each PDB entry queried. Additionally,
in the PDB entry view, the results for all patterns
identified in that particular PDB entry can be accessed to-
gether.
Useful statistics in the form of the atom and residue
composition are given for each extracted pattern, along
with all the metadata from the parent data set entry (PDB
entry). These can serve for further filtering of interesting
results. Each extracted pattern can be visualized interactively
(ChemDoodle, http://www.chemdoodle.com). Optionally,
the validation report can be readily accessed.
Limitations
The setup of the PatternQuery web application, particularly
in the PQ Service mode, is limited to 10 queries to
be executed during a single run. The maximum number
of results that can be returned by a single query execution
on our server is one million patterns or ten million atoms,
whichever is reached first. This limitation is not present in
the command line tool. Additional limitations are discussed
in detail in the supplementary materials (Limitations sec-
tion).
RESULTS AND DISCUSSION
We provide two case studies, which demonstrate the possible
usage of the PatternQuery web application. Additional biologically
relevant examples, together with the corresponding
PQ queries, are available on our wiki pages. All the
queries used in the case studies can be found in the supplementary
materials.
Figure 2. The PatternQuery Explorer mode is tailored for querying smaller user-defined datasets (up to 100 entries) uploaded in one of the supported
formats. Additionally, a subset of the PDB archive can be queried as well, based on PDB ID or a variety of metadata.
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4 Nucleic Acids Research, 2015
Case study I - LecB sugar binding sites
Pseudomonas aeruginosa is an opportunistic pathogen associated
with a number of chronic infections. This pathogen
forms a biofilm enabling it to survive both the response of
the host immune system, and antibiotic treatment (20). One
of the cornerstones of biofilm formation, in the case of P.
aeruginosa, is the presence of sugar-binding proteins on the
outer cell membrane –– LecA (PA-IL) and LecB (PA-IIL).
Their inhibition is considered to be a promising approach
for anti-pseudomonadal treatment (21).
LecB binds with the highest affinity to L-fucosides and
D-mannosides (22), however, other monosaccharides are
recognized as well (23). The sugar-binding domain is calcium
dependent, with two calcium ions stabilizing the binding
site. We employed PQ in the discovery of sugar binding
sites of similar geometry as the tetrameric LecB entry in the
PDB. Specifically, we have searched for 2 calcium ions at
most 4 ˚A apart, and all the residues with direct interaction
with either of these ions. Furthermore, just the molecular
patterns containing a residue with a furan or pyran ring
were preserved. The complete PQ query which identifies
such patterns is given as SI Query 1. Due to the fact that the
sugar-binding domain is calcium dependent, we were able to
restrict the search only to the biomacromolecules having a
calcium ion in their structure, and containing a pyranose or
furanose moiety (3074 PDB entries as of 25.4.2015), which
tremendously reduced query-running time. The initial analysis
of the PDB archive revealed 355 different patterns originating
from 231 PDB entries. However, the majority of the
sugar moieties originated from nucleotides. To filter them
out, a simple filter was employed (SI Query 2), which provided
108 distinct patterns originating from 36 PDB entries
of 7 different organisms. The majority of them originated
from P. aeruginosa, however other pathogens such as
R. solanacearum, B. cenocepacia or C. violaceum were identified
among the organisms of origin. The sugar-binding
domain in 87 of the patterns are composed of 3x Asp, 2x
Asn and Glu and Gly residues, which is the binding site referred
to as the sugar binding motif in the literature (24) for
a total of 24 PDB entries from 3 organisms. In 12 further
patterns a glycine residue was not present due to the fact
that the structure stored in the PDB is only the asymmetric
unit, rather than the expected biological unit, which is a
tetramer. Finally, the remaining 9 patterns, originating from
6 different pectate lyase (EC: 4.2.2.2) structures, exhibited a
different binding motif in comparison to the LecB protein.
These patterns contained ␣-D-galactopyranuronic acid and
its derivatives rather than a fucose or mannose derivative. A
detailed list of these sugar ligands is given in the Supplementary
Tables S1 and S2.
Finally, the quality of the 3D structure of the patterns
was examined. A total of 9 patterns originating from 3 PDB
entries exhibited a serious structural issue, i.e. half of the ␣L-fucose
ligands in complex with the 1oxc PDB entry exhibit
incorrect chirality at the C1 carbon atom. The details
of this analysis can be found in the supplementary materials
(SI Query Validation 1).
Case study II - C2H2 zinc fingers
The class of zinc finger DNA-binding proteins is the most
abundant across all biology (25). They fulfill a remarkable
range of diverse functions, including DNA recognition,
transcriptional activation, regulation of apoptosis or
lipid binding (25). Due to their specificity and modular architecture,
they often serve as a rational engineering target
for binding a wide range of DNA sequences to activate, repress,
cut or paste genes (26). The classical C2H2 zinc finger
domain is composed of a simple ␤␤␣ fold, which is stabilized
by a zinc ion coordinated by two histidine and two cysteine
residues. The fold is often described by the pattern of
X2-C-X2–4-C-X12-H-X3–5-H, where X stands for any amino
acid, C is cysteine and H is histidine. Nevertheless, atypical
variations also exist, which differ from the consensus
profile (27) (e.g. UniProt ID (28): P47043). The X12 region
of the consensus profile is usually further decomposed into
the sequence X3-[F|Y]-X5- -X2, where [F|Y] represents either
a phenylalanine or tyrosine residue, and denotes a
hydrophobic residue (29).
We have queried the whole PDB archive (access date
25.4.2015) using several different PQ queries. At first, we
searched just for patterns with primary sequences which
satisfy the basic consensus profile of the typical C2H2 zinc
finger domain, without further specification of the X12 region
(SI Query 3). We identified 595 patterns in 342 different
PDB entries. The results of such a query will inevitably
be plagued by a number of false positive hits, i.e. patterns
satisfying the primary sequence criteria, but which are not
zinc fingers. This is due to the fact that no further checks
for the presence of a zinc ion or stabilizing residues were included
in the query. Closer inspection of the results revealed
that the above-defined primary sequence corresponds not
only to the C2H2 zinc finger fold, but also to a variety of
fumarate reductases and hydrolases. In order to filter out
these false positive hits, we adjusted the query so that the
pattern must contain a zinc ion stabilized by two cysteine
and two histidine residues from the consensus profile (SI
Query 4). This final query resulted in 461 different patterns
originating from 278 PDB entries. The majority of the results
(356 patterns in 239 PDB entries) also satisfied the
special pattern of the X12 region between the second cysteine
and the first histidine (SI Query 5). The largest number
of structures was isolated from Eukaryotes, mainly Homo
sapiens, and determined by solution nuclear magnetic resonance
spectroscopy. However, a few structures originating
from viruses and bacteria were found as well. No residues
relevant for validation were detected inside the input patterns,
and therefore validated.
Furthermore, it has been reported that the zinc finger fold
may also be stabilized by other metals (30). We have modified
the query so that possible substitutions of zinc with
other metals can also be considered (SI Query 6). Running
this query returned five additional patterns from two PDB
entries, where the zinc ion was substituted by cobalt (31)
and cadmium (32). Although the cobalt-binding protein
contains 5 zinc finger domains, just 4 patterns were identified,
due to the alternate primary sequence in one of the
patterns. These primary sequence modifications can be ac-
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Nucleic Acids Research, 2015 5
counted for by modifying the regular expression in the PQ
query.
CONCLUSION
In this article, we presented PatternQuery, a novel web application
for rapid definition and extraction of 3D structural
patterns from the entire PDB. The web application
is easy to use and platform-independent. Results are presented
in a clear graphical and tabular form. Rich documentation
regarding both the underlying language and the
features of the web application, along with several biologically
relevant case studies are available at http://ncbr.muni.
cz/PatternQuery.
The innovative approach described in the present study
enables mining large databases (entire PDB or in-house
structural databases), a task which was unfeasible in the
past, or was difficult for patterns with more complex struc-
ture.
SUPPLEMENTARY DATA
Supplementary Data are available at NAR Online.
FUNDING
This work was funded by the Ministry of Education,Youth
and Sports of the Czech Republic [contract number
LH13055], the European Community’s Seventh Framework
Programme [CZ.1.05/1.1.00/02.0068] from the European
Regional Development Fund, and the Grant Agency
of the Czech Republic [14-29577S]. Support to CMI
was provided via the project ”Employment of Newly
Graduated Doctors of Science for Scientific Excellence”
[CZ.1.07/2.3.00/30.0009], co-financed from the European
Social Fund and the state budget of the Czech Republic.
Funding for open access charge: Institutional budget of the
National Centre for Biomolecular Research, Masaryk University,
Czech Republic.
Conflict of interest statement. None declared.
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High-quality and universal empirical atomic
charges for chemoinformatics applications
83
Geidl et al. J Cheminform (2015) 7:59
DOI 10.1186/s13321-015-0107-1
RESEARCH ARTICLE
High‑quality and universal empirical
atomic charges for chemoinformatics
applications
Stanislav Geidl1†
, Tomáš Bouchal1†
, Tomáš Raček1,2†
, Radka Svobodová Vařeková1*
, Václav Hejret1
, Aleš Křenek3
,
Ruben Abagyan4
and Jaroslav Koča1*
Abstract 
Background:  Partial atomic charges describe the distribution of electron density in a molecule and therefore provide
clues to the chemical behaviour of molecules. Recently, these charges have become popular in chemoinformatics, as
they are informative descriptors that can be utilised in pharmacophore design, virtual screening, similarity searches
etc. Especially conformationally-dependent charges perform very successfully. In particular, their fast and accurate
calculation via the Electronegativity Equalization Method (EEM) seems very promising for chemoinformatics applications.
Unfortunately, published EEM parameter sets include only parameters for basic atom types and they often miss
parameters for halogens, phosphorus, sulphur, triple bonded carbon etc. Therefore their applicability for drug-like
molecules is limited.
Results:  We have prepared six EEM parameter sets which enable the user to calculate EEM charges in a quality comparable
to quantum mechanics (QM) charges based on the most common charge calculation schemes (i.e., MPA, NPA
and AIM) and a robust QM approach (HF/6-311G, B3LYP/6-311G). The calculated EEM parameters exhibited very good
quality on a training set (R2 > 0.9) and also on a test set (R2 > 0.93). They are applicable for at least 95 % of molecules
in key drug databases (DrugBank, ChEMBL, Pubchem and ZINC) compared to less than 60 % of the molecules from
these databases for which currently used EEM parameters are applicable.
Conclusions:  We developed EEM parameters enabling the fast calculation of high-quality partial atomic charges for
almost all drug-like molecules. In parallel, we provide a software solution for their easy computation (http://ncbr.muni.
cz/eem_parameters). It enables the direct application of EEM in chemoinformatics.
Keywords:  Partial atomic charges, Electronegativity Equalization Method, EEM, Quantum mechanics, QM, Drug-like
molecules
© 2015 Geidl et al. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License
(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium,
provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license,
and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/
publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Background
Partial atomic charges are real numbers describing the
distribution of electron density in a molecule, thus providing
clues as to the chemical behaviour of molecules.
The concept of charges began to be used in physical
chemistry and organic chemistry. Afterwards, partial
atomic charges were adopted by computational chemistry
and molecular modelling, where they serve for calculating
electrostatic interactions, describe the reactivity of
the molecule etc. Specifically, they are applied in molecular
dynamics, docking, conformational searches, binding
site predictions etc. Recently, partial atomic charges also
became popular in chemoinformatics, as they proved to
be informative descriptors for QSAR and QSPR modelling
[1–9] and for other applications [10–12]; they can
be utilised in pharmacophore design [13–15], virtual
Open Access
*Correspondence: radka.svobodova@ceitec.muni.cz;
jkoca@chemi.muni.cz
†
Stanislav Geidl, Tomáš Bouchal and Tomáš Raček are joint first authors
1
National Centre for Biomolecular Research, Faculty of Science
and CEITEC, Central European Institute of Technology, Masaryk University
Brno, Kamenice 5, 625 00 Brno, Czech Republic
Full list of author information is available at the end of the article
Page 2 of 10Geidl et al. J Cheminform (2015) 7:59
screening [16–18], similarity searches [19–21], molecular
structure comparison [22–24] etc.
The partial atomic charges cannot be determined
experimentally or derived straightforwardly from the
results of quantum mechanics (QM), and many different
methods have been developed for their calculation.
The most common method for charge calculation is an
application of the QM approach and afterwards the utilisation
of a charge calculation scheme. Charge calculation
schemes can be based on orbital-based population
analysis, on wave-function-dependent physical observables
or on reproducing charge-dependent observables.
Examples of orbital-based population analyses are Mulliken
population analysis (MPA) [25, 26], Löwdin population
analysis [27] and Natural population analysis (NPA)
[28, 29]. Wave-function-dependent physical observables
are used in the atoms-in-molecules (AIM) approach [30,
31], Hirshfeld population analysis [32–34], CHELPG [35]
and Merz-Singh-Kollman (MK) [36, 37] method. The
reproduction of charge-dependent observables is applied
in the CM1, CM2, CM3, CM4, and CM5 approaches [38,
39].
Unfortunately, QM charge calculation approaches are
very time-consuming. A markedly faster alternative is to
employ empirical charge calculation approaches, which
can also provide high-quality charges. These approaches
can be divided into conformationally-independent,
which are based on 2D structure (e.g., Gasteiger’s and
Marsili’s PEOE [40, 41], GDAC [42], KCM [43], DENR
[44]) and conformationally-dependent, calculated from
3D structure (e.g., EEM [45], QEq [46] or SQE [47,
48]). We would like to highlight that conformationallydependent
charges are considered to be more suitable for
chemoinformatics applications [1–3, 7, 12, 20]. The reason
is that these charges contain extensive information
not only about chemical surrounding of atoms, i.e., its
topology (2D structure based charges) but also geometry
and “chemical quality” of the surrounding. Such information
is missing, for example, in force field charges which
use averaged atomic charges from large sets of structures.
Therefore we only focus on conformationally-dependent
atomic charges.
Electronegativity equalization method (EEM) is the
most frequently used conformationally-dependent
empirical charge calculation approach. It calculates
charges using the following system of linear equations:
(1)







B1
κ
R1,2
· · · κ
R1,N
− 1
κ
R2,1
B2 · · · κ
R2,N
− 1
...
...
...
...
...
κ
RN,1
κ
RN,2
· · · BN − 1
1 1 · · · 1 0







·






q1
q2
...
qN
¯χ






=






−A1
−A2
...
−AN
Q






where qi is the charge of an atom i; Ri,j is the distance
between atoms i and j; Q is the total charge of the molecule;
N is the number of atoms in the molecule; κ is the
molecular electronegativity, and Ai, Bi and κ are empirical
parameters. The parameters Ai and Bi vary for individual
atom types, where atom type is a combination of
element type and maximal bond order of the atom i. For
example, atom type C2 means that the atom is carbon
and it creates at least one double bond with its neighbors.
An atom X in the aromatic ring is therefore also
included into X2 atom type. The parameters Ai, Bi and
κ are molecule independent and they are calculated
from QM atomic charges by a process of EEM parameterization
[49]. EEM is not only a fast charge calculation
approach, but it can also provide highly accurate
charges, i.e., they can mimic the QM charges for which
EEM has been parameterized. On the other hand, EEM
charges can be outperformed in certain situations. Specifically,
QEq showed better agreement with experimental
dipole moments [46] and SQE is presented as an
extension of the EEM to obtain the correct size-dependence
of the molecular polarizability [47]. But this drawback
is compensated by a fact that the quality of EEM
charges was documented by many successful applications
[2, 3, 50–55] and they are clearly the most cited
empirical conformationally-dependent charges.
Therefore, many EEM parameter sets for various QM
charge calculation approaches were published later or
recently (see Table  1). In parallel, a few freely available
software tools also include an EEM charge calculation
method (see Table 2).
EEM recently began to be also used in chemoinformatics,
giving very promising results [1–3, 64, 65].
Because of their rapid calculation, they can be easily
computed for large sets of molecules (e.g., drug-like
compounds). Unfortunately, a broader utilisation of
EEM charges in chemoinformatics is now limited by
the fact that available EEM parameter sets can only
cover part of common organic molecules, as they only
contain the parameters for some elements and certain
bond orders (Table 1). For the above reasons, our aim
with this work is to provide EEM parameter sets that
cover most of the drug-like molecules and with accuracy
comparable to QM charges. Specifically, we have
parameterized EEM for frequently used charge calculation
schemes, high enough QM theory levels and a
large basis set. Afterwards, we compared the coverage
and quality of our EEM parameter sets with previously
published EEM parameter sets (see Table 1) and
with EEM parameter sets embedded in software tools
(see Table  2). Additionally, we have prepared a software
solution, enabling the user to easily calculate EEM
charges via our EEM parameters.
Page 3 of 10Geidl et al. J Cheminform (2015) 7:59
Methods
EEM parameterization (step 1)
All the steps performed during our work are depicted
in Fig.  1a. The most challenging part of our work was
the EEM parameterization. This step required several
tasks (see Fig. 1b) and the quality of the calculated EEM
parameters sets depends on the proper accomplishment
of all these tasks.
EEM parameterization: selection of atom types to be
parameterized
Our goal is to provide EEM parameter sets applicable
for most common drug-like molecules. Therefore, we
provide EEM parameters for the majority of atom types
occurring in these molecules. These atom types are summarized
in Table 3 (columns 1–3).
EEM parameterization: preparation of the training set
Our training set contains the 3D structures of 4475
distinct small organic molecules. The molecules were
obtained from the DTP NCI database [66] and their
3D structures were generated with CORINA 3.60 [67],
without any further geometry optimization. The DTP
NCI database collects compounds tested as anticancer
drugs (with positive or negative results), therefore it is
a database of common drug-like molecules. The training
set was created in such a way that each selected
atom type is contained in at least 100 molecules. The
occurrences of individual atom types in the training
set are summarized in Table  3. The list of training
set molecules, including their NSC numbers and
summary formulas, can be found in (Additional file 1:
Table S1).
Table 1  Summary information about published EEM parameters evaluated in this study
†
  An element symbol with no further information (e.g., C) means that the EEM parameters are available for this element bound by all possible bond orders. The
element symbol followed by a number (e.g., C1) means that the EEM parameters are only available for this element bound by a bond with an order described using
this number
‡
  For this parameter set, C1 represents sp3 hybridization, C2 sp2 hybridization, C3 sp hybridization, etc.
QM theory Level + basis set Charge calc. scheme EEM parameter set name Published by Elements and bond orders included†
HF/STO-3G MPA Baek1991 Baekelandt et al. [56] C, O, N, H, P, Al, Si
Svob2007_cbeg2 Svobodova et al. [49] C1, C2, O, N1, N2, H, S1
Svob2007_cmet2 Svobodova et al. [49] C1, C2, O, N1, N2, H, S1, Fe, Zn
Svob2007_chal2 Svobodova et al. [49] C1, C2, O, N1, N2, H, S1, Br, Cl, F, I
Svob2007_hm2 Svobodova et al. [49] C1, C2, O, N1, N2, H, S1, F, Cl, Br, I, Fe, Zn
HF/6-31G* MK Jir2008_hf Jirouskova et al. [57] C1, C2, O, N1, N2, H, S1, F, Cl, Br, Zn
B3LYP/6-31G* MPA Bult2002_mpa Bultinck et al. [58] C, O, N, H, F
NPA Bult2002_npa Bultinck et al. [58] C, O, N, H, F
Ouy2009‡ Ouyang et al. [59] C, O, N, H
Ouy2009_elem Ouyang et al. [59] C, O, N, H
Hir. Bult2002_hir Bultinck et al. [58] C, O, N, H, F
MK Bult2002_mk Bultinck et al. [58] C, O, N, H, F
Jir2008_mk Jirouskova et al. [57] C1, C2, O, N1, N2, H, S1, F, Cl, Br, Zn
CHELPG Bult2002_che Bultinck et al. [58] C, O, N, H, F
AIM Bult2004_aim Bultinck et al. [60] C, O, N, H, F
Table 2  Information about freely available software tools enabling EEM charge calculation
Software EEM parameters used by a software
OpenBabel [61] It contains the embedded EEM parameter set Bult2002_mpa, which was parameterized for B3LYP/6-31G*/MPA charges. It does not
allow any other EEM parameter set to be used
Balloon [23] It contains an embedded EEM parameter set published by Puranen et al. [62], which was calculated by fitting to the MEP field.
Balloon’s developers claim that the EEM charges calculated via Balloon should be comparable to B3LYP/cc-pVTZ/MPA. It does not
allow any other EEM parameter set to be used
EEM SOLVER [63] It allows the use of any input EEM parameter sets provided by the user. It does not contain any embedded EEM parameter sets
Page 4 of 10Geidl et al. J Cheminform (2015) 7:59
EEM parameterization: selection of QM charge calculation
approach
We performed the EEM parameterization for two QM
theory levels (B3LYP and HF), one basis set (6-311G)
and three charge calculation schemes (MPA, NPA and
AIM). We provide the EEM parameters for all combinations
of these theory levels, the basis sets and the charge
calculation schemes (see Table 4). Theory levels HF and
B3LYP were selected, because they are very often used
for QM charge calculation and were also successfully
used for EEM parameterization several times [49, 56–
60]. The basis set 6-311G was used, because it is robust,
also covers iodine and moreover, Pople basis sets are
very suitable for EEM parameterization. MPA and NPA
(a) (b)
Fig. 1  a Composition of steps performed within this work and b tasks performed during EEM parametrization
Table 3  Occurrence of atom types in the training set
Denotation of 
atom type
Element
symbol
Maximal bond
order
Number of atoms with this
atom type in the training set
Number of molecules containing
this atom type in the training set
H1 H 1 57,119 4442
C1 C 1 15,220 3447
C2 2 38,097 4149
C3 3 345 266
N1 N 1 4151 2483
N2 2 3383 1879
N3 3 345 266
O1 O 1 5016 2525
O2 2 5793 3069
F1 F 1 938 395
P1 P 1 153 143
P2 2 251 213
S1 S 1 1034 770
S2 2 1391 1211
Cl1 Cl 1 1084 676
Br1 Br 1 336 261
I1 I 1 1734 1365
Total – – 136,390 4475
Page 5 of 10Geidl et al. J Cheminform (2015) 7:59
population analyses were employed, because they are the
most known charge calculation schemes and additionally,
EEM is able to mimic MPA and NPA charges very
successfully [49, 58, 59]. AIM was selected, because it is
based on a different principle from the other two, and
EEM can also mimic AIM charges very efficiently [60].
Note that we do not provide EEM parameters for ESP
and RESP charges, because it is known that EEM does
not mimic these charges well [2, 58].
EEM parameterization: calculation of QM charges
For each molecule from the training set, six sets of QM
charges were calculated via the above-mentioned six QM
charge calculation approaches. The calculations of QM
charges were carried out using Gaussian09 [68]. With the
AIM population analysis, the output from Gaussian03
was further processed with the software package AIMAll
[69].
EEM parameterization: calculation of EEM parameter sets
For each set of QM charges, the EEM parameterization
was performed and the values of the parameters are provided
in (Additional file  2: EEM parameters). The software
NEEMP [70] was used for the parameterization.
This software implements the parameterization methodology
described by [49] and introduces several marked
improvements into it. NEEMP provides EEM parameter
sets together with their quality criteria, i.e., squared Pearson
correlation coefficient (R2), root mean square deviation
(RMSD), and average absolute error ( ), calculated
via Eqs. (2), (3) and (4), respectively
where qEEM
i is the EEM charge of an atom i; q
QM
i is the
QM charge of an atom i; qEEM is an average of all EEM
charges; qQM is an average of all QM charges, N is the
number of atoms in the molecule.
Coverage comparison (step 2)
For comparison, we used our six EEM parameter sets
and 15 published EEM parameter sets, described in
Table 1 (all 21 of these EEM parameter sets will be below
referred to as the tested EEM parameter sets). The coverage
comparison was done on four very well-known
databases of drug-like chemical compounds: DrugBank
[71, 72], ChEMBL [73], PubChem [74], and ZINC [75].
The number of compounds in all these databases (from
10th February 2015) are summarized in Table 5. For each
tested EEM parameter set, we analysed how many compounds
from the four databases can be covered by them
(i.e., contains only atom types present in the tested EEM
parameter sets). This coverage analysis was done using
NEEMP.
Quality comparison (step 3)
This evaluation was done for the 21 above-mentioned
tested EEM parameter sets and was performed on two
data sets—a test set (657 molecules) and an extended test
set (1226 molecules). The extended test set contained all
approved drugs (i.e., drugs which have received approval
in at least one country) from the DrugBank database
(downloaded 10th February 2015), for which it was possible
to calculate all QM charges necessary for testing.
The test set was a subset of the extended test set, which
contained only molecules covered by all the tested EEM
parameter sets. The 2D structures of all molecules were
obtained from DrugBank. The lists of molecules from
the test set and the extended test set, including their
DrugBank IDs and summary formulas, can be found in
(Additional file 3: Table S2a; Additional file 4: Table S2b,
respectively). The 3D structures of all the molecules were
(2)
R2
=
N
i=1
qEEM
i − qEEM q
QM
i − qQM
2
N
i=1
qEEM
i − qEEM 2 N
i=1
q
QM
i − qQM
2
(3)RMSD =
N
i=1
qEEM
i − q
QM
i
2
N
(4)=
N
i=1
qEEM
i − q
QM
i
N
Table 4  Quality criteria of our EEM parameter sets
EEM parameter set
name
Relevant QM charges R2
RMSD ¯
Cheminf_b3lyp_mpa B3LYP/6-311G/MPA 0.9007 0.1038 0.0727
Cheminf_b3lyp_npa B3LYP/6-311G/NPA 0.9651 0.0746 0.0540
Cheminf_b3lyp_aim B3LYP/6-311G/AIM 0.9499 0.0785 0.0558
Cheminf_hf_mpa HF/6-311G/MPA 0.9178 0.1125 0.0776
Cheminf_hf_npa HF/6-311G/NPA 0.9633 0.0805 0.0574
Cheminf_hf_aim HF/6-311G/AIM 0.9441 0.0919 0.0651
Table 5 Size of  database, used for  comparison of  EEM
parameter set coverages
Database Number of compounds
DrugBank 6874
ChEMBL 1,456,020
PubChem 63,676,639
ZINC 21,957,378
Page 6 of 10Geidl et al. J Cheminform (2015) 7:59
generated with CORINA 2.6 [67], without any further
geometry optimization. For all the molecules, we calculated
all the types of QM charges which corresponded
to the tested EEM parameters. This means we used the 8
QM charge calculation approaches mentioned in Table 1
and the six QM charge calculation approaches employed
for calculating our EEM parameter sets. The calculations
of QM charges were done with Gaussian09 and the
AIMAll software package was used for AIM charges. We
compared the quality of the tested EEM parameter set
on both the test set and the extended test set. The comparison
was done using NEEMP, which provided quality
criteria for all the tested EEM parameter sets. In the
extended test set, some molecules were not covered by
certain EEM parameter set(s). Therefore, we calculated
quality criteria based purely on the covered molecules
and in parallel, we also computed the coverage.
Quality comparison: EEM parameter sets embedded
in software tools
The calculation of EEM charges can be done with a few
software tools, e.g., EEM SOLVER, OpenBabel or Balloon.
The software tools OpenBabel and Balloon contain
embedded EEM parameter sets (see Table 2). Therefore,
we also evaluated the quality of these embedded EEM
parameter sets. This evaluation was done for the same
data sets and via the same procedure as with the tested
EEM parameter sets. The only difference was that the
EEM charges were not calculated with NEEMP, but with
OpenBabel and Balloon. Afterwards, these EEM charges
were compared with the relevant QM charges using R
statistical software [76], which provided their quality
criteria.
Software solution (step 4)
We provide the user two such solutions, the first based
on EEM SOLVER and the second on OpenBabel.
Results and discussion
EEM parameterization (step 1)
EEM parameterization was performed for six QM charge
calculation approaches, and a training set containing
4475 drug-like molecules was used. Squared Pearson
correlation coefficient (R2), root mean square deviation
(RMSD) and average absolute error ( ) of the obtained
EEM parameter sets, calculated for the training set, are
summarized in Table  4. These quality criteria describe
the correlation between QM charges and the corresponding
EEM charges and they were calculated using NEEMP
software.
These results show that the quality of our EEM parameter
sets is very high, i.e., all the R2 values are higher or
equal to 0.9. Table 4 also illustrates that QM theory levels
B3LYP and HF are both applicable for EEM parameterization,
and EEM charges based on them have similar
accuracy. From this table, we can also see that the quality
of EEM parameters based on NPA and AIM population
analysis is slightly better than for MPA.
Coverage comparison (step 2)
Information about the coverages of published EEM
parameter sets and our EEM parameter sets are summarized
in Table 6. The coverages were computed on four
well-known databases of drug-like molecules—DrugBank,
ChEMBL, PubChem and ZINC. Table 6 shows that
the coverages of the published EEM parameter sets are
low (<60 %). The only exception are the EEM parameter
sets published by Svobodova et al. and Jirouskova et al.,
which have coverage between 70 and 80 %. In contrast,
our EEM parameter sets have very high coverage—about
95 % or more for all the databases. The not covered molecules
include atom types rare for drug-like molecules,
e.g., metals or boron. An interesting fact is that the coverages
are very similar for all four analyzed databases.
Therefore, low EEM parameter set coverage is not merely
an isolated issue related to one database, but a general
problem.
Quality comparison (step 3)
Table  6 summarizes the main quality criteria (i.e., R2
values) of all tested EEM parameter sets for the test set,
which contained 657 approved drugs from DrugBank.
Other quality criteria (RMSD and ) can be found in
(Additional file  5: Table S3) and all values of partial
atomic charges (represented as tables and as graphs)
are in (Additional file 6). The table shows that our EEM
parameter sets are among the best performing EEM
parameter sets to have been published so far. The table
also illustrates that the quality of EEM parameters is
strongly influenced by the selection of QM charge calculation
scheme. Specifically, EEM parameters based on
MPA, NPA and AIM charges are very high quality, and
EEM parameters based on Hirshfeld charges are still
acceptable. EEM parameters based on MK and CHELPG
charges are very low quality, which is in agreement
with published data [2, 58]. Both theory levels (HF and
B3LYP) and all three basis sets used (STO-3G, 6-31G*
and 6-311G) are applicable for EEM parameterization.
These results also confirm that our selection of QM
theory level, basis set and charge calculation schemes is
appropriate.
For the extended test set, the quality criteria exhibit similar
trends (see Additional file 7: Table S4). In parallel, the
coverages for this data set are slightly higher than for the
complete DrugBank database. An interesting fact is that
even for such common compounds as approved drugs, the
Page 7 of 10Geidl et al. J Cheminform (2015) 7:59
coverages of published EEM parameter sets are low. Specifically,
most published EEM parameter sets have coverages
between 55 and 65 %. Further remarkable fact is that quality
criteria of our EEM parameters are better for the test set
than for the training set. The reason is that the training set
is much larger and heterogeneous than the test set.
Quality comparison: EEM parameter sets embedded
in software tools
EEM charges produced with OpenBabel were compared
with QM charges calculated with B3LYP/6-31G*/MPA.
The quality criteria for the test set were the same as for
the EEM parameters Bult2002_mpa (i.e., R2 about 0.97).
This was expected, because OpenBabel uses Bult2002_
mpa as its embedded EEM parameters. Very surprising
was the behavior of OpenBabel on the extended set. The
coverage was 100 %, but the quality criteria were markedly
lower (e.g., R2 about 0.82). The reason for this is that
OpenBabel replaces the EEM parameters for atom types
which are not provided in Bult2002_mpa with the EEM
parameters for some other atom types. Unfortunately,
this approach is not very reliable, i.e., the quality criteria
for molecules which are in the extended test set but
are not in the test set are very low (R2 = 0.66). Additionally,
this approach is relatively tricky. The user does not
know whether the correct or the estimated EEM parameters
are used and, therefore, whether the resulting EEM
charges will be of a good quality.
The EEM charges produced by Balloon were compared
with the QM charges calculated by the B3LYP/cc-pVTZ/
MPA approach. The coverage was close to 100 %, but the
correlation was also low (R2 < 0.8). On the other hand,
the Balloon developers mentioned that the EEM charges
provided by Balloon do not correspond directly to some
particular QM charges, and they should only be close to
B3LYP/cc-pVTZ/MPA charges.
Table 6  Summary information about coverage and quality of all tested EEM parameters (see below for meaning of colours)
Relevant QM charges
EEM parameter
set name
Coverage comparison
Quality
comparison
QM theory
level + basis set
Charge
calc.
scheme
Coverage [%] R2
Test setDrugBank ChEMBL PubChem ZINC
HF/STO-3G MPA
Baek1991 58.1 42.3 40.5 40.1 0.8981
Svob2007_cbeg2 55.0 49.5 47.3 51.9 0.9758
Svob2007_chal2 71.7 75.2 77.2 80.2 0.9668
Svob2007_chm2 72.2 75.2 77.3 80.2 0.9623
Svob2007_cmet2 55.5 49.5 47.3 51.9 0.9676
HF/6-31G* MK Jir2008_hf 70.8 74.7 76.5 79.8 0.6872
B3LYP/6-31G*
MPA Bult2002_mpa 55.4 49.4 48.2 49.6 0.9658
NPA
Bult2002_npa 55.4 49.4 48.2 49.6 0.8131
Ouy2009 49.0 41.1 39.1 40.0 0.9655
Ouy2009_elem 50.0 41.2 39.1 40.0 0.9633
Hirshfeld Bult2002_hir 55.4 49.4 48.2 49.6 0.9061
MK
Bult2002_mk 55.4 49.4 48.2 49.6 0.7844
Jir2008_mk 70.8 74.7 76.5 79.8 0.7022
CHELPG Bult2002_che 55.4 49.4 48.2 49.6 0.7803
AIM Bult2004_aim 55.4 49.4 48.2 49.6 0.9739
HF/6-311G
MPA Cheminf_hf_mpa
94.6 95.7 96.9 100.0
0.9606
NPA Cheminf_hf_npa 0.9713
AIM Cheminf_hf_aim 0.9791
B3LYP/6-311G
MPA Cheminf_b3lyp_mpa 0.9552
NPA Cheminf_b3lyp_npa 0.9695
AIM Cheminf_b3lyp_aim 0.9800
Coverage > 90% > 80% > 70% > 60% < 60%
R2
> 0.95 > 0.9 > 0.85 > 0.8 < 0.8
Page 8 of 10Geidl et al. J Cheminform (2015) 7:59
All the quality criteria and coverages for EEM parameter
sets embedded in OpenBabel and Balloon are summarized
in (Additional file 8: Table S5).
Coverage comparison and quality comparison combined
To date, there have been no EEM parameter sets available
which would provide both high coverage and high-quality
EEM charges (see Table  6). On the other hand, the
EEM parameter sets calculated in this paper solve this
problem, because they exhibit coverage close to 100  %
and excellent quality criteria. Therefore, they can be used
for chemoinformatics applications.
Software solution (step 4)
For the actual applicability of EEM in chemoinformatics,
the user doesn’t just need EEM parameter sets that
are high quality and cover almost all molecules. They also
need a software package that embeds these EEM parameter
sets and calculates EEM charges based on them. We
provide the user with two such solutions. First, we provide
our EEM parameter sets in a format that can be
directly used in EEM SOLVER (Additional file  2: EEM
parameter sets). Second, we provide an OpenBabel patch
which allows our EEM parameter sets to be used directly
in OpenBabel (Additional file  9: OpenBabel patch). All
the information including documentation is also accessible
on the web: http://ncbr.muni.cz/eem_parameters.
The parameters are also accessible via ACC web application
[77].
Conclusion
We provide here six EEM parameter sets which enable
the user to calculate EEM charges with quality comparable
to frequently used QM charges computed by wellknown
charge calculation schemes (i.e., MPA, NPA and
AIM) and based on a robust QM approach (HF/6-311G,
B3LYP/6-311G). The training set for EEM parameterization
contained more than 4000 molecules from the DTP
NCI drug database, and all six calculated EEM parameter
sets exhibited a very good quality on this training set
(R2 > 0.9).
The coverage of these computed EEM parameter
sets was then compared with the coverages of 15 EEM
parameter sets published in the past. This comparison
was done on four key databases of drug-like molecules—
DrugBank, ChEMBL, Pubchem and ZINC. The comparison
showed that our EEM parameter sets enable us to
calculate EEM charges for almost all molecules in these
databases.
We then compared the quality of computed and
published EEM parameter sets on two test data sets
composed of approved drugs from DrugBank. This comparison
also included EEM parameter sets embedded in
the software tools OpenBabel and Balloon. The comparison
showed that our EEM parameter sets are among the
best performing EEM parameter sets published to date
(R2 > 0.93).
To summarize, charge calculation methodology suitable
for chemoinformatics applications like virtual
screening or QSAR should be fast, conformationallydependent
and accurate. EEM fulfils all these requirements.
However, EEM parameter sets that would exhibit
high coverage of drug-like molecule databases and provide
high quality charges have not been available to
date. The EEM parameters calculated in this paper solve
this problem. They exhibit coverage close to 100 % and
excellent quality criteria, therefore they are applicable in
chemoinformatics.
Last but not least, we provide a software solution for
the easy computing of EEM charges based on these EEM
parameter sets—input files for EEM SOLVER and OpenBabel
patch.
Authors’contributions
The concept of the study originated from JK and was reviewed and extended
by RA, while the design was put together by RSV and SG and reviewed by JK
and RA. TB and SG prepared the input data (molecules and published EEM
parameters). TB, SG and VH performed QM charge calculation. TR updated
and extended NEEMP software. TB and TR performed EEM parameterizations,
EEM charges validation and calculation of statistical data. VH prepared an
automatic workflow, which is able to reproduce all steps preformed in the
article. AK reviewed, corrected and improved this workflow. TR wrote the
OpenBabel patch. The data were analyzed and interpreted by RSV, SG and JK.
The manuscript was written by RSV in cooperation with JK, and reviewed by
all authors. All authors read and approved the final manuscript.
Additional files
Additional file 1: Table S1. List of training set molecules, including their
NSC numbers and summary formulas.
Additional file 2: EEM parameters. Values of EEM parameter sets for
these six charge calculation approaches (i.e. B3LYP/6-311G/MPA,B3LYP/6-
311G/NPA, B3LYP/6-311G/AIM, HF/6-311G/MPA, HF/6-311G/NPA, and
HF/6-311G/AIM). These EEM parameter sets are in a format which can be
used as an input file for EEM SOLVER.
Additional file 3: Table S2a. A list of molecules from the test set including
their DrugBank IDs and summary formulas.
Additional file 4: Table S2b. A list of molecules from the extended test
set including their DrugBank IDs and summary formulas.
Additional file 5: Table S3. RMSD and values of all tested EEM parameter
sets on the test set.
Additional file 6: Charge details. Values of partial atomic charges (represented
as tables and as graphs) for all tested EEM parameter sets on the
testset.
Additional file 7: Table S4. R2
, RMSD, and coverage values of all
tested EEM parameter sets on the extended test set.
Additional file 8: Table S5. RMSD and values for OpenBabel and Balloon
on the test set and extended test set.
Additional file 9: OpenBabel patch. A patch for OpenBabel, which enables
it to use the EEM parameter sets calculated in this paper.
Page 9 of 10Geidl et al. J Cheminform (2015) 7:59
Author details
1
 National Centre for Biomolecular Research, Faculty of Science and CEITEC,
Central European Institute of Technology, Masaryk University Brno, Kamenice
5, 625 00 Brno, Czech Republic. 2
 Faculty of Informatics, Masaryk University
Brno, Botanická 68a, 602 00 Brno, Czech Republic. 3
 Institute of Computer
Science, Masaryk University Brno, Botanická 68a, 602 00 Brno, Czech Republic.
4
 Skaggs School of Pharmacy and Pharmaceutical Sciences, University of California,
9500 Gilman Drive, San Diego, MC 0657, USA.
Acknowledgements
This work was supported by the Grant Agency of the Czech Republic
[13-25401S]; the European Community’s Seventh Framework Programme
(CZ.1.05/1.1.00/02.0068) from the European Regional Development Fund;
and by the European Social Fund and the state budget of the Czech Republic
(CZ.1.07/2.3.00/20.0042, CZ.1.07/2.3.00/30.0009).
This work was also supported in part by NIH Grants R01 GM071872,
U01 GM094612, and U54 GM094618 to R.A.. The access to MetaCentrum
supercomputing facilities provided under research intent MSM6383917201 is
greatly appreciated.
Authors’information
Stanislav Geidl, Tomáš Bouchal and Tomáš Raček wish it to be known that, in
their opinion, the first three authors should be regarded as joint First Authors.
Radka Svobodová Vařeková and Jaroslav Koča wish it to be known that, in
their opinion, they should be regarded as joint Corresponding Authors.
Competing interests
The authors declare that they have no competing interests.
Received: 7 July 2015 Accepted: 16 November 2015
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How does the methodology of 3D Structure
preparation inﬂuence the quality of pKa
prediction?
94
How Does the Methodology of 3D Structure Preparation Inﬂuence
the Quality of pKa Prediction?
Stanislav Geidl,†
Radka Svobodová Vařeková,*,†
Veronika Bendová,†
Lukáš Petrusek,†
Crina-Maria Ionescu,†
Zdeněk Jurka,†
Ruben Abagyan,‡
and Jaroslav Koča*,†
†
National Centre for Biomolecular Research, Faculty of Science, and CEITEC - Central European Institute of Technology, Masaryk
University Brno, Kamenice 5, 625 00 Brno-Bohunice, Czech Republic
‡
Skaggs School of Pharmacy and Pharmaceutical Sciences, University of California, 9500 Gilman Drive, MC 0657, San Diego,
California 92161, United States
*S Supporting Information
ABSTRACT: The acid dissociation constant is an important
molecular property, and it can be successfully predicted by
Quantitative Structure−Property Relationship (QSPR) models,
even for in silico designed molecules. We analyzed how the
methodology of in silico 3D structure preparation inﬂuences
the quality of QSPR models. Speciﬁcally, we evaluated and
compared QSPR models based on six diﬀerent 3D structure
sources (DTP NCI, Pubchem, Balloon, Frog2, OpenBabel,
and RDKit) combined with four diﬀerent types of
optimization. These analyses were performed for three classes
of molecules (phenols, carboxylic acids, anilines), and the QSPR model descriptors were quantum mechanical (QM) and
empirical partial atomic charges. Speciﬁcally, we developed 516 QSPR models and afterward systematically analyzed the inﬂuence
of the 3D structure source and other factors on their quality. Our results conﬁrmed that QSPR models based on partial atomic
charges are able to predict pKa with high accuracy. We also conﬁrmed that ab initio and semiempirical QM charges provide very
accurate QSPR models and using empirical charges based on electronegativity equalization is also acceptable, as well as
advantageous, because their calculation is very fast. On the other hand, Gasteiger-Marsili empirical charges are not applicable for
pKa prediction. We later found that QSPR models for some classes of molecules (carboxylic acids) are less accurate. In this
context, we compared the inﬂuence of diﬀerent 3D structure sources. We found that an appropriate selection of 3D structure
source and optimization method is essential for the successful QSPR modeling of pKa. Speciﬁcally, the 3D structures from the
DTP NCI and Pubchem databases performed the best, as they provided very accurate QSPR models for all the tested molecular
classes and charge calculation approaches, and they do not require optimization. Also, Frog2 performed very well. Other 3D
structure sources can also be used but are not so robust, and an unfortunate combination of molecular class and charge
calculation approach can produce weak QSPR models. Additionally, these 3D structures generally need optimization in order to
produce good quality QSPR models.
■ INTRODUCTION
The acid dissociation constant, Ka, and its logarithmic version,
pKa, are important molecular properties and their values are of
interest in chemical, biological, environmental, and pharmaceutical
research.1−3
Experimental pKa values are usually
unavailable for all compounds from the chemical catalogues.
Therefore, they cannot be used for example in virtual screening,
which requires predictions of physicochemical properties for
large sets of in silico designed molecules. Several pKa prediction
methodologies have been published to date. They are
summarized in review articles,4−7
but reliable and accurate
pKa prediction is still a challenge and a topic of intensive
research.8−10
A popular and frequently used pKa prediction approach is
based on the QSPR (Quantitative Structure−Property
Relationship) methodology.11−13
Various types of input values
(so-called descriptors) can be used for the calculation of pKa via
QSPR models. Partial atomic charges are deﬁnitely relevant
descriptors for pKa calculations12,14−17
and can be calculated
directly from the 3D structure of the molecule. The partial
atomic charges cannot be determined experimentally or derived
from the results of quantum mechanics (QM) in a
straightforward manner. For this reason, many diﬀerent
methods have been developed for their calculation. The most
common method for charge calculation is using a quantum
mechanical approach (a combination of a theory level and a
basis set) and the subsequent application of a charge calculation
scheme. For example, for pKa prediction via QSPR models, ab
initio QM charges calculated via HF or B3LYP theory levels and
STO-3G or 6-31G* basis sets proved suitable. The most
appropriate charge calculation schemes for these purposes seem
Received: December 21, 2014
Published: May 26, 2015
Article
pubs.acs.org/jcim
© 2015 American Chemical Society 1088 DOI: 10.1021/ci500758w
J. Chem. Inf. Model. 2015, 55, 1088−1097
to be MPA (Mulliken population analysis), NPA (natural
population analysis), and AIM (atoms in molecules).8,15,17
Semiempirical QM charges have also been employed in QSPR
models for pKa prediction (e.g., AM1, PM3, or PM6 theory
levels in combination with MPA).11,14,17−19
A major drawback
of the QM charges is the computational eﬀort required for the
calculation of the wave function. For this reason, the
computational complexity of obtaining QM charges is at least
θ(B4
), where B is the number of basis functions. Therefore, the
calculation of ab initio QM charges is very time consuming,
while the calculation of semiempirical QM charges is also
relatively slow. The Electronegativity Equalization Method20
is
an empirical charge calculation approach that presents a faster
alternative to the QM methods. EEM is able to provide partial
atomic charges with comparable accuracy to QM charges, and it
is markedly less time consuming than QM charge calculation
approaches. EEM is even able to mimic a certain QM charge
calculation approach (i.e., the combination of a theory level, a
basis set, and a charge calculation scheme) because it includes
parameters based on the QM charges. EEM charges also proved
applicable for pKa prediction via QSPR.8
Last but not least, pKa
predicting QSPR models based on conformationally independent
empirical charges (so-called topological charges, e.g.,
Gasteiger-Marsili charges) have also been evaluated.13,19
Therefore, in principle, we can prepare a straightforward and
time-eﬃcient workﬂow for obtaining pKa values for molecules
designed in silico: Use the 3D structures of molecules prepared
in silico, calculate partial atomic charges for them, employ the
charges as descriptors in QSPR models, and predict the
required pKa values. Such a workﬂow can be applied in virtual
screening. We can also design similar workﬂows for other
biologically important properties such as logP, biodegradability,
dioxin-like activity, etc.
Nonetheless, before implementing the workﬂow, we need to
answer a key question: How does the methodology of in silico
3D structure preparation inﬂuence the quality of QSPR models
for pKa prediction? In previous works focused on pKa
prediction via QSPR,8,17,19,21,22
3D structures were mainly
obtained from the DTP NCI database23
(which uses CORINA
to generate the 3D structures) or directly designed by
CORINA.24
But there are other tools and databases that are
often used as sources of 3D structures, for example, the
database Pubchem25
(employing the software Omega26
) or
software tools such as Balloon,27
Frog2,28
OpenBabel,29
or
RDKit.30
These tools create 3D structures via a data or
knowledge-based approach (CORINA, OpenBabel, Omega),
distance geometry approach (Balloon, RDKit), or other
approaches (Frog2). Speciﬁcally, Frog2 ﬁrst generates a graph
of rings and acyclic elements and afterward performs a Monte
Carlo search. Can we use any of these 3D structure sources for
the QSPR modeling of pKa? Or is it that only some
methodologies for 3D structure preparation provide acceptable
QSPR models? In parallel, another important question is
whether the 3D structures need to be optimized before they
can be used in QSPR models or not. Some articles on this topic
use optimization,14,15,22,31,32
while some provide accurate
models even without it.8,11,17
In this study, we addressed the above questions. Speciﬁcally,
we evaluated and compared QSPR models based on six
diﬀerent 3D structure sources combined with four diﬀerent
types of optimization. The 3D structure sources were the
databases DTP NCI and Pubchem and the software tools
Balloon, Frog2, OpenBabel, and RDKit. The optimization was
either skipped or done by molecular mechanics (MMFF94 for
all 3D structure sources, MM-UFF for RDKit) or quantum
mechanics (B3LYP/6-31G*). These analyses were performed
for three classes of molecules (phenols, carboxylic acids,
anilines). We mainly focused on ab initio QM charges, which
provide the most accurate pKa predicting QSPR models, and on
empirical EEM charges, which are a faster and comparably
accurate alternative to ab initio QM charges. Speciﬁcally, we
used four types of QM charges (HF/STO-3G/MPA, B3LYP/6-
31G*/MPA, B3LYP/6-31G*/NPA, and B3LYP/6-31G*/
AIM) and four corresponding types of EEM charges. To
create a complete overview, we provide also QSPR models
based on semiempirical charges (i.e., PM6 charges) and on
conformationally independent empirical charges (i.e., Gasteiger-Marsili
charges). Thus, we developed 516 QSPR models
and afterward systematically analyzed the inﬂuence of the 3D
structure source and other factors on their quality.
■ METHODS
Data Sets. Our training data set is composed of three
classes of molecules (i.e., phenols, anilines, and carboxylic
acids), which represent common classes of organic molecules.
These types of molecules are also frequently used for the
evaluation of QSPR models.8,11,14−17,19,22,31
The data set
contains 190 molecules: 60 phenols, 82 carboxylic acids, and
48 anilines. Additionally, we used a test data set containing 53
phenols that were not included in the training data set. The list
of molecules including their ﬁgures, NCS numbers, and CAS
numbers can be found in the Supporting Information (Table
S1).
pKa Values. The experimental pKa values were taken from
the Physprop database.33
The pKa values of all molecules can be
found in the Supporting Information (Table S1).
2D Structure of Molecules. Information about the 2D
structure of individual molecules was obtained from the DTP
NCI database. The 2D structures were described in SMILES
format. The SMILES of all molecules are given in the
Supporting Information.
Sources of 3D Structure of Molecules. For each
molecule, the 3D structure was obtained from six diﬀerent
sources. Speciﬁcally, the structure was obtained from two
databases (Pubchem, DTP NCI) and in parallel generated by
four diﬀerent freely available software tools (Balloon, Frog2,
OpenBabel, and RDKit). These sources were selected because
they appear to be the most popular, and they also represent the
main approaches for 3D structure preparation.
Optimization. Each molecule was thus associated with six
diﬀerent 3D structures, obtained by the six approaches
described above. Afterward, each 3D structure was processed
in two diﬀerent ways. Speciﬁcally, two types of optimization
were performed: optimization via quantum mechanics (QM)
and optimization via molecular mechanics (MM). The QM
optimization was performed by Gaussian 0934
using B3LYP/6-
31G*, and the MM optimization was done with RDKit using
MMFF94. These approaches were selected because they are
common and frequently used representatives of QM and MM
optimization. Additionally, we also performed an optimization
via the MM force ﬁeld UFF (Universal Force Field) for
structures prepared with RDKit. The reason is that the RDKit
developers recommend applying this particular force ﬁeld for
the structures generated with RDKit.
3D Structures in Training and Test Data Sets. Each
molecule in our training data set was associated with 19
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diﬀerent structures because there were six sources of 3D
structure and three types of optimization for each (no
optimization, QM optimization, and MM optimization) plus
an additional UFF optimization for RDKit. The test data set
contained only phenol molecules. Each molecule was associated
with two diﬀerent structures because we selected two sources of
3D structure (i.e., DTP NCI and RDKit) and one type of
optimization for each (no optimization).
In our QSPR models, we used neutral forms of all the
molecules and also dissociated forms of phenols and carboxylic
acids and associated forms of anilines (Figure 1). The
dissociated forms of molecules were created by removing the
hydrogen atom of the dissociating group. The associated forms
of anilines were created by adding one hydrogen atom to the
amino group. The adding of the atom was done via an in-house
script that applies the Bioshell library,35,36
and a detailed
description of the procedure is given in the Supporting
Information.
In this way, our training data set contained 19 (6 × 3 + 1)
diﬀerent structures for each molecule, and 7220 (= 19 × 190 ×
2) structures in total. In parallel, our test data set included two
diﬀerent structures for each molecule, therefore, 212 (= 2 × 53
× 2) structures in total.
QM Charges. For each of the 7220 structures from the
training set, we calculated ab initio QM partial atomic charges
via four QM charge calculation approaches (i.e., HF/STO-3G/
MPA, B3LYP/6-31G*/MPA, B3LYP/6-31G*/NPA, and
B3LYP/6-31G*/AIM) and semiempirical QM charges using
PM6. These approaches were selected because they represent
the main types of charge calculation approaches that have been
reported as successful for pKa prediction via QSPR.8,15,17
The
second reason for selection of the ab initio QM approaches was
that corresponding EEM parameters are available for them. For
each of the 212 structures from the test set, we calculated ab
initio QM charges via B3LYP/6-31G*/NPA. This charge
calculation approach was selected based on the results obtained
on the training set. All the ab initio and semiempirical QM
charges were calculated by Gaussian 09.34
EEM Charges. For each of the 7220 structures in our data
set, the EEM charges were calculated by the program EEM
SOLVER37
using the four EEM parameter sets described in
Table 1. EEM charges calculated using these parameter sets
should mimic QM charges calculated by the relevant QM
charge calculation approaches.
Gasteiger-Marsili Charges. We calculated also empirical
Gasteiger-Marsili charges for all the molecules from the training
set, including their dissociated or associated forms, therefore for
380 (= 2 × 190) molecules. Gasteiger-Marsili charges are based
on 2D structure; therefore, they do not depend on the source
of 3D structure and on the optimization. All these charges were
calculated by RDKit.30
Descriptors and QSPR Models. The descriptors used for
QSPR modeling were partial atomic charges from atoms that
are close to the dissociation or association site. We employed
both charges from neutral and from dissociated (or associated)
molecules. The linear model is justiﬁed by the linear
relationship between pKa and the electrostatic potential at the
protonation site combined with the linear dependence of the
potential on the surrounding charges. The distance dependences
are absorbed by the p coeﬃcients derived from the
experimental data.
Thus, the QSPR model employed in this study for phenol
molecules has the following equation:
= · + · + · + ·
+ · +
K p q p q p q p q
p q p
p
C
a p(H) H p(O) O p(C1) C1 p(OD) OD
p( 1D) C1D p (1)
where qH is the atomic charge of the hydrogen atom from the
phenolic OH group of the neutral molecule; qO is the charge on
the oxygen atom from the phenolic OH group of the neutral
molecule; qC1 is the charge on the carbon atom binding the
phenolic OH group of the neutral molecule; qOD is the charge
on the phenoxide O−
from the dissociated molecule; and qC1D
is the charge on the carbon atom binding this oxygen in the
dissociated molecule (Figure 1a). The symbols pp(H), pp(O),
Figure 1. (a) Dissociation of phenols. (b) Dissociation of carboxylic acids. (c) Association of anilines. The particular atomic charges used in our
QSPR models are marked by their denotations.
Table 1. Summary Information about EEM Parameter Sets
Used in This Study
parameter set name QM charge calculation approach published by
Svob2007_chal2 HF/STO-3G/MPA Svobodova et al.38
Chaves2006 B3LYP/6-31G*/MPA Chaves et al.39
Bult2002_npa B3LYP/6-31G*/NPA Bultinck et al.40
Bult2004_aim B3LYP/6-31G*/AIM Bultinck et al.41
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pp(C1), pp(OD), pp(C1D), and pp are parameters of the QSPR
model.
The QSPR model employed in this study for carboxylic acids
uses the following equation:
= · + · + · + ·
+ · + · + · +
K p q p q p q p q
p q p q p q p
p a c(H) H c(O1) O1 c(O2) O2 c(C1) C1
c(O1D) O1D c(O2D) O2D c(C1D) C1D c
(2)
where qH and qO1 are the atomic charge of the hydrogen and
oxygen atoms from the OH group of the neutral molecule,
respectively; qO2 is the charge on the oxygen atom from the
carbonyl group of the neutral molecule; qC1 is the charge on the
carbon atom binding in the COOH group of the neutral
molecule; qO1D is the charge on the O−
oxygen from the
dissociated molecule; qO2D is the charge on the oxygen atom
from the carbonyl group of the dissociated molecule; and qC1D
is the charge on the carbon atom in the carboxyl group of the
dissociated molecule (Figure 1b). Because the structures of
dissociated carboxylic acid molecules were created by removing
the H atom with no further correction of the structure, the
values qO1D, qO2D, and qC1D describe charge distribution
immediately after removing of this hydrogen atom. The
symbols pc(H), pc(O1), pc(O2), pc(C1), pc(O1D), pc(O2D), pc(C1D), and
pc are parameters of the QSPR model.
The QSPR model employed in this study for anilines is based
on the following equation:
= · + · + · + ·
+ · + · +
K p q p q p q p q
p q p q p
p a a(H) H a(N) N a(C1) C1 a(HA) HA
a(NA) NA a(C1A) C1A a (3)
where qH is the average of charges located on both hydrogens in
the amino group of the neutral molecule; qN is the charge of the
nitrogen from the amino group of the neutral molecule; qC1 is
the charge on the carbon atom binding the amino group in the
neutral molecule; qHA is the average of charges located on the
three hydrogens in the amino group of the associated molecule;
qNA is the charge on the nitrogen from the amino group of the
associated molecule and qC1A is the charge on the carbon atom
binding the amino group in the associated molecule (Figure
1c). The symbols pa(H), pa(N), pa(C1), pa(HA), pa(NA), pa(C1A), and pa
are parameters of the QSPR model.
The QSPR model eqs 1 and 2 were published by Svobodová
and Geidl et al.,8
and they proved useful for pKa prediction
based on QM and EEM charges. Equation 3 was inspired by
these two equations.
In this way, we created one QSPR model for each of our
three classes of molecules (phenols, carboxylic acids, anilines),
19 types of structures (six sources of 3D structures × three
methods of optimization + RDKit with MM-UFF), and nine
types of charges (ﬁve types of QM charges and four types of
EEM charges). For each class of molecules, we additionally
created one QSPR model based on Gasteiger-Marsili charges.
Thus, we created 516 (= 3 × 19 × 9 + 3) QSPR models.
Speciﬁcally, 228 QSPR models based on ab initio QM charges
(denoted QM QSPR models), 57 models based on semiempirical
charges (denoted semiempirical QM QSPR models),
228 models based on EEM charges (denoted EEM QSPR
models), and three models based on Gasteiger-Marsili charges
(GM QSPR models). The parametrization of the QSPR models
was done by multiple linear regression (MLR) using the
software QSPR Designer.42
Cross-Validation. The robustness of all 516 QSPR models
was tested by cross-validation. The k-fold cross-validation
procedure was used,43,44
where k = 5. Speciﬁcally, for each
QSPR model, its training data set was divided into ﬁve parts
(each contained 20% of the molecules). This division was done
randomly and included stratiﬁcation by pKa value. Afterward,
ﬁve cross-validation steps were performed. In the ﬁrst step, the
ﬁrst part was selected as a test set, and the remaining four parts
were taken together as the training set. The test and training
sets for the other cross-validation steps were prepared in a
similar manner.
Table 2. R2
Describing the Correlation between Calculated and Experimental pKa for QM QSPR Models
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■ RESULTS AND DISCUSSION
The quality of the QSPR models, i.e., the correlation between
experimental pKa and the pKa calculated by each model, was
evaluated using the squared Pearson correlation coeﬃcient
(R2
), root-mean-square error (RMSE), and average absolute
pKa error (Δ), while the statistical criteria were the standard
deviation of the estimation (s) and Fisher’s statistics of the
regression (F).
Tables 2 and 11 and Table S2 in Supporting Information
summarize the squared Pearson correlation coeﬃcients for all
QM QSPR models, EEM QSPR models, and semiempirical
QM QSPR models, respectively. Table S3 in the Supporting
Information contains all the quality criteria (R2
, RMSE, Δ) and
statistical criteria (s and F) for all the QSPR models analyzed.
All these models are statistically signiﬁcant at p = 0.01. Because
our data sets contained 60 phenols, 82 carboxylic acids, and 48
anilines, the appropriate F values to consider were those for 60
samples, 80 samples, and 50 samples, respectively. The QSPR
models for phenols, carboxylic acids, and anilines contained 5,
7, and 6 descriptors, respectively. Thus, the QSPR models for
phenols are statistically signiﬁcant (at p = 0.01) when F > 3.34,
the QSPR models for carboxylic acids when F > 2.87, and the
QSPR models for anilines when F > 3.19.
The parameters of the QSPR models are summarized in the
Supporting Information (Table S4).
Quality of QM QSPR Models: General Summary. The
results summarized in Tables 2 and 3 conﬁrmed that the QSPR
models based on QM charges are able to predict pKa with high
accuracy. Speciﬁcally, about 24% of the models have excellent
quality (R2
≥ 0.95), close to 40% have very good quality (R2
≥
0.9), 30% have lower quality but are still applicable (R2
≥ 0.8),
and only about 6% have low quality (R2
< 0.8).
Predictivity of QM QSPR Models. In general, the
predictivity of QSPR models calculating pKa based on charges
was shown in the literature11−13
. Additionally, high quality of
QM QSPR models based on the same charge descriptors as our
models was shown by Svobodová Vařeková et al.17
To conﬁrm
the predictivity, we did a cross-validation for all our QSPR
models. Cross-validation results for selected QSPR models are
in Table 4 (i.e., based on B3LYP/6-31G*/NPA charges and
nonoptimized OpenBabel 3D structures, which show average
quality in comparison with other QM QSPR models). All the
cross-validation results can be found in the Supporting
Information (Table S5). These results showed that the values
of R2
are similar for the test set, the training set, and the
complete set; therefore, the models are stable.
For further conﬁrmation of our QSPR models predictivity,
we tested selected QSPR models on an independent test data
set prepared only for testing purposes, with a size comparable
to that of the training data set. Speciﬁcally, the test data set
includes 53 phenol molecules, and we used it for testing two
selected QM QSPR models for phenols, namely, one of the
best quality models (B3LYP/6-31G*/NPA charges and
nonoptimized 3D structures from NCI) and one of the worst
quality models (HF/STO-3G/MPA charges and nonoptimized
3D structures from RDKit). The quality criteria for the test set
and the training set are in Table 5. These results demonstrate
that the QSPR models perform comparably for the test set and
the training set.
Inﬂuence of ab initio QM Charge Calculation
Approach. The results (Tables 2 and 6) show that all four
of the ab initio QM charge calculation approaches tested here
provide a comparable quality of pKa prediction. These results
therefore conﬁrmed that all the selected charge calculation
approaches are suitable for the QSPR prediction of pKa.
Additionally, all the charge calculation approaches are
applicable for all three classes of molecules. Speciﬁcally, for
each class of molecules, any ab initio QM charge calculation
Table 3. Number and Percentage of QM QSPR Models with
R2
Higher than a Deﬁned Limit
R2
≥0.95 (0.95, 0.9> (0.9, 0.8> <0.8
number of models 55 90 69 14
percentage of models 24% 39% 30% 6%
Table 4. R2
Values for Cross-Validation of Selected QM
QSPR Models
QSPR model description: phenols. Charges: B3LYP/6-31G*/NPA. 3D
structure: OpenBabel with no optimization.
cross-validation step 1 2 3 4 5
R2
for training set 0.955 0.956 0.964 0.959 0.957
R2
for test set 0.956 0.967 0.939 0.952 0.957
R2
for complete set 0.957
QSPR model description: carboxylic acids. Charges: B3LYP/6-31G*/NPA. 3D
structure: OpenBabel with no optimization.
cross-validation step 1 2 3 4 5
R2
for training set 0.818 0.825 0.889 0.863 0.852
R2
for test set 0.928 0.785 0.609 0.850 0.816
R2
for complete set 0.845
QSPR model description: anilines. Charges: B3LYP/6-31G*/NPA. 3D
structure: OpenBabel with no optimization.
cross-validation step 1 2 3 4 5
R2
for training set 0.966 0.965 0.973 0.963 0.970
R2
for test set 0.937 0.925 0.910 0.988 0.932
R2
for complete set 0.966
Table 5. Quality Criteria for Testing of Selected QM QSPR
Models
QSPR model description: phenols. Charges: B3LYP/6-31G*/NPA. 3D
structure: NCI with no optimization.
quality criteria R2
RMSE Δ
training set 0.960 0.415 0.333
test set 0.948 0.532 0.437
QSPR model description: phenols. Charges: HF/STO-3G/MPA. 3D
structure: RDKit with no optimization.
quality criteria R2
RMSE Δ
training set 0.782 1.067 0.896
test set 0.715 0.421 0.328
Table 6. Number and Percentage of QM QSPR Models with
R2
Higher than a Deﬁned Limit for Individual Charge
Calculation Approaches
R2
QM charge calculation approach ≥0.9 (0.9, 0.8> <0.8 Rchrg
2
*
HF/STO-3G/MPA 67% 30% 4% 0.914
B3LYP/6-31G*/MPA 60% 25% 16% 0.888
B3LYP/6-31G*/NPA 68% 28% 4% 0.906
B3LYP/6-31G*/AIM 60% 39% 2% 0.898
*
Rchrg
2
is the average value of R2
for all QSPR models, which use
charges calculated by a given QM charge calculation approach.
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approach provides good quality QSPR models (R2
close to 0.9)
at least for some sources of 3D structures. An interesting
ﬁnding is that the suitability of a certain charge calculation
approach strongly depends on the class of molecules. For
example, B3LYP/6-31G*/MPA charges work very well for
anilines and markedly poorer for carboxylic acids. The next
interesting ﬁnding is that the charge calculation approach HF/
STO-3G/MPA, which uses the smallest basis set (STO-3G)
and the simplest population analysis (MPA), performs very
well.
Inﬂuence of the Class of Molecules. It is shown in
Tables 2 and 7 that some classes of molecules are more easily
handled by QSPR modeling, while some are more challenging.
Speciﬁcally, QSPR models work very well for anilines and
phenols. These models have high R2
for all charge calculation
approaches and for most of the 3D structure sources. On the
other hand, QSPR models provide markedly weaker pKa
predictions for carboxylic acids. Namely, only a few 3D
structure sources are applicable for QSPR modeling for
carboxylic acids. One reason for the lower quality of QSPR
models for the carboxylic acids is that the carboxyl group bound
some arbitrary chemical scaﬀold. In contrast, the −OH group of
phenols and −NH2 group of anilines have the same conserved
neighborhoodthe phenolic ring. In parallel, the phenolic ring
also allows higher delocalization of electrons, which is better
suited for the calculation of QM descriptors than the more rigid
electron localization in carboxylic acids.
Inﬂuence of 3D Structure Preparation Methodology
on Quality of the QM QSPR Model. Tables 2, 8, and 9 show
that an appropriate selection of 3D structure source and
optimization method is essential for the QSPR modeling of
pKa.
These results imply that the most appropriate 3D structures
were obtained from the DTP NCI and Pubchem databases (i.e.,
structures prepared with the tools CORINA and Omega,
respectively). The QSPR models based on these structures are
very accurate, and these 3D structures do not require
optimization. A great feature of these 3D structures was that
they performed very well for all the tested QM charge
calculation approaches and classes of molecules. An interesting
ﬁnding is that the QM optimization of such 3D structures can
markedly decrease the accuracy of the models.
Frog2 also seems to be applicable. QSPR models based on
3D structures from Frog2 are accurate even when the structures
were not optimized, and the MM optimization of these
structures mainly improves the models. They can be
successfully used for all the classes of molecules and all the
QM charge calculation approaches tested here.
RDKit, OpenBabel, and Balloon are slightly troublesome
sources of 3D structures. They can provide accurate QSPR
models (R2
> 0.9) for some classes of molecules. In this case,
the MM optimization of 3D structures improves the models.
But when we process other classes of molecules (carboxylic
acids), the QSPR models are weak (R2
∼ 0.85) for most of the
charge calculation approaches. For certain charge calculation
approaches, the QSPR models can even be unsatisfactory (R2
<
0.7). An interesting fact is that the structures generated by
RDKit with no optimization provide the worst-performing
QSPR models of the whole study. The explanation is clear.
These 3D structures are just the raw results of RDKit, and as
mentioned in its manual, they need to be optimized by RDKit’s
internal force ﬁeld UFF. This case study shows how weak
QSPR models can be when based on problematic structures.
Particular geometrical properties, which are incorrectly
modeled in certain 3D structure preparation methodologies
and which cause worse performance of QSPR models, are
summarized in the Supporting Information.
Table 7. Number and Percentage of QM QSPR Models with
R2
Higher than a Deﬁned Limit for Individual Classes of
Molecules
R2
class of molecules ≥0.9 (0.9, 0.8> <0.8 Rmol
2
*
phenols 32% 49% 17% 0.927
carboxylic acids 0% 29% 57% 0.849
anilines 41% 41% 17% 0.929
*
Rmol
2
is the average value of R2
for all QSPR models, which were built
for a given class of molecules.
Table 8. Percentage of QM QSPR Models with Given R2
for
Individual 3D Structure Sourcesa
R2
source optimization ≥0.95
(0.95,
0.9>
(0.9,
0.85>
(0.85,
0.8> <0.8
Balloon none 0% 42% 8% 42% 8%
MM 8% 33% 33% 17% 8%
QM 8% 42% 25% 17% 8%
Frog2 none 0% 50% 50% 0% 0%
MM 33% 58% 0% 8% 0%
QM 33% 42% 25% 0% 0%
NCI none 50% 42% 8% 0% 0%
MM 50% 42% 8% 0% 0%
QM 8% 58% 33% 0% 0%
OpenBabel none 58% 8% 17% 8% 8%
MM 58% 8% 17% 8% 8%
QM 33% 17% 17% 25% 8%
PubChem none 8% 75% 17% 0% 0%
MM 25% 50% 25% 0% 0%
QM 8% 50% 33% 8% 0%
RDKit none 0% 0% 33% 25% 42%
UFF 42% 25% 17% 17% 0%
MM 25% 50% 8% 0% 17%
QM 8% 58% 17% 8% 8%
a
Optimization procedures that produce the best QSPR models for
each source of 3D structures are marked in bold font.
Table 9. Sensitivity of 3D Structure Source to Change of
Molecular Classa
percent of insensitive QSPR models
Optimization source
Balloon Frog2 NCI OpenBabel PubChem RDKit
none 50% 100% 25% 0% 75% 75%
MM 50% 25% 75% 0% 50% 0%
QM 25% 50% 75% 0% 75% 25%
UFF − − − − − 25%
total 42% 58% 58% 0% 67% 31%
a
Sensitivity of a particular QSPR model to a change of molecular class
was analyzed via a statistical test, which compared the correlation
coeﬃcient of three independent populations (i.e., molecular classes),
employed Fisher’s z-transformation, and used the signiﬁcance level
0.05. Detailed information about this statistical test is in the
Supporting Information.
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Semiempirical QM QSPR Models: Quality, Predictivity,
and Inﬂuences. The results summarized in Table 10 and
Table 2 of the Supporting Information show that the quality of
these models is comparable to the quality of QSPR models
based on ab initio QM charges, just slightly lower for phenols
and anilines and slightly better for carboxylic acids. The crossvalidation
results (Supporting Information, Table S5) conﬁrmed
the robustness of the semiempirical QM QSPR models.
When we evaluated the inﬂuence of the class of molecules and
the 3D structure preparation methodology, we saw the same
trends as for the ab initio QM QSPR models (Table 10 and
Table S2, Supporting Information).
Quality of EEM QSPR models: General Summary. The
results summarized in Tables 11 and 12 show that the quality of
EEM QSPR models is in general lower than for QM QSPR
models but still suﬃcient. Speciﬁcally, about 36% of the models
are very good quality (R2
≥ 0.9), most of the models are
acceptable quality (R2
between 0.9 and 0.8), and only about 2%
are low quality (R2
< 0.8). On the other hand, the number of
weak models is lower than for QM QSPR models, and there are
no models with (R2
< 0.75).
Predictivity of EEM QSPR Models. A high quality of EEM
QSPR models based on the same charge descriptors as our
models was shown in ref 8. We tested the predictivity of our
EEM QSPR models the same way as we did for the QM QSPR
modelsby cross-validation and by testing on a larger set of
independent molecules. These results are summarized in the
Supporting Information (Table S5 and S6, respectively) and
conﬁrm that our EEM QSPR models are robust and can handle
molecules outside the training set.
Inﬂuence of EEM Parameter Set. The results in Table 11
and Table S7 of the Supporting Information show that all four
EEM parameter sets tested here are applicable for pKa
prediction. The quality of the QSPR models obtained by all
the EEM parameter sets is comparable. The parameter set
Chaves2006 (mimicking B3LYP/6-31G*/MPA charges) performed
slightly better than the remaining sets.
Inﬂuence of the Class of Molecules. As with QM
charges, some classes of molecules are more challenging for the
QSPR modeling of pKa (i.e., carboxylic acids), see Table 11 and
Table S8, Supporting Information. Nonetheless, the diﬀerences
between the quality of EEM QSPR models for various classes of
molecules are markedly smaller than for the QM QSPR models.
Inﬂuence of 3D Structure Preparation Methodology
on Quality of the EEM QSPR Model. Table 8 and Table S6
of the Supporting Information show that EEM QSPR models
are markedly less sensitive to the selection of 3D structure
source and optimization method.
As with QM QSPR models, 3D structures from DTP NCI
and Pubchem can be successfully used for all of the tested
molecular classes and all EEM parameter sets, even without
optimization (i.e., more than 90% of EEM QSPR models based
on nonoptimized NCI 3D structures and all EEM QSPR
models based on nonoptimized Pubchem 3D structures have R2
> 0.85).
Frog2 also preforms very well. More than 80% of EEM
QSPR models based on nonoptimized Frog2 3D structures
have R2
> 0.85. Additionally, these models seem to be
Table 10. Number and Percentage of Semiempirical QM
QSPR Models with R2
Higher than a Deﬁned Limit
R2
≥0.95 (0.95, 0.9> (0.9, 0.8> <0.8
number of models 15 25 17 0
percentage of models 26% 44% 30% 0%
Table 11. R2
Describing the Correlation between Calculated and Experimental pKa for EEM QSPR Models
Table 12. Number and Percentage of EEM QSPR Models
with R2
Higher than a Deﬁned Limit
R2
≥0.95 (0.95, 0.9> (0.9, 0.8> <0.8
number of models 82 106 38 2
percentage of models 36% 46% 17% 1%
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1094
applicable for all molecular classes and all EEM parameter sets
tested here.
For the other four tools, the accuracy of EEM QSPR models
depends on the molecular class and EEM parameter set, as
certain combinations of these can produce lower accuracy
QSPR models.
For all six sources of 3D structures tested in this study, QM
optimization produces an improvement in the EEM QSPR
models in most cases.
Quality of GM QSPR Models. Gasteiger-Marsili charges do
not depend on the 3D structure of molecules; therefore, we
prepared only one QSPR model for each class of molecules.
The R2
values of these models are given in Table 13, and
further quality criteria are available in Table S3 of the
Supporting Information. These results show that GM QSPR
models are markedly less accurate than EEM QSPR models,
and therefore, GM charges are not applicable for pKa
prediction. These conclusions are in agreement with results
published in the past.15
■ CONCLUSION
Our results conﬁrmed that QSPR models based on QM and
EEM partial atomic charges are able to predict pKa with high
accuracy. Speciﬁcally, more than 60% of ab initio and
semiempirical QM QSPR models and nearly 40% of EEM
QSPR models are very good quality (R2
≥ 0.9). We also
conﬁrmed that ab initio and semiempirical QM charges provide
very accurate QSPR models and using EEM charges is also
acceptable and moreover advantageous because their calculation
is very fast. Afterward, we evaluated the predictivity of
our QM, semiempirical QM, and EEM QSPR models via crossvalidation
and via testing on an independent test data set. This
way, we veriﬁed that all the types of ab initio and semiempirical
and EEM charges used are applicable for QSPR modeling. On
the contrary, QSPR models based on empirical GasteigerMarsili
charges showed low quality, suggesting that GasteigerMarsili
charges are not suitable descriptors for the prediction of
pKa.
We then focused on the inﬂuence of molecular class. We
found that some molecular classes are more amenable to QSPR
modeling (phenols and anilines), while some are more
challenging (carboxylic acids).
In this context, we compared the inﬂuence of the diﬀerent
3D structure sources. We found that the selection of 3D
structure source and optimization method can strongly
inﬂuence the quality of QSPR models for pKa prediction.
The 3D structures from the DTP NCI and Pubchem databases,
i.e., structures generated by CORINA and Omega, respectively,
exhibited the best performance. These 3D structures provided
very accurate QSPR models for all the tested molecular classes
and charge calculation approaches, and they do not require
optimization. Frog2 also performed very well for all of the
tested molecular classes and charge calculation approaches.
Other 3D structure sources can also be used, but they are not
so robust. An unlucky combination of molecular class and
charge calculation approach can lead to weak QSPR models.
Additionally, these structures generally need to be optimized in
order to produce high quality QSPR models. Speciﬁcally, the
best approach is to apply MM optimization to 3D structures
used with QM QSPR models and QM optimization to 3D
structures used with EEM QSPR models.
The main point of this article is that a workﬂow for the fast
and accurate prediction of pKa or other important properties
for in silico designed molecules can be as follows: Preparation of
3D structures by CORINA or Omega (with no further
optimization), calculation of EEM charges for these structures,
and then the EEM QSPR calculation of pKa.
■ ASSOCIATED CONTENT
*S Supporting Information
List of molecules, including their ﬁgures, NCS numbers, CAS
numbers, SMILES and experimental pKa values (Table S1); ﬁle
with the SMILES of the molecules; description of the
procedure, which was used for the creation of dissociated and
associated forms of molecules; table summarizing R2
values of
the correlation between calculated and experimental pKa for
semiempirical QM QSPR models (Table S2); quality criteria
and statistical criteria of all the QSPR models (Table S3);
parameters of all the QSPR models (Table S4); cross-validation
results for all QSPR models (Table S5); quality criteria for
testing of selected EEM QSPR models (Table S6); number and
percentage of EEM QSPR models with R2
higher than a deﬁned
limit for individual charge calculation approaches (Table S7);
number and percentage of EEM QSPR models with R2
higher
than a deﬁned limit for individual classes of molecules (Table
S8); percentage of QM QSPR models with given R2
for
individual 3D structure sources (Table S9); information about
geometrical properties, which are incorrectly modeled in certain
3D structure preparation methodologies; information about the
statistical test used for analysis of a 3D structure source
sensitivity to a change of molecular class; and information
about QSPR models limitations. The Supporting Information is
available free of charge on the ACS Publications website at
DOI: 10.1021/ci500758w.
■ AUTHOR INFORMATION
Corresponding Authors
*Phone: +420 549 494 860. E-mail: svobodova@chemi.muni.cz
(R.S.V.).
*Phone: +420 549 494 947. E-mail: jkoca@chemi.muni.cz
(J.K.).
Author Contributions
The authors wish it to be known that, in their opinion, S. Geidl
and R. Svobodová Vařeková should be regarded as joint ﬁrst
authors.
Notes
The authors declare no competing ﬁnancial interest.
■ ACKNOWLEDGMENTS
This work was supported by the Ministry of Education, Youth
and Sports of the Czech Republic (LH13055); the European
Community’s Seventh Framework Programme (CZ.1.05/
1.1.00/02.0068) from the European Regional Development
Fund and the Capacities speciﬁc program (286154); and the
European Social Fund and the state budget of the Czech
Republic (CZ.1.07/2.3.00/20.0042, CZ.1.07/2.3.00/30.0009).
This work was also supported in part by NIH Grants R01
GM071872, U01 GM094612, and U54 GM094618 to R.A. The
Table 13. R2
Describing Correlation between Calculated and
Experimental pKa for GM QSPR Models
class of molecules phenols carboxylic acids anilines
R2
0.747 0.737 0.870
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1095
access to MetaCentrum supercomputing facilities provided
under the research intent MSM6383917201 is greatly
appreciated.
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AtomicChargeCalculator: interactive
web-based calculation of atomic charges in
large biomolecular complexes and drug-like
molecules
105
Ionescu et al. J Cheminform (2015) 7:50
DOI 10.1186/s13321-015-0099-x
SOFTWARE
AtomicChargeCalculator: interactive
web‑based calculation of atomic charges
in large biomolecular complexes and drug‑like
molecules
Crina‑Maria Ionescu1†
, David Sehnal1,2,3†
, Francesco L. Falginella1
, Purbaj Pant2
, Lukáš Pravda1,2
,
Tomáš Bouchal1,2
, Radka Svobodová Vařeková1,2
, Stanislav Geidl1,2
and Jaroslav Koča1,2*
Abstract 
Background:  Partial atomic charges are a well-established concept, useful in understanding and modeling the
chemical behavior of molecules, from simple compounds, to large biomolecular complexes with many reactive sites.
Results:  This paper introduces AtomicChargeCalculator (ACC), a web-based application for the calculation and
analysis of atomic charges which respond to changes in molecular conformation and chemical environment. ACC
relies on an empirical method to rapidly compute atomic charges with accuracy comparable to quantum mechani‑
cal approaches. Due to its efficient implementation, ACC can handle any type of molecular system, regardless of size
and chemical complexity, from drug-like molecules to biomacromolecular complexes with hundreds of thousands
of atoms. ACC writes out atomic charges into common molecular structure files, and offers interactive facilities for
statistical analysis and comparison of the results, in both tabular and graphical form.
Conclusions:  Due to high customizability and speed, easy streamlining and the unified platform for calculation and
analysis, ACC caters to all fields of life sciences, from drug design to nanocarriers. ACC is freely available via the Internet
at http://ncbr.muni.cz/ACC.
Keywords:  Conformationally dependent atomic charges, Biomacromolecules , Drug-like molecules, Paracetamol,
Benzoic acids, Protegrin, Proteasome, Allostery, Chemical reactivity
© 2015 Ionescu et al. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License
(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium,
provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license,
and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/
publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Background
Partial atomic charges are real numbers meant to quantify
the uneven distribution of electron density in the
molecule, and have been used for decades in theoretical
and applied chemistry in order to understand the chemical
behavior of molecules. Atomic charges are extensively
used in many molecular modeling and chemoinformatics
applications. With respect to biomacromolecules,
charges can elucidate electrostatic effects critical for long
range molecular recognition phenomena, protein folding,
dynamics and allostery, directed adduction of substrates
and egression of products in enzymes, ligand binding
and complex formation for proteins and nucleic acids,
etc. [1–3]. With respect to drug-like molecules, atomic
charges provide information related to reactivity and can
be used in the prediction of various pharmacological,
toxicological or environmental properties [4, 5].
Although, in principle, it is possible to estimate atomic
charges based on experimental measurements (e.g.,
[6, 7]), such calculations are impractical. Most commonly,
atomic charges are estimated based on theoretical
approaches. Quantum mechanical (QM) approaches
first solve the Schrödinger equation [8] and calculate the
electron density using a combination of theory level and
basis set. They then partition the obtained molecular
Open Access
*Correspondence: jaroslav.koca@ceitec.muni.cz
†
Crina-Maria Ionescu and David Sehnal contributed equally
2
National Centre for Biomolecular Research, Faculty of Science, Masaryk
University, Kotlářská 2, 611 37 Brno, Czech Republic
Full list of author information is available at the end of the article
Page 2 of 13Ionescu et al. J Cheminform (2015) 7:50
electron density (or a density-derived quantity) into
atomic contributions (atomic partial charges) according
to various population analyses [9–19]. Empirical
approaches to atomic charge calculation (e.g., [20–27])
have been proposed as resource-efficient alternatives to
QM approaches, as they do not require the demanding
step of solving the Schrödinger equation. In particular,
approaches based on the equalization of molecular
electronegativity [22, 23, 28–35] are of interest because
they are sensitive to both the chemical environment and
molecular conformation.
Due to the essential role of atomic charges, many modeling
tools currently include atomic charge calculation
capabilities (e.g., [36–50]). However, in the case of druglike
molecules, only a few tools can provide QM quality
charges which respond to changes in conformation or
chemical environment without needing to first obtain
the QM electron density or electrostatic potential [47,
48, 50]. Moreover, these tools are not sufficiently general,
resource-efficient or interactive. In the case of biomacromolecules,
no freely available software tool can readily
provide atomic charges of QM quality, despite repeated
reports that such quality is necessary [51–54]. We have
accepted these challenges and set out to provide a robust
and accessible software solution for atomic charge calculation
for molecules of all nature and size.
This contribution presents the AtomicChargeCalculator
(ACC), a free web application for the calculation and
analysis of atomic charges which respond to changes in
molecular conformation and chemical environment. The
calculation is based on the electronegativity equalization
method (EEM [22]), a powerful empirical approach
which can provide atomic charges similar to those generated
by various QM approaches, but using much
lower computational resources. Along with the classical
EEM algorithm, ACC implements two additional
EEM approximations with increased efficiency, specifically
tailored for studying very large molecular systems.
A single calculation may take from less than a second
(small molecules), to a few minutes (large biomacromolecular
complexes). ACC outputs the most common
molecular structure formats containing atomic charges.
Additionally, it provides facilities for statistical analysis
and comparison of the results, in tabular and graphical
form. ACC also includes interactive 3D visualization of
the molecules based on atomic charges. A command line
version is also available.
Implementation
The challenge was to provide a robust web based software
solution for atomic charge calculation for molecules of all
nature and size. Therefore, we first focused on identifying
and optimizing a suitable algorithm for atomic charge
calculation, and then on implementing the optimal workflow
for setting up an ACC calculation and interpreting
the results.
The application was constructed using the client-server
architecture (Fig.  1): the charge computation is carried
out on the server and implemented in the C# programming
language. The JavaScript Object Notation (JSON) is
used to transfer data to the client that provides the user
interface (UI) implemented using HTML5 and JavaScript.
Additionally, the UI uses the WebGL technology to
provide a custom built 3D visualization of the computed
charges.
Computational details
The Electronegativity Equalization Method (EEM) is the
general approach followed by ACC to calculate atomic
charges. EEM-based methods have been successfully
applied to zeolites and metal-organic frameworks, small
organic molecules, polypeptides and proteins [55–61].
EEM is an empirical approach which relies on parameters
usually fitted to data from reference QM calculations.
The values of atomic charges computed using
EEM support chemical reasoning, and generally correlate
well with values from reference QM calculations.
The accuracy of each set of EEM parameters is
documented in the respective literature. On the other
hand, classical EEM approaches incorrectly predict
superlinear scaling of the polarizability with increasing
molecular size, making the models developed on
small molecules difficult to transfer to extended systems
like biomacromolecules [62, 63]. This artifact can be
Fig. 1  ACC application architecture. The client allows the user to
setup the calculation via the user interface. The settings are sent to
the web server in the form of a configuration file. The charge compu‑
tation takes place on the web server. The results are sent back to the
client for visualization and download by the user
Page 3 of 13Ionescu et al. J Cheminform (2015) 7:50
tempered by applying charge conservation constraints
to small molecular units. Such extensions to EEM have
been proposed [24, 64].
Computationally efficient implementations of EEMbased
methods are integrated in tools specialized for
reactive molecular dynamics simulations [65] and for
generating conformers of drug-like molecules [50,
66]. However, ACC is the first to implement EEM in
a manner which is not only computationally efficient,
but also independent of the subsequent intended
application, and specifically designed to allow users
with little background in computational sciences to
run charge calculations and interactively analyze the
results.
ACC can solve the EEM matrix equation (see the
Computational details section of the Additional file 1)
if the following input is provided: the 3D structure of
the molecular system, the total molecular charge, and a
set of EEM parameters. Solving the EEM matrix equation
requires solving a dense system of equations. The
computational complexity of this procedure is O(N3).
The space complexity, which refers to the memory
required to store the EEM matrix, is O(N2), where N
is the number of atoms. For very large molecules with
tens of thousands of atoms, the EEM approach is too
demanding on conventional desktop hardware. We
thus propose two new approaches for solving the EEM
matrix, namely EEM Cutoff and EEM Cover. These
approaches work by splitting the EEM matrix into multiple
smaller matrices.
Within the EEM Cutoff approach, for each atom in
the molecule, ACC generates a fragment made up of
all atoms within a cutoff radius R of the original atom.
Thus, for a molecule containing N atoms, the EEM Cutoff
approach solves N smaller EEM matrices, for a set of
N overlapping fragments of the original molecule. EEM
Cutoff effectively reduces the time complexity of the
calculation to O(R6N + R2NlogN), and the space complexity
to O(R4N + NlogN). A detailed description of
the EEM Cutoff approach is given in the Computational
details section of the Additional file 1.
To further enhance the run-time and memory efficiency
of calculations in ACC, we propose EEM Cover,
an approach for tackling molecules with hundreds of
thousands of atoms. EEM Cover also splits the EEM
matrix into smaller matrices, but it generates fragments
only for a subset of atoms in the molecule. While the
asymptotic complexity remains the same, the number
of EEM matrices that need to be solved is reduced by at
least 50 % compared to EEM Cutoff, while maintaining
high accuracy. A detailed description of the EEM Cover
approach is given in the Computational details section of
the Additional file 1.
Workflow
The ACC workflow is organized into four phases, namely:
upload, setup, calculation and results. Each phase is characterized
by a set of operations as follows:
1.	 Upload molecules Multiple molecules can be uploaded
in the most common file formats (PDB, PDBx/mmCIF,
PQR, MOL, MOL2, SDF, or .zip with multiple files of
a suitable format). The molecular structures should be
complete and properly protonated. There is no limitation
regarding the size, number or nature of the chemical
entities in a single structure file (proteins, nucleic
acids, ligands, water, etc.), as all these are loaded and
identified as a single molecule within ACC. The total
size of the upload is limited to 50 MB.
2.	 Setup Upon uploading the molecule(s), ACC parses
the molecular structure to identify the number and
types of atoms in the system, as well as the interatomic
distances. Based on this information, ACC
tries to prefill the submission form with suitable
default settings (see the Default settings section of the
Additional file 1). These settings can be adjusted by
the user before the calculation is started. Each distinct
setup (Fig. 2) will result in a certain number of ACC
Fig. 2  Setup of jobs in AtomicChargeCalculator. The setup of an
ACC calculation takes place in three steps, each step referring to one
of three aspects: the molecule and its total charge, the set of EEM
parameters to be used in the EEM equation, and the computation
options. These three aspects uniquely define an ACC job. A single
setup may lead to running several ACC jobs. Based on the informa‑
tion in the uploaded structure files, ACC suggests a default setup,
which can be adjusted by the user prior to starting the calculation.
Explanations are available in the interactive guides, tool tips and Wiki
pages
Page 4 of 13Ionescu et al. J Cheminform (2015) 7:50
jobs, each defined by the molecule, total molecular
charge, the set of EEM parameters, and the computation
options. For the command line version of ACC,
the setup workflow is identical to the steps described
below, and is scripted into a configuration file.
2.1.	 Total molecular charge The total molecular
charge quantifies the amount of charge that will
be distributed across the molecule during the
EEM calculation. By default, ACC assumes that
all uploaded molecules are neutral. The user
must provide the correct total molecular charge
for each non-neutral molecule uploaded.
2.2.	 Set of EEM parameters EEM employs special
parameters for each type of atom (H, C, N, O,
halogens, metals, etc., depending on the target
molecules). EEM parameters are generally developed
based on reference QM calculations. The
applicability domain of a given EEM parameter
set is generally limited to the target molecules,
and closely related to the applicability domain of
the particular QM approach used as reference.
Performance is further influenced by the procedure
used when fitting the EEM parameters to
the reference data. Many EEM parameter sets
have been published in literature, and are available
in ACC as built-in sets [28, 34, 67–70] with
full information regarding the parameter development
procedure (atom types covered, target
molecules, QM reference data, literature reference).
By default, ACC tries to select one of
these sets based on the atom types present in the
uploaded molecules. The user can select a different
set of EEM parameters by choosing from the
list of available built-in sets, or even uploading
customized sets in an XML template. Multiple
sets of EEM parameters can be tested in a single
ACC run.
2.3 	 Computation options ACC may compute atomic
charges based on one of the three available EEM
approaches implemented, namely Full EEM,
EEM Cutoff, and EEM Cover. Further options
refer to the precision (64 or 32-bit representation
of numbers), cutoff radius parameter, and
including water molecules into the calculation.
By default, ACC picks computation options
most suitable to the size of the uploaded molecules.
These computation options can be
adjusted by the user. Up to 10 computation
options can be tested in a single ACC run.
3.	 Calculation Once the setup phase is complete, the
calculation is launched. A single ACC run may consist
of multiple atomic charge calculation jobs. Each
job is uniquely defined by the molecule, total molecular
charge, set of EEM parameters, and computation
options, and produces one set of atomic charges.
Each job may use a different amount of time and
memory resources, depending on the size of the molecule
and the complexity of the computation.
4.	 Results The ACC results are organized into hierarchical
reports which are stored on the server for download
or inspection for up to a month, at a unique URL
visible only to the user. The command line version of
ACC produces the same overall and single molecule
reports described below, but does not facilitate interactive
3D visualization.
4.1.	The overall report contains information and
downloadable content (molecular structure
files containing atomic charges, statistics of the
results, information about all jobs) for all molecules.
Single molecule reports are also accessible
from here.
4.2.	The single molecule report (Fig. 3), which can be
downloaded or examined directly in the browser,
consists of a few sections:
4.2.1.	 Summary report containing general information
about the input molecule (molecular formula, total
charge), calculation setup, a list of all sets of charges
produced during the calculation, information about
all ACC jobs (duration, warnings, errors) for that mol-
ecule.
4.2.2.	 Interactive list of values for all sets of charges produced
by all ACC jobs for that molecule. The atomic
charges and residue charges are given.
4.2.3.	 Statistics within each set of charges, in both tabular
and graphical form. The statistics are available for
both atomic and residue charges, and are computed
for relevant properties such as chemical element,
type of residue, etc. The statistical indicators are the
minimum value, maximum value, standard deviation,
average, median, etc.
4.2.4.	 Pairwise comparison statistics between sets of
charges resulted from different ACC jobs, or uploaded
by the user. A graphical representation for each comparison
is also provided. The comparison is available
for atomic and residue charges. The comparison indicators
computed are the squared Pearson’s correlation
coefficient, Spearman’s rank correlation coefficient,
RMSD, sum of absolute differences.
4.2.5.	 Interactive 3D visualization of molecules. The
3D model can be built based on atomic positions,
Page 5 of 13Ionescu et al. J Cheminform (2015) 7:50
and colored based on atomic charges, or built based
on residue positions, and colored based on residue
charges. The coloring scheme can also use differences
in charges resulted from distinct ACC jobs, or
uploaded by the user.
The applicability of ACC is limited by three main
aspects: related to the concept of atomic partial charges
and its definitions, related to the concept of EEM and
its parameters, and related to the 3D structure of the
molecule and its total charge. These aspects are discussed
in detail in the Limitations section of the Additional
file 1.
Full documentation explaining the methodology, functionality
and interface, along with interesting examples
are provided on the web page. Embedded interactive
guides assist first-timers and beginners in setting up their
calculations and interpreting the results. A command line
version of the application is available as an executable for
users who wish to streamline more complex calculations.
Results and discussion
Implementation benchmark
We have evaluated the accuracy and computational efficiency
of the EEM Cutoff and EEM Cover approaches
in a benchmark. The evaluation was performed against
reference calculations which solved the full EEM
matrix, with a few exceptions. We give here a brief
overview (Fig. 4), whereas the full details can be found
in the Benchmark section of the Additional file 1. Both
EEM Cutoff and EEM Cover are sufficiently accurate,
but EEM Cutoff is slightly more accurate. Using a cutoff
radius of 8 Å may lead to deviations of up to 0.015e,
but on average less than 0.008e. Using a cutoff radius of
12 Å may lead to deviations of up to 0.008e, but on average
less than 0.004e. The approaches are time efficient
compared to Full EEM only when the molecule contains
at least 10,000 atoms, but they are always more memory
efficient.
Below we provide a few brief examples of uses for
AtomicChargeCalculator in the form of case studies.
These case studies are focused on a direct interpretation
of the ACC results, and show how important hints about
the reactivity of a molecule can be obtained in just a few
seconds.
Case study I: atomic charges and chemical reactivity
in small drug‑like molecules
N-acetyl-p-aminophenol, commonly known as paracetamol,
is a widely used analgesic and antipyretic. Its mechanism
of action is believed to be the inhibition of the
protein cyclooxygenase 2, regulating the production of
Fig. 3  Single molecule report provided by AtomicChargeCalculator. It can be downloaded or inspected in the browser, and consists of several
sections: summary information about the molecule, interactive list of values for all sets of charges, statistics within each set of charges, pairwise
comparison statistics between sets of charges, and interactive 3D visualization of molecules
Page 6 of 13Ionescu et al. J Cheminform (2015) 7:50
pro-inflammatory compounds [71]. The metabolic breakdown
of paracetamol has been the subject of intense
study, since it holds the key to both its therapeutic action
and toxicity.
We calculated atomic charges in paracetamol using
ACC. The geometry of the paracetamol molecule corresponded
to the ideal coordinates [wwPDB CCD: TYL].
The default ACC settings were used. The computation
took less than 1s, and the complete results are available
on the ACC web page at http://ncbr.muni.cz/ACC/
CaseStudy/Paracetamol.
A quick analysis reveals that the phenolic H (position
HO4 in Fig. 5) is the most acidic proton (highest positive
charge) in the molecule, suggesting a faster and easier
dissociation of this O–H bond. Indeed up to 90 % of metabolic
degradation happens at position HO4  (glucuronidation,
sulphonation) [72]. Additionally, up to 15 % of
metabolic degradation involves oxidation at the phenolic
(HO4) and amidic positions (HN) [72], the two most positive
H in the paracetamol molecule. While paracetamol
is a very small molecule with few polar sites, the same
principle can be applied in reasoning out highly reactive
sites in more complex molecules.
Having found out that the most probable dissociation
site on the paracetamol molecule is the phenolic H, we
were able then to calculate the acid dissociation constant
pKa, a property which significantly affects the ability of
the drug to cross cellular membranes and thus exert its
therapeutic effect. For this purpose we used Quantitative
Structure-Property Relationship (QSPR) modeling,
as atomic partial charges have been shown to be successful
QSPR descriptors in pKa prediction [58, 73, 74],
and QSPR models are available in literature for this
purpose. Because the dissociating group on paracetamol
is phenolic, we chose a QSPR model specifically
developed for the prediction of pKa in phenols [58], and
which employed descriptors based on the EEM charges
we computed in our interpretation of local reactivity in
paracetamol. The necessary descriptors consisted of the
partial charges on the phenolic oxygen (qO4) and hydrogen
(qHO4), and on the carbon atom binding the phenolic
group (qC4). The equation and parameters of the QSPR
model are given in Fig. 5.
We thus computed a pKa value for paracetamol of 9.36,
which is close to the experimental value of 9.38 [75]. The
computed pKa  suggests that paracetamol is completely
unionized at stomach pH, and only 1.1 % ionized at physiological
pH, therefore highly efficient at crossing cellular
membranes both via oral and intravenous delivery.
While the above described approach was able to provide
useful information for paracetamol, it is important
to keep in mind that there are limitations to the accuracy
of EEM charges. We illustrate such limitations on a series
of benzoic acid derivatives. For this purpose, we downloaded
the structures of 45 molecules representing benzoic
acid derivatives from the NCI Open Database [76].
The data set contained benzoic acids with a wide range
of donating and accepting substituents on the phenyl
ring in o-, m- and p- positions (Fig. 6a; Additional file 1:
Table S3). We chose only compounds for which pKa values
were available in Physprop [77]. Furthermore, we did
a
b
c
Fig. 4  Benchmark of the EEM Cover approach. Full details can be
found in the Benchmark section of the Additional file 1. a EEM Cover
is sufficiently accurate, and its accuracy increases with the value of
the cutoff radius. The root mean square deviation (RMSD) is calcu‑
lated by comparison against the reference calculation which solves
the entire EEM matrix (Full EEM), using 64-bit precision numbers. Due
to the limitation on computational resources, for some molecules the
reference calculation was *EEM Cutoff, with a cutoff radius of 17 Å. b
EEM Cover is significantly faster than Full EEM only for molecules with
over 10,000 atoms. c EEM Cover is always more memory efficient than
Full EEM
Page 7 of 13Ionescu et al. J Cheminform (2015) 7:50
not include compounds with halogens because the EEM
parameter set used in this particular case study cannot
treat halogens.
We first wanted to know if and how the effect of different
substituents in different positions on the phenyl
ring is visible on the charge of the atoms of the carboxyl
group. For this purpose, we used Gaussian [36] to
compute reference QM atomic charges from a natural
population analysis on the electron density obtained at
the B3LYP/6-31G* level of theory. Despite the different
nature and position of the substituents, the spread
of reference QM charges for the atoms in the carboxyl
group is very narrow (Fig.  6b). Specifically, the QM values
for O1 are within 0.06e, the values for O2 within
0.01e, and the values for H within 0.01e. On the other
hand, the EEM parameter set employed here is expected
to reproduce the reference QM values within 0.09e [34].
Based on the documented accuracy, we do not expect
EEM charges to reflect suitable changes based on the
nature or position of the substituents. We used ACC to
compute EEM charges for the benzoic acid derivatives,
in the same manner as for paracetamol. The computation
took less than 2s, and the complete results (structures,
QM charges, EEM charges) are available on the
ACC web page at http://ncbr.muni.cz/ACC/CaseStudy/
BenzoicAcids.
Indeed, we found that EEM charges could not accurately
reflect the QM spread for the charges on the carboxyl
atoms (Fig. 6b). We then wondered if this accuracy,
though unable to reflect suitable changes depending on
the nature or position of the substituents, was sufficient
to build acceptable QSPR models for pKa prediction. No
suitable QSPR models are available for benzoic acids,
but such models for aliphatic carboxylic acids have been
reported [58, 78]. The descriptors used by these QSPR
models consist of charges on the atoms of the carboxylic
group in both the neutral (qH, qO1, qO2, qC1) and dissociated
forms (qO1D, qO2D, qC1D). We thus built QSPR models
for benzoic acids based on these descriptors (Fig. 6c).
We obtained the structures of the dissociated acids by
removing the carboxylic H atoms. We computed EEM
charges for the dissociated molecules using the same
ACC setup, but setting the total charge for each molecule
at −1. We then built QSPR models using multilinear
regression. We performed a 5-fold cross-validation of
the QSPR models, whereby, in each round, 35 randomly
chosen molecules were used to train the model, and the
remaining 10 molecules were used to validate the model.
The QSPR model parameters and full details of the crossvalidation
procedure are given in the Additional file  1:
Table S4. The models showed adequate predictive capability
(Fig. 6c; Additional file 1: Table S4). On average, the
mean absolute error during validation was 0.27 pKa units
compared to experiment, suggesting that EEM charges
can be used to predict dissociation constants for benzoic
acids, despite their inability to reflect local changes
caused by different substituents.
Case study II: atomic charges and activity of antimicrobial
peptides
Protegrins are a family of antimicrobial peptides active
against a wide range of pathogens [79]. Protegrin-1 (PG1,
Fig. 7) has been intensely studied for its potential in treating
infections caused by antibiotic resistant bacteria
[80–82]. PG1 shows activity against several pathogens,
but also toxicity against the host. Useful mutations are
those which maintain the antimicrobial activity, and at
the same time reduce toxicity [83].
Fig. 5  Atomic charges reveal reactive sites involved in the metabolic degradation of paracetamol. In the picture on the right, the atoms are colored
according to their charge. The majority of metabolic degradation of paracetamol (glucuronidation, sulphonation, oxygenation) involves the phe‑
nolic (HO4) and amidic (HN) positions, the two most acidic protons in the paracetamol molecule (labels marked in bold) [72]. The relatively higher
positive charge on these H atoms marks more active bonds compared to the rest of the molecule. In the equation of the QSPR model, qHO4 is the
charge on the phenolic H, qO4 is the charge on the phenolic O, qC4 is the charge on the C binding the phenolic OH, and pHO4, pO4, pC4 and p are the
parameters of the QSPR model, taken from the QSPR model 3d EEM Ouy2009_elem [58]
Page 8 of 13Ionescu et al. J Cheminform (2015) 7:50
We calculated atomic charges in PG1 using ACC. The
geometry of the PG1 molecule corresponded to a low
energy NMR model [PDB: 1PG1] [84]. The system contained
all H atoms expected at pH 6.5, as they were listed
in the NMR model. The total molecular charge was +7,
owing to the many ARG residues. The EEM parameter
set used was EX-NPA_6-31Gd_gas [70], but it was necessary
to add to this set EEM parameters for deuterium (D),
because this element was present in the input file. The
EEM parameters for D were identical to the parameters
for H. The rest of the ACC default settings were kept. The
computation took less than 1s, and the complete results
are available on the ACC web page at http://ncbr.muni.
cz/ACC/CaseStudy/Protegrin.
The calculation produced one set of atomic charges.
PG1 contains 18 residues, and rather than analyzing
atomic charges, we analyzed the residue charges,
which are also reported by ACC (Fig.  7b). PG1 is special
because of its high positive charge. It contains 6
ARG residues. However, not all have the same charge. In
particular, ARG at positions 4 and 9 have the least positive
charge (around +0.5e), whereas the rest have much
higher positive charge (over +0.8e). Keeping in mind
that these charges are likely affected by the polarizability
a
c b
Fig. 6  Limitations of EEM charges illustrated on a series of substituted benzoic acid derivatives. a Denotation of relevant atomic charges in the neu‑
tral and dissociated molecules. b The reference QM charges have a narrow spread despite the different position and wide range of electron donat‑
ing or withdrawing effects of the subsituents. EEM charges are not accurate enough to reflect the small changes induced by different substituents.
c The QSPR descriptors are EEM charges of the atoms of the carboxylic group in both the neutral (qH, qO1, qO2, qC1) and dissociated forms (qO1D, qO2D
, qC1D). The symbols pH, pO1, pO2, pC1, pO1D, pO2D, pC1D, and p are parameters of the QSPR model. The graph displays the correlation between experi‑
mental pKa values, and the values predicted by one of the QSPR models developed in this study. EEM charge descriptors are sufficiently accurate for
the prediction of dissociation constants of benzoic acid derivatives
Page 9 of 13Ionescu et al. J Cheminform (2015) 7:50
exaggeration artifact of EEM described in the Computational
details section, the results suggest that mutations
of ARG into a neutral residue at positions 4 or 9 would
have a lower effect than mutations at positions 1, 10, 11
or 18.
A literature search reveals that many mutants and
derivatives of PG1 have been studied [83, 85–87]. In particular,
Ostberg and Kastnessis [83] have logged the antimicrobial
and toxic activity of sixty-two PG1 mutants
and PG1-analogue peptides. Out of these, there are two
single point mutants where one ARG was mutated into
a neutral residue. These mutants are PC3 (R4G) and PC5
(R10P). The study found that, indeed, the mutation of
ARG 4 in PC3 alters the antimicrobial activity against C.
albicans significantly less than the mutation of ARG 10
of PC5 (Fig. 7c). Such biologically relevant insight can be
gained by analyzing the residue charges on a single structure
of PG1.
Case study III: atomic charges and allostery of large
biomacromolecular complexes
The 26S proteasome is a large biomacromolecular complex
which facilitates the targeted degradation of intracellular
proteins, and thus plays an essential role in keeping
protein homeostasis [88]. It consists of a core particle,
made up of alpha rings and beta rings, controlled by
regulatory particles, which are made up of a number of
proteins (Fig. 8a). The proteasome is an intricate molecular
machine which requires complex regulation to unfold
and deubiquitylate the substrate, and push it through the
catalytic machinery located in the beta rings [89]. Necessarily,
the proteasome undergoes large conformational
changes during its operation. However, due to its size,
such changes are very difficult to study. Recent work in
the field of cryo-electron microscopy [90] has led to the
discovery of intermediate conformers during the initial
binding of ubiquitylated substrates. While the conformational
changes in the regulatory particle are easily distinguishable
(average backbone atom RMSD 10.4 Å), the
changes in the core particle are very subtle (average backbone
atom RMSD 1.5 Å), due to the fact that all studied
conformers refer to the initial phase of substrate binding.
Using ACC, we calculated atomic charges in these
intermediate conformers of the 26S proteasome [PDB:
4CR2, 4CR3, 4CR4]. The default ACC settings were used.
The computation took 130s, and the complete results are
available on the ACC web page at http://ncbr.muni.cz/
ACC/CaseStudy/Proteasome.
The calculation produced one set of atomic charges for
each conformer of the 26S proteasome. Since the proteasome
is very large, we analyzed the residue charges,
which are also reported by ACC, and subsequently the
charges for the various subunits that make up the proteasome
(details regarding the charge analysis on subunits
can be found in the section Case study III of the
Additional file 1). The first observation was that, during
a b
c
Fig. 7  Residue charges in protegrin-1 (PG1) indicate relevant
mutation sites. a Cartoon representation of the structure of PG1. b
Schematic representation of the PG1 residues and their charge. Each
residue position is represented by a sphere, the coordinates of which
correspond to the average coordinates of all atoms in the residue.
The color of the sphere is given by the residue charge, and the size of
the sphere is proportional to the absolute charge. Cystein bridges are
also displayed. The ARG residues at positions 4 and 9 are signifi‑
cantly less positive than the rest of the ARG residues, indicating that
mutations at these positions may be less effective. c Antimicrobial
activity (against five pathogens) and toxicity (cytotoxicity, hemolysis)
of PG1 and two single mutants, namely PC3 (R4G) and PC5 (R10P)
[83]. Although both mutants have increased activity, the mutation
of ARG 4 in PC3 alters the antimicrobial activity against C. albicans
significantly less than the mutation of ARG 10 in PC5, as predicted by
the residue charges
Page 10 of 13Ionescu et al. J Cheminform (2015) 7:50
the conformational changes from state 1, to state 2, and
then to state 3, a significant amount of electron density is
transferred between the core particle and the regulatory
particle (Fig. 8b). This suggests that, even though there is
no significant movement observed for the core particle,
allosteric information is exchanged with the core particle,
and this information can be tracked at the electrostatic
level. The next observation is that significant information
is disseminated not only horizontally (within the alpha
ring, or within the beta ring), but also vertically. In the
overall transition it appears that the alpha ring loses electron
density to the regulatory particle. By checking the
intermediate state 2 it is possible to see that there is also
transfer between the alpha ring and beta ring (Fig. 8c).
This vertical shuttling of electron density within the core
particle suggests that the activity of alpha and beta subunits
may cross-correlate. Such phenomena have indeed
been reported. For example, alpha5 and beta1 may translocate
together [91], while knockdown of alpha1 leads to
loss of chymotrypsin activity associated with beta5 [92].
Further analysis can even yield the residues involved in
the allosteric regulation, as those residues which exhibit a
high variation in total charge (e.g., approximately 10 sites
on the Rpn-13 regulatory subunit).
It is important to note that the structures used in the
EEM calculation were incomplete. Specifically, due to
the size of these molecular machines, the resolution
of the structures was too low to distinguish H atoms or
even parts of residues. No modifications were made to
the structures of the proteasome conformers prior to the
EEM calculation. Thus, the charge distribution of each
conformer is not expected to be physically relevant taken
on its own. Moreover, the results are very likely affected
by the polarizability exaggeration artifact of EEM, discussed
in the Computational details section. Therefore,
the analysis here focused on how the amount of charge
in functional parts of the proteasome changes with the
conformation. This case study shows how a brief calculation
using only a crude structural approximation can give
insight regarding allosteric regulation in large biomolecular
complexes.
Conclusions
We present AtomicChargeCalculator (ACC), a webbased
application for the calculation and analysis of
atomic charges which respond to changes in molecular
conformation and chemical environment. ACC also provides
interactive facilities for statistical analysis and comparison
of the results. We illustrate how direct analysis of
atomic charges can give basic information about chemical
reactivity in paracetamol, and how residue charges
hold clues about biochemical relevance in the antimicrobial
peptide protegrin-1. Additionally, ACC provides
molecular structure files containing atomic charges,
which can be used in further modelling studies. We illustrate
how such data can be used for pKa calculation using
QSPR models. Another advantage of ACC is that it can
Fig. 8  Using information about total subunit charge to track allos‑
teric regulation in the 26S proteasome. a Surface representation of
the structure of half of the 26S proteasome in state 1 [PDB: 4CR2]. The
regulatory particle (red) enables the substrate to unfold and enter the
core particle, which is made up of alpha (yellow) and beta rings (blue).
b As the proteasome evolves from state 1 [PDB: 4CR2], through state
2 [PDB: 4CR3], to state 3 [PDB: 4CR4], the movement of the regulatory
particle is translated into information which is exchanged with the
core particle. The difference in total particle charge is a clear indica‑
tion of regulation, despite the negligible movement observed in the
core particle. c Information is transferred not just within each particle,
but also vertically, between the alpha and the beta ring, and between
the alpha ring and the regulatory particle. This suggests that vertical
structures such as pairs of alpha-beta subunits may act in a correlated
manner
Page 11 of 13Ionescu et al. J Cheminform (2015) 7:50
handle any type of molecular system, regardless of size
and chemical complexity, from drug-like molecules to
biomacromolecular complexes with hundreds of thousands
of atoms. We show how the direction and intensity
of allosteric regulation can be tracked in large biomacromolecular
systems like the proteasome even in the
absence of high resolution structures. ACC thus caters to
all fields of life sciences, from drug design to nano-carriers.
AtomicChargeCalculator is freely available online at
http://ncbr.muni.cz/ACC.
Availability and requirements
• • Project name AtomicChargeCalculator
• • Project home page http://ncbr.muni.cz/ACC
• • Operating system(s) Web server - platform independent.
Command line application—Windows, Linux,
Mac OS
• • Programming language C#
• • Other requirements For the web-server - modern
internet browser with JavaScript enabled, WebGL
support for 3D visualization. For the command line
application - NET 4.0 for Windows based systems,
Mono framework 3.10 or newer (http://www.monoproject.com)
for other OS.
• • License ACC license for the downloadable command
line version.
• • Any restrictions to use by non-academics Free of
charge. No login requirement for running or accessing
the results in the web server.
• •
Authors’contributions
CMI, RSV and JK conceived the study, and participated in its design and coor‑
dination. DS designed and optimized the algorithms. DS, SG and LP imple‑
mented the web-application. CMI, DS, FLF, SG and PP performed extensive
testing of the web-application. CMI and FLF prepared the documentation. CMI
and TB performed the calculations for the case studies. CMI, TB and LP wrote
the manuscript. All authors read and approved the manuscript.
Author details
1
 CEITEC‑Central European Institute of Technology, Masaryk University,
Kamenice 5, 625 00 Brno, Czech Republic. 2
 National Centre for Biomolecular
Research, Faculty of Science, Masaryk University, Kotlářská 2, 611 37 Brno,
Czech Republic. 3
 Faculty of Informatics, Masaryk University, Botanická 68a, 602
00 Brno, Czech Republic.
Acknowledgements
This work was supported by the Grant Agency of the Czech Republic [13-
25401S] and the European Community’s Seventh Framework Programme
[CZ.1.05/1.1.00/02.0068] from the European Regional Development Fund.
Additional support was provided by the project“Employment of Newly Gradu‑
ated Doctors of Science for Scientific Excellence”[CZ.1.07/2.3.00/30.0009] to
CMI, co-financed from the European Social Fund and the state budget of the
Czech Republic. The authors thank Mr. Ravi Ramos and Mr. Tomáš Raček for
useful discussions.
Additional file
Additional file 1. Full computational details, benchmark and limitations
of ACC, along with supporting information for case studies I and III.
Competing interests
The authors declare that they have no competing interests.
Received: 20 June 2015 Accepted: 8 October 2015
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Anatomy of enzyme channels
119
RESEARCH ARTICLE Open Access
Anatomy of enzyme channels
Lukáš Pravda1†
, Karel Berka2†
, Radka Svobodová Vařeková1
, David Sehnal1,3
, Pavel Banáš2
, Roman A Laskowski4
,
Jaroslav Koča1*
and Michal Otyepka2*
Abstract
Background: Enzyme active sites can be connected to the exterior environment by one or more channels passing
through the protein. Despite our current knowledge of enzyme structure and function, surprisingly little is known
about how often channels are present or about any structural features such channels may have in common.
Results: Here, we analyze the long channels (i.e. >15 Å) leading to the active sites of 4,306 enzyme structures. We
find that over 64% of enzymes contain two or more long channels, their typical length being 28 Å. We show that
amino acid compositions of the channel significantly differ both to the composition of the active site, surface and
interior of the protein.
Conclusions: The majority of enzymes have buried active sites accessible via a network of access channels. This
indicates that enzymes tend to have buried active sites, with channels controlling access to, and egress from, them,
and that suggests channels may play a key role in helping determine enzyme substrate.
Background
Channels inside biomacromolecular structures (proteins,
nucleic acids and their complexes) play many significant
biological roles as they enable traffic between the interior
spaces and the exterior. In enzymes they allow passage
of substrates and products to/from the active site
[1-12], in the ribosome they allow nascently synthetized
proteins to pass from the proteosynthetic center to the
outside [13], and in membrane proteins they provide
high specificity of passage in either direction through
the membrane [14,15]. Thus channels have attracted the
attention of many researchers, who have rationalized
their biological roles using a variety of experimental and
theoretical methods. The ribosome, for example, prevents
nascently synthetized polypeptides getting stuck in
its polypeptide egress channel by lining the wall of the
channel with a mosaic of alternating negative and positive
electrostatic potentials [13,16]. Gramicidin provides
polar holes for biomembranes, enabling free diffusion of
monovalent ions and water through the membrane
[17-19], while transmembrane ion channels maintain
their high selectivity by a combination of structural
and electrostatic features of the channel-lining amino
acids [14,20].
Enzymes are proteins that catalyse reactions changing
substrates to products. The enzymatic reactions occur in
the enzymes’ active sites. Thanks to the many analyses
of enzymatic reactions, we now have a better understanding
of how active site chemistry works [21-24] and
which amino acids are present in the sites [25]. However,
relatively little is known about how substrates enter active
sites and how the respective products leave them.
While some active sites are positioned on the protein’s
surface, in clefts or pockets, other enzymes have deeply
buried active sites, which are connected to the outside
by one or more channels. Here we focus on these channels,
as the active site access paths play an important
role in substrate and product trafficking between active
site and outside. It has been shown that mutations in enzymes’
active site access channels alter the substrate
preferences of haloalkane dehalogenase enzymes and
may be utilized in rational design of enzymes [26,27].
The amino acids lining the access channels of cytochrome
P450 (CYP) are important for the selectivity of these enzymes
[28] while the flexibility of these channels, i.e. their
* Correspondence: jaroslav.koca@ceitec.muni.cz; michal.otyepka@upol.cz
†
Equal contributors
1
National Centre for Biomolecular Research, Faculty of Science and CEITEC,
Central European Institute of Technology, Masaryk University Brno, Kamenice
5, Brno-Bohunice 625 00, Czech Republic
2
Department of Physical Chemistry, Regional Centre of Advanced
Technologies and Materials, Faculty of Science, Palacký University Olomouc,
tř. 17. listopadu 12, Olomouc 771 46, Czech Republic
Full list of author information is available at the end of the article
© 2014 Pravda et al.; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain
Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article,
unless otherwise stated.
Pravda et al. BMC Bioinformatics 2014, 15:379
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opening and closing motions, contributes to the broad
substrate specificity of CYP [10,29].
Despite a large effort, and recent progress in the field,
an in-depth analysis of enzyme channels is lacking. Here,
we use an advanced software tool, MOLE 2.0, developed
for analysis of biomacromolecular channels [30], to survey
4,306 enzymes annotated in the Catalytic Site Atlas
(CSA). We identify that more than 64% of enzyme structures
contain channels at least 15 Å long from the active
site. A typical enzyme channel is ~20 Å long and its
walls are made preferentially of histidine, arginine, tryptophan
and tyrosine residues and, to a lesser extent, by
phenylalanine, asparagine, and aspartic acid (Figure 1).
These residues can be considered as gate-keepers controlling
the entry to and from the active site.
Results
Geometry features
We identified that at least 64.2% of enzymes contain channels
at least 15 Å long (Table 1) and 86.8% contain channels
at least 5 Å long. However, as the short channels may
correspond to paths connecting cleft-like active sites with
the exterior, we decided to use only channels longer than
15 Å for our analysis. Enzymes with channels (of ≥15 Å in
length) leading to a buried active site contained on average
two such channels (Table 2). Some had more than five
such channels, the highest number being 68 in 6,7dimethyl-8-ribityllumazine
synthase from Aquifex aeolicus
(PDBID: 1NQU; Additional file 1: Figure S1). Whereas
one might expect larger proteins to contain larger numbers
of channels, we found that the number of long channels
does not correlate with protein size (Additional file 1:
Figure S2). The median channel length is 27.7 Å (Table 2
and Additional file 1: Figure S3), 40% of channels are 15–
30 Å long and 10% of enzymes contain channels longer
than 50 Å. The longest channel (172 Å long) was found in
Penicillium vitale catalase from Penicillium janthinellum
(PDBID: 2IUF; Additional file 1: Figure S1). It should be
noted that although the size of small enzymes (i.e. those
containing fewer than 5,000 atoms) does not limit the number
of long channels they contain, it does limit the maximum
length these channels can have (Additional file 1:
Figure S2).
Channel occurrence and length varies among the enzymatic
classes (Table 2). The highest percentage (77.8%)
of proteins with channels longer than 15 Å was identified
in oxidoreductases (EC1), while the lowest percentage
(51.8%) applied to hydrolases (EC3). The number of channels
is slightly elevated in oxidoreductases (EC1), transferases
(EC2) and isomerases (EC5). Oxidoreductases (EC1)
have median channel length longer by about 2 Å than
other enzymes, whereas transferases (EC2) and ligases
(EC6) have average channel length shorter, also by about
2 Å (Figure 2). As a result, oxidoreductases stand out of
Figure 1 An example of an enzyme channel identified by
MOLE 2.0. Internal, middle and external parts of the channel in
pyridoxal-5'-phosphate-dependent acyl-CoA transferase (PDBID: 3KKI)
are colored orange, red and magenta, respectively. Active site amino
acids (present in the internal part of the channel) are shown in green,
amino acids in the middle part making the wall of a local minimum
(channel narrowing) are in yellow, and amino acids in the external part
lining the bottleneck are in blue.
Table 1 Number of enzyme entries in each EC class, and
numbers of channels of different lengths
EC Enzyme class Number
of
enzymes
Enzymes with channels of length
≥ 5 Å ≥10 Å ≥ 15 Å ≥ 20 Å
EC1 Oxidoreductases 879 781 736 684 612
EC2 Transferases 1096 963 863 747 639
EC3 Hydrolases 1455 1228 1019 749 542
EC4 Lyases 465 401 361 318 262
EC5 Isomerases 252 226 204 165 140
EC6 Ligases 159 139 118 98 88
Sum 4306 3738 3301 2761 2283
Numbers of enzymes in the dataset containing at least one channel of the
given length. Bold values indicate 15 Å threshold for channel detection used
thorough the study.
Table 2 Geometrical channel features for all enzyme
classes
EC Na P Ma
L
EC1 6518 77.8 3 29.8
EC2 4728 68.2 3 26.3
EC3 3454 51.8 2 27.5
EC4 5780 68.4 2 27.9
EC5 5107 65.5 3 26.4
EC6 5289 61.6 2 25.2
All 4823 64.2 2 27.7
a
Enzymes not containing channels were excluded.
Average number of atoms (Na), percentage of enzymes containing at least
one channel from the active site longer than 15 Å (P in %), median number of
channels (M), and median length of channels (L in Å) for each enzyme class.
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the crowd, as they have both higher channel occurrence
and longer channels (Additional file 1: Figure S2).
Physico-chemical features
For each channel, we calculated basic physico-chemical
features such as hydropathy [31] and polarity [32] using
the method introduced in our previous paper [30]. In
brief, the method sums up the length-weighted physicochemical
properties of the amino acids lining the channel.
As the algorithm is rather approximate, we would like to
note that the estimated physico-chemical properties
should be interpreted with care. The average channel hydropathy
is −0.92 (Table 3) and this value is close to the
hydropathy of tyrosine and tryptophan (it is worth noting
that the hydropathy of amino acids varies from −4.5 of
Arg to 4.5 of Ile). The distribution plots of hydropathy
(Additional file 1: Figure S3) also indicate that the values
are shifted in most channels to negative values indicating
that hydrophilic channels are more preferred over hydrophobic
ones.
The average channel polarity is 16.5, which falls between
the values of highly polar amino acids (Asp, Glu, Lys, Arg
and His having polarities of 49.5 – 52.0) and those of
other amino acids (with polarities of 0.0 – 3.5). It indicates
that the channels are rather polar as well as hydrophilic.
Taking all this information into account we may conclude
that the average channel has slightly negative hydropathy
and higher polarity. However, highly hydrophobic and
nonpolar, as well as highly hydrophilic and polar, channels
were also detected. We also analyzed the presence of
charged amino acid side chains (Asp, Glu, His, Lys and
Arg) in channels walls (Additional file 1: Table S2). On
average the channel walls are lined by two negative and
two positive side chains resulting in sum neutral channel
walls (Table 3).
We also identified channels with significant extreme
physico-chemical properties (Additional file 1: Table S3
and Additional file 1: Figure S1). Here we present two
examples. A highly hydrophilic channel (hydropathy
index −3.8) of length 18.7 Å occurs in 3-deoxy-D-arabinoheptulosonate-7-phosphate
synthase (PDB ID: 1N8F)
from E. coli. The high hydrophilicity of the channel is
in accord with its function [33] since this enzyme catalyses
a condensation reaction between two highly polar substrates:
phosphoenolpyruvate and erythrose-4-phosphate.
It is worth noting that transferases (EC2) show the largest
variability in hydrophobicity as illustrated by the fact that
six times transferases are in the top 10 having highly
hydrophilic channels, and four occur in the top 10 with
highly hydrophobic channels.
At the other extreme is peroxidase (PDBID: 1LYK)
from the fungus Coprinus cinereus [34] which has a
highly hydrophobic channel (hydropathy index of 3.59)
Figure 2 Properties of channels in different enzymatic classes.
The topmost panel shows the variability of average channel length
in individual enzymatic classes in comparison with the overall average
channel length. The middle panel shows the average channel polarity
for each enzyme class as well as the polarity of individual parts of the
channels. The colors of the bars correspond to different parts of the
channels, as shown in the key at the bottom. The bottom panel shows
the variability in average hydropathy. Error bars show the standard
error of the mean.
Table 3 Physicochemical features of channels
EC Hydropathy Polarity N(+) N(−) Δ
EC1 −0.64 ± 0.05 14.2 ± 0.4 3 2 1
EC2 −0.97 ± 0.06 17.2 ± 0.4 3 2 1
EC3 −1.05 ± 0.05 17.2 ± 0.4 3 2 0
EC4 −1.05 ± 0.08 17.4 ± 0.6 3 2 1
EC5 −1.07 ± 0.11 17.9 ± 0.9 3 2 1
EC6 −1.30 ± 0.15 20.7 ± 1.3 4 2 1
All −0.92 ± 0.03 16.5 ± 0.2 3 2 0
Internal −1.11 ± 0.04 18.7 ± 0.3 1 1 0
Middle −0.78 ± 0.03 15.4 ± 0.2 1 0 0
External −1.25 ± 0.04 18.8 ± 0.3 1 1 0
The average hydropathy and polarity are shown for each enzyme class as well
as for the internal, middle and external parts of channels. Also shown are the
median number of charged amino acid side chains lining the channels (N(+):
positive Arg, Lys and His, N(−): negative Asp and Glu, and Δ: median of overall
charge). Bold values indicate features of all channels.
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of length 23.8 Å. This channel enables transport of simple
phenols and smaller aromatic dye molecules for their oxidation
in lignin decomposition [35] in a process which has
been exploited in biotechnology as a dye-transfer inhibitor
in a laundry detergent [36].
These examples show that enzymatic classes differ in
their average physico-chemical properties: (i) oxidoreductases
(EC1) show the most hydrophobic as well as
the least polar channels among the enzyme classes, while
(ii) ligases (EC6), and to some extent also isomerases
(EC5), lyases (EC4) and hydrolases (EC3), show the most
hydrophilic as well as the most polar channels (Figure 2,
Table 3 and Additional file 1: Table S3).
We also identified that some physicochemical features
differ across the three channel layers: internal, middle
and external (Table 3). The polarity of middle part of the
channel is always lower than polarity of both internal
and external parts, respectively. The lower polarity of
the middle part of channel is also reflected by its significantly
more hydrophobic behaviour. The charged residues
occur mainly in external parts of enzyme channels,
while the internal and middle part contains more aromatic
residues.
Channel-lining residues
We calculated the frequencies of channel-lining amino
acids and compared them with frequencies of amino
acids in the same enzyme structures. On the basis of this
data, the channel propensities of individual amino acids
can be defined as a ratio of the frequency of amino acid
in the channel walls to the frequency of amino acid anywhere
within the protein structure. The resulting channel
propensities of the individual amino acids differ
significantly. The rather bulky and aromatic amino acids
(His, Tyr, Trp, Arg), occur over 1.25 times more frequently
in the channel walls than in the whole enzyme.
Additionally, other amino acids (Asn, Phe, Asp, Thr,
Met, Ser) also show a slightly higher frequency in the
channel walls than in the rest of the protein. Conversely,
nonpolar aliphatic amino acids (Pro, Gly, Ile, Leu, Ala,
and Val) are significantly less localized in channel walls
(Figure 3). We also looked at the amino acid composition
at each channel’s local minimum. Whereas this
reflected the composition of the whole channel, the
channel bottlenecks contain significantly more cysteine
(Cys), histidine (His) and tyrosine (Tyr) residues than
usual and much fewer small aliphatic amino acids (Pro,
Gly and Ala) (Additional file 1: Figure S4). As histidine
(His) and cysteine (Cys) have unique binding properties,
it is possible to hypothesize that these binding properties
might provide a gate-keeping activity at the channel bottlenecks,
whereas small aliphatic residues cannot undergo
large changes and as such cannot serve as gate-keepers.
The frequencies of amino acids in active sites, on the
protein surface and inside the protein, or in general
channels, are markedly different from both the average
protein amino acid composition and the composition of
the channels (Figure 4). The active sites contain significantly
more amino acids that can be part of a catalytic
cycle (His, Asp, Cys, Glu, Arg, Tyr, Lys) enabling proton
and electron shuffling and covalent bond reorganization.
On the other hand, the frequency of less reactive amino
acids (Trp, Thr, Gln, Phe) or amino acids with nonreactive
side-chain (Met, Ala, Pro, Ile, Val, Leu) is lower in
Figure 3 Channel propensity of amino acids. Enhancement of
frequencies of individual amino acids in channels indicates which
amino acids are more likely to occur in the channel walls than
anywhere else in the protein structure. Hydrophobic aliphatic residues
are shown in gray, aromatic amino acids in magenta, polar residues in
green, negatively charged in red, positively charged in blue and
cysteine in yellow.
Figure 4 Enhancement of amino acid frequency in different
parts of the enzyme structure. Amino acids that are found more
often than average in different regions of an enzyme structure. Their
labels are scaled to reflect their propensity for each compartment;
the key in the bottom right-hand corner indicates how the label size
relates to propensity. Hydrophobic aliphatic residues are shown in
gray, aromatic amino acids in magenta, polar residues in green,
negatively charged in red, positively charged in blue and cysteine
in yellow.
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the active sites. These results are in perfect agreement
with data published by Holliday and coworkers [37]. Protein
cores are rich in hydrophobic aliphatic (Ile, Leu, Val,
Ala, Met) and aromatic amino acids (Phe, Trp) as well as
in cysteines (Cys). These amino acids have a structural
function to maintain the formation and stability of protein
hydrophobic cores [38] and the formation of disulphide
bonds [39]. Conversely, the surface regions contain mainly
charged (Lys, Arg, Glu, Asp) and polar residues (Asn,
Gln), which facilitate contact with the polar water environment.
Also, the surface has a higher than average frequency
of prolines (Pro) as these helix-breaker amino
acids are common in turns in the protein structures rigidifying
the protein fold (Additional file 1: Figure S4).
Channel-lining amino acids are not uniformly distributed
along the length of the channel. Internal parts of
the channel tend to contain more aromatic residues
(His, Trp, Tyr) together with cysteine (Cys), while glutamine
and glutamate (Gln and Glu) and aliphatic amino
acids (Pro, Ala, Leu) are underrepresented. These trends
are similar to the catalytic site propensities, as discussed
in the previous paragraph. The frequencies of amino
acids in the middle regions of the channels correspond
to the frequencies in the entire channel with the exception
of glycine (Gly) and aromatic amino acids (Trp, Tyr, Phe),
which are present more frequently. We may hypothesize
that the higher frequency of glycine (Gly) in the middle
channel parts is because it facilitates flexibility, which may
be important for substrate/product channeling between
the active site and protein surface [29], whereas aromatic
amino acids can serve as gate-keepers. External parts of
the channel bear more charged residues than any other
part (Arg, Lys, Glu, Asp) together with proline (Pro) and
glutamine (Gln), whereas other polar residues (Ser, Thr)
are surprisingly less common in the external parts even
though that both Ser and Thr are evenly distributed
within the structure of proteins (Additional file 1:
Figure S4). External parts of channels are less occupied
by aliphatic (Ile, Ala, Val) and aromatic amino acids
(Phe, Tyr) as well as typical catalytic amino acids – histidine
(His), aspartate (Asp) and cysteine (Cys). A higher frequency
of charged or rather bulky and aromatic amino
acids in channels may have functional implications because
such amino acids may work as gate-keepers,
regulating traffic between active site and surface via
conformational changes. It is worth noting that some mutations
of such residues have been shown to alter the catalytic
efficiency and substrate preferences in haloalkane
dehalogenases [26].
All the results above concern channels leading to buried
enzyme active sites. For comparison, we also analyzed
all channels of length greater than 15 Å connecting a
cavity in the protein interior to the outside exterior
(Additional file 1: Figure S4). We compared the amino
acid compositions of the two types of channels. The active
site access channels have higher frequencies of aromatic
(Tyr, Trp and Phe), polar amino acids (Asn, Thr
and Ser), catalytically active amino acids (Cys and His),
and glycine (Gly). On the other hand, they contain
fewer aliphatic amino acids (Pro, Leu, Ile and Val),
charged and some polar amino acids (Lys, Glu, Arg and
Gln). In sum, the active site access channels contain
more functional amino acids than generic channels.
This finding agrees with the idea that some amino acids
bear functional roles in channels, e.g., as gate keepers
or to maintain their flexibility.
The analysis of amino acids leading to active sites, divided
according to the six enzymatic groups, shows that
amino acid channel propensities correspond to overall
channel propensities. However, some differences were
identified (Additional file 1: Figure S4). As can be expected
from their higher hydropathy and lower polarity,
channels in oxidoreductases (EC1) have significantly lower
frequencies of charged lining amino acids (Arg, Asp, Lys,
Glu), but higher frequencies of aliphatic lining amino
acids (Met, Pro, Ile, Leu, Ala, Val). Channels in transferases
(EC2) contain fewer aromatic (Trp) and more
charged (Arg, Asp, Lys) amino acids. Channels in hydrolases
(EC3) contain fewer arginine (Arg), threonine
(Thr) and aliphatic amino acids (Pro, Ile, Ala, Val),
whereas they contain more aromatic (Trp, Tyr) and
smaller charged (Lys, Asp, Glu) amino acids. Channels
in lyases (EC4) show only lower amounts of aromatic
(Trp) and sulphur containing (Met, Cys) amino acids.
Channels in isomerases (EC5) contain fewer glycines
(Gly). Channels in ligases (EC6) are the most hydrophilic
channels, so it is not surprising that their channels
contain fewer cysteine (Cys), aromatic (Trp, Tyr)
and aliphatic (Pro, Leu) amino acids and more charged
(Arg, Lys, Glu) amino acids and glycine (Gly). It should
be noted that the differences between the individual enzyme
classes should be interpreted with care because of
larger statistical error bars, especially in the case of less
populated EC5 and EC6 classes.
Discussion
Long channels (>15 Å) are a common feature of enzymes,
with over 64% containing at least two such channels.
This shows that the majority of enzymes have
buried active sites accessible via a network of access
channels. Hence there is an apparent tendency for enzymes
to bury their active site, i.e., to limit and control
direct connection of active sites with the surrounding
environment. This may be the result of two evolutionary
pressures; i) steric, because active sites have to be structurally
well arranged – a buried active site enables full
spatial arrangement better than a pocket-like active site
can give that half of the space of the latter is open to
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surrounding environment and ii) functional, as active
site access paths may enable pre-selection of substrates,
and may be involved in features co-determining enzyme
substrate preferences. In another words, the active site
access channels may limit access to the enzyme active
sites and function as keyholes, enabling passage only of
some classes of substrates.
The amino acid frequencies in the whole protein structures
and channel walls differ significantly. Aliphatic
amino acids are more involved in the formation of enzyme
hydrophobic cores, which are important to maintain a
protein fold. In turn, they are less frequently involved in
channel wall lining or within the active sites. The aromatic,
charged and polar amino acids occur more frequently
in the channels walls. In addition, we identified a
higher frequency of glycine in the middle parts of channels,
which may function here to support channel flexibility
enabling the channelling of bulkier substrates to active
sites. This finding can be explained by the fact that the
polar and charged amino acids line the channels to enable
passage of polar substrates/products and water. The enhanced
frequency of rather bulky and aromatic amino
acids in channel external parts may have functional implications,
because such amino acids may work as gatekeepers,
regulating traffic between active site and outside.
The functional implications deduced from these global
analyses are also supported by the fact that individual
enzyme classes differ in their channel features. Typically
oxidoreductases have the most hydrophobic, the least
polar and longest channels among the enzyme classes,
while ligases have the most hydrophilic, the most polar
and the shortest channels. This indicates that evolution
of enzymatic substrate preferences might also include
evolution of active site access channels.
Conclusions
To conclude, we analyzed channels in 4,306 enzyme structures
annotated in the Catalytic Site Atlas. We identified
that at least 64% of enzyme structures contain on average
two channels longer than 15 Å leading to the catalytic site.
Consequently, we may anticipate that the same number of
enzymes have buried active sites. The longest, and also the
most hydrophobic, channels are found in oxidoreductases,
while the smallest number of channels can be found in hydrolases
and the shortest and also the most hydrophilic
channels in ligases. The composition of channel walls differs
from the average composition of enzyme structures as
well as from the composition of the protein surface.
Hydrophobic aliphatic amino acids, which are the most
common amino acids present in protein cores, occur in
channel walls less frequently, whereas aromatic, charged
and polar amino acids occur more frequently in channel
walls. All these findings indicate that the active site access
channels bear significant biological function as they are involved
in co-determining enzyme substrate preferences.
Methods
Dataset
We analyzed 4,306 enzymes which were annotated in the
Catalytic Site Atlas (CSA) database release of 4th March
2013 [25,40]. The dataset contained structures determined
by X-ray diffraction at a resolution better than 2.5 Å, and
had no two structures with a sequence identity higher
than 90% (more quality checks can be found in Additional
file 1: Table S1). It should be noted that when we used a
dataset containing structures with a sequence identity less
than 50%, the results did not significantly differ from the
results obtained with the dataset containing structures
with a sequence identity less than 90%. The enzymes in
the dataset were grouped according to their Enzymatic
Commission (EC) class (Table 1).
Channel Identification
An active site is a cavity, which walls contain amino
acids residues annotated in the CSA. A channel is a
pathway inside an active site cavity connecting the deepest
apex of the cavity with an exterior. The MOLE 2.0
program [30] was used for channel identification and
characterization. Briefly, the MOLE 2.0 algorithm calculates
the Delaunay triangulation/Voronoi diagram of the
atomic centers, splitting it into several smaller parts and
identifying suitable start and end points in the interior
and surface, respectively. Dijkstra's algorithm is used to
identify tunnels as the shortest paths between the start
and end points (see Additional file 1 for further details).
This algorithm is used also in the MOLEonline 2.0 web
application [41]. The setup of MOLE 2.0 for these calculations
was as follows: Probe Radius and Origin Radius
5 Å, Interior Threshold 1.1 Å and default values for
Bottleneck Length, Bottleneck Radius, Cutoff Ratio and
Surface Cover Radius. The CSA active sites were used as
starting points. We used biological assemblies for the
enzymes structures, which were obtained from the PDB
database as *.pdb1 files. [42] Ten structures of EC 3.6.4
group were removed from the dataset. Hydrogen atoms
and ligands not covalently bound to the structure were
deleted prior to calculation. In cases where the system
contained more than one active site, the site having the
most channels was used. In order to study only relevant
channels, we analysed only those channels longer than
15 Å. Table 1 shows the numbers of channels of different
lengths for each of the six different enzyme classes,
which are listed together with their properties in
Additional file 2.
In the text we use the following terminology (Figure 1);
Lining amino acids are all the amino acids fully encapsulating
the detected channel and are divided into three
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classes: internal, middle, and external according to their
respective positions in the layers perpendicular the channel
centerline. Internal or external lining amino acids
are those lying within a 5 Å distance of the start or end
point, respectively, with middle amino acids constituting
the remainder. A bottleneck is where the channel radius
is a minimum.
Additional files
Additional file 1: Description of MOLE methodology, and explanation
of statistical methods used for channel analysis, Supplementary Figures
S1–S4 and Supplementary Tables S1–S3.
Additional file 2: Full set of channels in csv format. The MOLE 2.0
application and enzymatic data set are available for download at
http://mole.chemi.muni.cz/enzymes.
Competing interests
The authors declare that they have no competing interests.
Authors' contributions
LP carried out channel calculations. KB calculated the statistical analysis of
the data and drafted the manuscript. RSV contributed to the design of the
study and data interpretation. DS wrote the software used. PB participated in
statistical analysis of the data. RAL participated in the design of the study
and data interpretation. JK coordinated the study and wrote the manuscript.
MO conceived of the study, designed and coordinated the study and wrote
the manuscript. All authors read and approved the final manuscript.
Acknowledgements
This work was supported by the Czech Science Foundation [P208/12/G016
to M.O., P303/12/P019 to K.B.] and the Operational Program Research and
Development for Innovations–European Regional Development Fund
[CZ.1.05/2.1.00/03.0058 to M.O., K.B., P.B. and CZ.1.05/1.1.00/02.0068 to J.K.
and R.S.V.], European Social Fund [CZ.1.07/2.3.00/20.0058 to K.B.]. D.S.
acknowledges Brno City Municipality for financial support provided through
the program Brno Ph.D. Talent. Access to the MetaCentrum supercomputing
facilities provided under the research intent MSM6383917201 is gratefully
acknowledged.
Author details
1
National Centre for Biomolecular Research, Faculty of Science and CEITEC,
Central European Institute of Technology, Masaryk University Brno, Kamenice
5, Brno-Bohunice 625 00, Czech Republic. 2
Department of Physical Chemistry,
Regional Centre of Advanced Technologies and Materials, Faculty of Science,
Palacký University Olomouc, tř. 17. listopadu 12, Olomouc 771 46, Czech
Republic. 3
Faculty of Informatics, Masaryk University Brno, Botanická 68a,
Brno 602 00, Czech Republic. 4
European Molecular Biology Laboratory,
European Bioinformatics Institute (EMBL-EBI), Wellcome Trust Genome
Campus, Hinxton, Cambridge CB10 1SD, UK.
Received: 19 July 2014 Accepted: 5 November 2014
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Bioinformatics 2014 15:379.
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MotiveValidator: interactive web-based
validation of ligand and residue structure in
biomolecular complexes
128
Nucleic Acids Research, 2014 1
doi: 10.1093/nar/gku426
MotiveValidator: interactive web-based validation of
ligand and residue structure in biomolecular
complexes
Radka Svobodov´a Vaˇrekov´a1,2,†
, Deepti Jaiswal1,†
, David Sehnal1,2,3
, Crina-Maria Ionescu1
,
Stanislav Geidl1,2
, Luk´aˇs Pravda1,2
, Vladim´ır Horsk´y3
, Michaela Wimmerov´a1,2,*
and
Jaroslav Koˇca1,2,*
1
CEITEC - Central European Institute of Technology, Masaryk University Brno, Kamenice 5, 625 00 Brno, Czech
Republic, 2
National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kotl´aˇrsk´a 2, 611 37
Brno, Czech Republic and 3
Faculty of Informatics, Masaryk University Brno, Botanick´a 68a, 602 00 Brno, Czech
Republic
Received January 30, 2014; Revised May 02, 2014; Accepted May 2, 2014
ABSTRACT
Structure validation has become a major issue in
the structural biology community, and an essential
step is checking the ligand structure. This paper
introduces MotiveValidator, a web-based application
for the validation of ligands and residues in
PDB or PDBx/mmCIF format ﬁles provided by the
user. Speciﬁcally, MotiveValidator is able to evaluate
in a straightforward manner whether the ligand
or residue being studied has a correct annotation
(3-letter code), i.e. if it has the same topology and
stereochemistry as the model ligand or residue with
this annotation. If not, MotiveValidator explicitly describes
the differences. MotiveValidator offers a userfriendly,
interactive and platform-independent environment
for validating structures obtained by any
type of experiment. The results of the validation are
presented in both tabular and graphical form, facilitating
their interpretation. MotiveValidator can process
thousands of ligands or residues in a single
validation run that takes no more than a few minutes.
MotiveValidator can be used for testing single
structures, or the analysis of large sets of ligands
or fragments prepared for binding site analysis,
docking or virtual screening. MotiveValidator is
freely available via the Internet at http://ncbr.muni.cz/
MotiveValidator.
INTRODUCTION
Validation arose as a major issue in the structural biology
community when it became apparent that some published
structures contained serious errors (1–6). Various
tools for the validation of the protein and nucleic acid 3D
structures are well established, such as WHAT CHECK (7),
PROCHECK (8), MolProbity (9) and OOPS (10).
An essential step in the validation process is checking the
ligand structure. Ligands are chemical compounds which
form a complex with a biomacromolecule (e.g. sugar, drug,
heme) and play a key role in its function. The ligands
are also the main source of errors in structures (11,12).
Nonetheless, ligand validation is a very challenging task
(13), because of the high diversity and nontriviality of their
structure and the general lack of information about correct
structures. Therefore, early validation tools focused on selected
types of ligands (PDB-care (14) focused on carbohydrates)
and their scope only widened later (ValLigURL
(15)). Ligand validation features were recently added to
existing software (e.g. Mogul (16), Coot (17)). New tools
such as PHENIX (18) were developed to include ligand validation
functionality. However, the functionality of some
available tools (i.e. ValLigURL, Mogul, Coot, PHENIX) is
aimed at the validation of selected properties (atom clashes,
bond lengths, bond angles, etc.) or is limited to a selected
type of molecules (e.g. PDB-care validates only carbohy-
drates).
This article presents the web-based application MotiveValidator,
which offers a user-friendly, interactive and
platform-independent environment for the validation of ligands
and residues in PDB (http://www.wwpdb.org/docs.
html) or PDBx/mmCIF (19) files provided by the user.
*To whom correspondence should be addressed. Tel: +420 54949 4947; Fax: +420 54949 2556; Email: Jaroslav.Koca@ceitec.muni.cz
Correspondence may also be addressed to Michaela Wimmerov´a. Tel: +420 54949 3805; Fax: +420 54949 2690; Email: michaw@chemi.muni.cz
†
The authors wish it to be known that, in their opinion, the first two authors should be regarded as Joint First Authors.
C The Author(s) 2014. Published by Oxford University Press on behalf of Nucleic Acids Research.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by-nc/3.0/), which
permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact
journals.permissions@oup.com
Nucleic Acids Research Advance Access published May 21, 2014
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2 Nucleic Acids Research, 2014
Residues refer to any component of a biomacromolecule
or a biomacromolecular complex (i.e. amino acids, nucleotides,
ligands). Specifically, MotiveValidator is able to
evaluate in a straightforward manner whether the ligand
or residue under study has a correct annotation (3-letter
code), i.e. if it has the same topology and stereochemistry
as the model ligand or residue with this annotation. If not,
MotiveValidator explicitly describes the differences. Validation
is performed against so-called model residues, which
can be either correct structures of the residue obtained
from the wwPDB Chemical Components Dictionary (20)
(accessed via the web interface provided by LigandExpo
(21)), or against templates provided by the user. The output
provides a report of the validation results, including summary
and detailed information in both tabular and graphical
form. MotiveValidator can process thousands of ligands
or residues in a single validation run that takes no more than
a few minutes.
MotiveValidator can be used for testing single structures,
or the analysis of large sets of ligands or fragments prepared
for binding site analysis, docking or virtual screening.
A significant advantage of MotiveValidator is the ability to
process structures obtained by any type of experiment and
not requiring the user to have any additional knowledge in
the field of X-ray crystallography or nuclear magnetic reso-
nance.
DESCRIPTION OF THE TOOL
MotiveValidator incorporates several tools for the detection
and extraction of residues (MotiveQuery; D. Sehnal
et al., unpublished work), motif superimposition (SiteBinder
(22)), chirality verification (OpenBabel (23)), statistical
evaluation of results (in-house program) and interactive
visualization of 3D structures (ChemDoodle, http:
//www.chemdoodle.com). All these tools are integrated into
a single program which runs on a server and is accessible
under any operating system. The built-in 3D molecular visualizer
requires an up-to-date web browser with WebGL
enabled. In addition to running validations on the server, a
command line version of MotiveValidator is also available.
MotiveValidator enables three kinds of validation to be
performed, accessible via three modules. Residue Validation
is the most general module, meant for any residue,
including ligands. Sugar Validation is focused on carbohydrates
and Motif/Fragment Validation on biomolecular
fragments (motifs). A motif can in principle be any part
of a biomacromolecule. Nonetheless, MotiveValidator is focused
on the validation of residues, thus here motif generally
refers to the residue under study, together with its immediate
environment. Validation via any module involves
three steps, namely setup, calculation and finally visualization
and the analysis of results. We provide here an extensive
description of the Residue Validation module and then
briefly point out the differences for the other two modules.
Residue validation
Setup. Two kinds of input are required, namely the structure
of a biomolecule or biomolecular complex to be validated
and a model residue to serve as the reference template
for validation (Supplementary Figure S1). The structure to
be validated and model residue must be uploaded in PDB
format, or can be retrieved in this format from the mirrors
of the Protein Data Bank (24) and LigandExpo databases
maintained on the MotiveValidator server and updated every
week. The structure to be validated can also be uploaded
in PDBx/mmCIF format. A single MotiveValidator
run can validate multiple residues in multiple structures.
Calculation. After the setup, the validation proceeds in
several steps. The sequence of steps performed during validation
is as follows (see also Supplementary Figure S2 for
a graphical dictionary of the main terms that appear in this
section):
(i) In the structure(s) to be validated, find all instances
of residues with the same 3-letter code as the model
residue.
(ii) Extract the identified residues (i.e. residues to be validated)
together with their immediate surroundings (i.e.
atoms within one or two bonds of any atom of the
residue to be validated), to obtain input motifs for val-
idation.
(iii) For each input motif:
(a) Superimpose the input motif with the model
residue to find the best atom pairing, i.e. the correspondence
(mapping) between atoms from the
model residue and from the input motif. Mathematically,
it is the bijection which matches the most
atoms from the input motif to the most atoms from
the model residue and provides the lowest RMSD
(root mean square deviation) for the structural superimposition.
PDB names of atoms are not used
in this step. The subset of atoms from the input
motif paired with atoms in the model residue forms
the validated motif. The atoms in a validated motif
are checked for connectivity, to ensure that it is the
same as in the model residue. Report any discrepancy
between the inter-atomic bonds in the validated
motif and in the model residue (section Processing
Errors/Warnings).
(b) Establish the validated motif according to the best
atom pairing identified in the previous step. Based
on the validated motif, detect and report errors:
r missing atoms: atom in the model residue with
no corresponding atom in the validated struc-
ture
r missing rings: missing atoms originating from
cycles (rings)
r wrong chirality: atom from the validated motif
with different chirality than the corresponding
atom from the model residue;
and warnings:
r substitutions: atom from the validated motif
with different chemical symbol than the corresponding
atom in the model residue (e.g. O
mapped to N)
r different atom name: atom from the validated
motif with different PDB name than the corresponding
atom from the model residue (e.g. the
C1 atom mapped to the C7 atom)
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Nucleic Acids Research, 2014 3
r foreign atoms: atom from the model residue
mapped to atom from outside the validated
residue (i.e. from its surroundings).
Note: An occurrence of a warning does not mean that
the validated motif is wrong. The warning serves only as
information to the user.
Visualization and processing of results. All setup information,
along with all input and output structures and files are
deposited on the server in a unique directory, translated as
a unique URL accessible for visualization and download
for at least a month. The MotiveValidator output provides
a straightforward report of the validation results, including
a summary and detailed information in both tabular
and graphical form, along with a 3D structure visualizer for
closer inspection of the problematic structures.
The Summary section first provides a description of the
validation process and then a validation report for each
validated residue (Figure 1). The report contains information
about the model residue (annotation, 2D structure)
and an overview (table and pie chart) of issues found during
validation, namely, the number of residues with missing
atoms, missing (incomplete) rings, wrong chirality, correct
chirality, substitutions, different atom names and foreign
atoms. A list of specific issues and their localization within
the residue (i.e. number of residues with particular missing
atoms or atoms having wrong chirality) is also given.
The Details section (Figure 2, top) provides detailed information
for each validated motif. It is organized into a
table with one line per motif, containing basic identification
of the motif inside the original input file and a list of
all issues identified during validation. Each motif can be examined
in the 3D space and a complete validation report is
available in graphical form using the individual motif links
(Figure 2, bottom).
The additional section Processing Errors/Warnings lists
the issues found while processing the input files. Processing
warnings are issues that may cause incorrect validation,
such as atoms that are too close in the 3D space. Processing
errors are major issues preventing the finalization of the
validation, such as parts of the residue which are completely
disconnected from the rest of the structure, probably due to
missing atoms at multiple locations throughout the struc-
ture.
Sugar validation
A notable case of ligand validation is the analysis of carbohydrate
structures because they have complex topology
and many chiral atoms. Carbohydrates are involved in a
variety of fundamental biological processes and have significant
pharmaceutical and diagnostic potential. Additionally,
more than 60% of nontrivial-sized ligands (>10
atoms) from the PDB contain a carbohydrate. For these
reasons, MotiveValidator includes the mode Sugar Validation,
which was developed specifically for the validation of
carbohydrates. Unlike Residue Validation, the Sugar Validation
setup stage requires only one input, namely the
biomolecule(s) containing residues to be validated. This
mode enables the automatic validation of all carbohydrate
residues identified in the input structure(s). Specifically,
MotiveValidator identifies all motifs containing pyran or
furan rings as saccharides and validates them against the
corresponding model residues (same 3-letter code) retrieved
from the LigandExpo mirror.
Motif/fragment validation
The Motif/Fragment Validation mode uses the model
residue and fragments of biomolecules as the input, as
opposed to entire biomolecules in the Residue Validation
mode. The motifs (fragments) should contain the validated
residue and its closest surrounding. The surrounding can
include, e.g. atoms within one or two bonds of any atom of
the validated residue or more. However, it must stay clear,
which residue is the validated one. Therefore, the surrounding
can contain just fragments of neighboring residues, but
not the whole neighboring residues. It is very useful for the
efficient processing of very large amounts of data, such as
validating all instances of a residue in the entire PDB. The
calculation skips steps (i) and (ii) related to residue detection
and extraction, and instead starts directly with the superimposition
[step (iii)] of the model residue and validated
fragments. The fragments can be prepared manually or automatically.
The MotiveValidator website also provides the
utility MotifExtractor to enable automatic extraction of the
desired motifs (residues and their surroundings) from large
datasets of biomolecular structures.
RESULTS AND DISCUSSION
We provide examples of uses for MotiveValidator in the
form of case studies for each of the three validation modes.
Residue validation: all proteins containing cholic acid
Cholic acid (CHD) is the best known bile acid and includes
four rings and 11 chiral atoms. It contains three 6-member
rings A, B and C in chair conformation and a 5-member
ring D (Supplementary Figure S3A and B) (25). The PDB
contains 299 instances of CHD as ligand in a total of 55
PDB entries (access date: 5.1.2014). We collected all 55
structures and validated all occurrences of CHD using the
Residue Validation mode in MotiveValidator. The validation
(Figure 1) took 15 s and showed that all 299 CHD instances
are complete (no missing atoms). However, the validation
revealed that almost 13% of the CHD ligands have
incorrect chirality. The problematic molecules can be organized
into three groups. The first group contains 18 ligands
from nine PDB entries, with incorrect chirality at atoms C3,
C8, C9, C12 and C14. The errors are caused by the unnatural
boat conformation of rings A, B and C in these particular
structures (Supplementary Figure S3C). All these
structures come from bovine heart cytochrome c oxidase
and were published by the same lab. The second group contains
18 ligands from the same nine PDB entries, with incorrect
chirality at atoms C8, C9, C12, C14 and C17. The
errors are caused by the unnatural twist-boat conformation
of rings A, B and C (Supplementary Figure S3D). The third
group contains two ligands from the H240A variant of human
ferrochelatase (PDB ID 3AQI), with incorrect chirality
at atom C20.
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4 Nucleic Acids Research, 2014
Figure 1. The Summary tab first provides a description of the validation process and a summary of the results in tabular and graphical form. An overview
of the issues related to incomplete structure or incorrect chirality is given here, along with other useful notes. The problematic atoms are further highlighted
to better localize the problems in the structures.
The complete results are available at the MotiveValidator
website as a Sample calculation (http://ncbr.muni.cz/
MotiveValidator/ProteinsWithCHD).
Sugar validation: nipah G attachment glycoprotein complexed
with ephrin-B3
Nipah virus infection may lead to severe respiratory disease
and fatal encephalitis in humans. The Nipah virus relies
on the Nipah G attachment glycoprotein for host cell
recognition. The crystal structure of the glycoprotein complexed
with its receptor ephrin-B3 (PDB ID 3D12, (26))
contains 30 instances of 11 different carbohydrates, each
with one ring and five chiral atoms: ␤-D-glucose (BGC), ␤D-mannose
(BMA), ␤-D-gulopyranose (GL0), ␣-D-glucose
(GLC), ␣-L-galactopyranose (GXL), 2-(acetylamino)-2deoxy-␤-D-gulopyranose
(LXB), 2-(acetylamino)-2-deoxy␣-D-idopyranose
(LXZ), ␣-D-mannose (MAN), N-acetylD-glucosamine
(NAG), N-acetyl-D-galactosamine (NGA)
and 2-(acetylamino)-2-deoxy-␣-L-glucopyranose (NGZ).
Note that the names of the carbohydrates were obtained
from LigandExpo and prefixes alpha- and beta- were replaced
with ␣− and ␤− (see Supplementary Table TS1
for IUPAC systematic names). We validated all carbohydrate
structures in this biomacromolecular complex using
the Sugar Validator mode. The validation showed that 13 of
these ligands had incorrect chirality (Supplementary Figure
S4). In the few cases with GLC or NGA ligands, all five chiral
atoms exhibited incorrect chirality. Manual inspection
of the structure showed further discrepancies in the ligand
part. This is discussed in details in the Supplementary material
(Supplementary Figure S5).
The complete results are available at the MotiveValidator
website as a Sample calculation (http://ncbr.muni.cz/
MotiveValidator/ComplexedGlycoprotein).
Motif/fragment validation: all N-acetyl-D-glucosamine
residues from PDB
N-acetyl-D-glucosamine (NAG) is the second most frequent
hetero-atom chemical component found in the PDB,
amounting to 24 357 instances as ligands in a total of
3905 PDB entries (access date: 9.1.2014). NAG includes
one pyran ring and five chiral atoms (Supplementary Figure
S6A). We extracted all 24 357 NAG instances from the
PDB using MotifExtractor. Each file contained one NAG
motif, composed of a NAG residue and the atoms in its immediate
surroundings (atoms within one or two bonds of
the NAG residue). These motifs were validated using the
Motif/Fragment Validation mode. The validation (Figure
2) took 195 s and revealed that 94% of NAG instances in
the PDB are complete and have correct chirality. In addition,
several issues were reported.
First, 16 NAG residues exhibit serious problems: some
only contain a few atoms, others have errors in their bond
information described by CONNECT keywords (see exam-
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Nucleic Acids Research, 2014 5
Figure 2. The Details tab enables the issues in selected groups of motifs to be inspected by specifying the residue name and type of issue. All information
pertaining to a given motif is provided in a single row. Further, each motif can be examined in the 3D space and a complete validation report is accessible
via the individual motif links.
ple in Supplementary Figure S6B). Second, approximately
3.5% of NAG residues are missing at least one atom. In most
cases, the O1 atom is missing. Third, 2.7% of NAG residues
have wrong chirality, mostly at C1, since that is the main site
of covalent connection to other residues, which can cause a
change in chirality. Some of the chirality errors are caused
by incorrect placement of the ligand inside the electron density
map. For example, residue NAG 2 A from the PDB entry
3A4X exhibits incorrect chirality at atom C2 (Supplementary
Figure S6C). Using Coot and the corresponding
electron density maps downloaded from the EDS server at
Uppsala University (27), we found that NAG is not placed
correctly in the electron density map, leading to a deformation
in the vicinity of C2. New positioning leads to a conformation
which fits the experimental 3D electron density
map markedly better and which has the correct chirality at
position C2 (Supplementary Figure S6D).
Additionally, MotiveValidator found that over 60% of
NAG residues in the PDB have a nitrogen substitution at
O1, which indicates their participation in N-glycosylation.
The ability to process and validate also residues with substitutions
is an advantage of MotiveValidator.
The complete results are available at the MotiveValidator
site as a Sample calculation (http://ncbr.muni.cz/
MotiveValidator/MotifsNAG).
Limitations
MotiveValidator is limited in three main ways. First, there
is the requirement to ensure that the model residue serv-
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6 Nucleic Acids Research, 2014
ing as the reference during validation is indeed correct.
This limitation is overcome by using high-quality reference
residues from LigandExpo. Second, the superimposition
phase might not identify the optimal matching between
the atoms of the model residue and those of the validated
residue if their 3D structures are too different. Finally, software
and data handling on the server currently limits the
maximum size of the input file with structures to be validated
(PDB or ZIP file) to 300 MB. We plan to minimize
these limitations in the next version of MotiveValidator. For
example, we will explore the use of additional metrics to improve
the second limitation.
CONCLUSION
In this article we introduced MotiveValidator, a web-based
interactive tool for validating ligand and residue structure
in biomolecular complexes. The MotiveValidator interface
is easy to use and platform-independent, enables interactive
analyses with a high degree of automation, e.g. retrieving
structures from local mirrors of the PDB and LigandExpo
databases, automatic detection and extraction of sugars or
selected residues, including their immediate surroundings.
Results are presented in a clear graphical and tabular form,
facilitating their interpretation and further processing.
SUPPLEMENTARY DATA
Supplementary Data are available at NAR Online.
ACKNOWLEDGMENTS
The authors wish to thank Prof. Gerard Kleywegt and Dr
Sameer Velankar, both EMBL-EBI, Hinxton, UK, for their
useful comments on the manuscript.
FUNDING
This work was funded by the Ministry of Education,
Youth and Sports of the Czech Republic [LH13055],
the CEITEC - Central European Institute of Technology
[CZ.1.05/1.1.00/02.0068] from the European Regional
Development Fund, the “Capacities” specific program
[286154] and by INBIOR [CZ.1.07/2.3.00/20.0042] from
the European Social Fund and the state budget of the
Czech Republic. Additional support was provided by the
project ”Employment of Newly Graduated Doctors of Science
for Scientific Excellence” [CZ.1.07/2.3.00/30.0009] cofinanced
from the European Social Fund and the state budget
of the Czech Republic. Funding for open access charge:
INBIOR [CZ.1.07/2.3.00/20.0042] from the European Social
Fund and the state budget of the Czech Republic.
Conflict of interest statement. None declared.
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MOLE 2.0: advanced approach for analysis
of biomacromolecular channels
136
SOFTWARE Open Access
MOLE 2.0: advanced approach for analysis of
biomacromolecular channels
David Sehnal1,2
, Radka Svobodová Vařeková1
, Karel Berka3
, Lukáš Pravda1
, Veronika Navrátilová3
, Pavel Banáš3
,
Crina-Maria Ionescu1
, Michal Otyepka3*
and Jaroslav Koča1*
Abstract
Background: Channels and pores in biomacromolecules (proteins, nucleic acids and their complexes) play
significant biological roles, e.g., in molecular recognition and enzyme substrate specificity.
Results: We present an advanced software tool entitled MOLE 2.0, which has been designed to analyze molecular
channels and pores. Benchmark tests against other available software tools showed that MOLE 2.0 is by comparison
quicker, more robust and more versatile. As a new feature, MOLE 2.0 estimates physicochemical properties of the
identified channels, i.e., hydropathy, hydrophobicity, polarity, charge, and mutability. We also assessed the variability
in physicochemical properties of eighty X-ray structures of two members of the cytochrome P450 superfamily.
Conclusion: Estimated physicochemical properties of the identified channels in the selected biomacromolecules
corresponded well with the known functions of the respective channels. Thus, the predicted physicochemical
properties may provide useful information about the potential functions of identified channels. The MOLE 2.0
software is available at http://mole.chemi.muni.cz.
Keywords: Channels, Tunnels, Pores, Protein structures, Cytochrome P450, CAM, BM3
Background
The number of known three-dimensional (3D) structures of
biomacromolecules (proteins, nucleic acids and their complexes)
has increased rapidly over recent years, enabling relationships
between structure and function to be analyzed at
an atomic level. The functions of biomacromolecules usually
depend on interactions with other biomacromolecules as
well as ions and small molecules, such as water, messenger
and endogenous compounds, pollutants and drugs, which
can occupy “otherwise empty spaces” in biomacromolecular
structures [1]. Thus, information about the nature of empty
spaces in a biomacromolecule can provide valuable insights
into its functions.
Biomacromolecular empty spaces can be classified as
pockets, cavities, voids, channels (tunnels) or pores
(Figure 1). A pocket usually refers to a shallow depression
on a biomacromolecular surface, whereas a cavity describes
a deeper pocket or cleft. If the cavity is encapsulated inside
a biomolecule (having no connection to a water accessible
surface), it is called a void. A channel or tunnel is a pathway
inside a cavity connecting an internal point (typically the
deepest apex) with an exterior. A pore is considered here as
a channel that passes through the biomacromolecule from
one point on the surface to another.
The present work focused on pores and channels because
they have been shown to play significant roles in
many biologically relevant systems. For example, internal
pores of ion channels maintain a highly selective ionic
balance between the cell interior and exterior, [2-6]
photosystem II channels are involved in photosynthesis,
[7,8] ribosomal polypeptide exit channels allow nascent
peptides to leave the ribosome during translation, [9]
and active site access/egress channels enable substrate/
product to enter/leave the occluded active sites of various
enzymes (e.g., cytochrome P450, [10-15] acetylcholinesterase,
[16-18] etc.). Information about the
nature of active site access paths can also be utilized in
biotechnology applications aimed at designing more effective
and selective enzymes [19-21]. Unquestionably,
* Correspondence: michal.otyepka@upol.cz; jaroslav.koca@ceitec.muni.cz
3
Department of Physical Chemistry, Regional Centre of Advanced
Technologies and Materials, Faculty of Science, Palacký University Olomouc,
tř. 17. listopadu 12, 771 46 Olomouc, Czech Republic
1
National Centre for Biomolecular Research, Faculty of Science and CEITECCentral
European Institute of Technology, Masaryk University Brno, Kamenice
5, 625 00 Brno-Bohunice, Czech Republic
Full list of author information is available at the end of the article
© 2013 Sehnal et al.; licensee Chemistry Central Ltd. This is an Open Access article distributed under the terms of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited.
Sehnal et al. Journal of Cheminformatics 2013, 5:39
http://www.jcheminf.com/content/5/1/39
identification and characterization of channels are fundamental
to understanding numerous biologically relevant
processes and serve as a starting point for rational
drug design, protein engineering and biotechnological
applications.
Over the last few years, numerous computational approaches
have been developed for detection and
characterization of empty spaces in biomacromolecules,
particularly proteins [22]. The main strategies used in
the developed algorithms can be grouped into four classes
[23]. The first class comprises grid-based methods,
which project biomacromolecular structures onto a 3D
grid, process the void grid voxels and connect them into
pockets or tunnels. These methods are used in numerous
software tools, such as POCKET [24], LIGSITE
[25,26], dxTuber [27], HOLLOW [28], 3V [29], CAVER
1.x [30] and CHUNNEL [31]. Sphere-filling methods
belong to a second class. These methods carpet
biomacromolecules with spheres layer by layer. A cluster
of carpeting spheres is considered a pocket. This method
is implemented in PASS [32] and SURFNET [33]. The
third class involves slice and optimization methods.
These methods split a biomacromolecular structure into
slices along a start vector defined by the user and then
optimization methods are used to determine the largest
sphere. These approaches are implemented in the software
HOLE [34] and PoreWalker [35]. The fourth class
represents methods utilizing Voronoi diagrams, in which
the shortest path is searched from a starting point to the
biomacromolecular surface. This approach was used in
the previous version of MOLE 1.x [19] and it is also utilized
in other software tools, e.g., MolAxis [36,37],
CAVER 2.0 [38] and CAVER 3.0 [39].
Here, we present an advanced and fully automatic software
tool, MOLE 2.0, based on a new, fast and robust algorithm
for finding channels and pores. MOLE 2.0
provides an improved approach for channel identification.
The algorithm introduces several preprocessing steps that
result in increased speed (up to several times faster), accuracy
(more relevant channels are identified) and robustness.
New capabilities include the computation of pores
and better identification of channel start points. It contains
extended options for starting point selection and allows
improved computation of channel profiles together
with estimation of their basic physicochemical properties.
The implemented automatic filtering of obtained channels
facilitates selection of the relevant channels. MOLE 2.0
offers an innovative user experience, as it can be used effectively
even without knowledge of the underlying algorithms
whilst at the same time allows the tunnel detection
algorithm to be tweaked interactively, such that the results
are immediately available for inspection and comparison.
MOLE 2.0 also introduces a new, intuitive and userfriendly
interface. MOLE 2.0 can be used as a stand-alone
application or as a plugin for the widely used software
PyMOL [40]. Some functionality is also available in a
platform-independent manner via the web-based application
MOLEonline 2.0 [41].
Figure 1 Classification of biomacromolecular “empty spaces”: A) pockets, B) cavities, C) channels (or tunnels), and D) pores.
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Implementation
MOLE 2.0 algorithm
The algorithm for finding channels implemented in
MOLE 2.0 involves seven steps: i) computation of the
Delaunay triangulation/Voronoi diagram of the atomic
centers, ii) construction of the molecular surface, iii)
identification of cavities, iv) identification of possible
channel start points, v) identification of possible channel
end points, vi) localization of channels, and vii) filtering
of the localized channels (Figure 2).
Step i: computing the delaunay triangulation/voronoi
diagram
In the first step, the Delaunay triangulation of the
atomic centers is computed using an incremental algorithm
that utilizes pre-sorted input points according to
the Hilbert curve [19,42]. The Voronoi diagram is then
constructed as the dual of the Delaunay triangulation.
The Voronoi diagram can be represented as a graph with
vertices corresponding to the circumcenters of the
Delaunay tetrahedrons and edges present if two tetrahedrons
share a common side (i.e., share exactly three
vertices).
Steps ii and iii: approximating the molecular surface and
identifying cavities
The molecular surface is approximated by iterative removal
of boundary tetrahedrons from the outermost
layers (i.e., tetrahedrons found at the interface between
the molecule and the external environment). Boundary
tetrahedrons produced by the triangulation are removed
in this step if they are sufficiently large to fit a sphere
with a given probe radius (tetrahedron T fits a sphere S
with probe radius r if the center C of sphere S can be
placed inside the tetrahedron and the distance to all
vertices of T is greater than or equal to the sum of r,
with the van der Waals radius of an atom corresponding
to the given vertex). Next, tetrahedrons that are too
small to fit a sphere with interior radius are removed.
Remaining tetrahedrons form one or more connected
components. We call the components that contain at
least one tetrahedron on the molecular surface cavity diagrams.
It should be noted here that the cavity diagram
is a purely geometrical concept to help identify regions
of space (volume) that can contain tunnels and only very
loosely corresponds to the cavities shown in Figure 1B).
Steps iv and v: identifying possible start and end points of
channels
The algorithm includes two ways to specify potential
channel start and end points:
 Computed: Start and end points are defined as the
centers of the deepest tetrahedrons in each cavity.
The depth of the tetrahedron is defined as the
number of Voronoi edges from the closest boundary
tetrahedron.
 User-defined: Specified by a 3D point (that can also
be defined as a centroid of several residues). Next,
cavities that have at least one tetrahedron with a
centroid within the origin radius from the userspecified
point are found. Finally, for each such
cavity, the start point is selected as the
circumsphere center of the tetrahedron closest to
the original point. Potential channel end points are
placed in the centers of certain boundary
tetrahedrons in such a way that the distance
between two end points is at least the cover radius.
This is achieved by picking the largest boundary
tetrahedron and marking it as an exit, then
Figure 2 Scheme showing the steps i-vii involved in the channel calculation algorithm (see the text for details). Illustrated for
cytochrome P450 3A4 (PDB ID: 1TQN).
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removing all boundary tetrahedrons within the cover
radius. This process is repeated until all non-exit
boundary tetrahedrons are removed.
Step vi: computing channels
Once the potential start and end points have been identified,
channels are computed as the shortest paths between all
pairs of start and end points in the same cavity diagram. To
achieve this, Dijkstra’s algorithm is used with edge weights
given by the following formula:
w eð Þ ¼
l eð Þ
d eð Þ2
þ ε
; ð1Þ
where l(e) is the length of the edge, d(e) is the distance of
the edge to the closest atom van der Waals sphere and ε is a
small number to avoid division by zero [19].
At this stage, each channel is represented by a sequence
of tetrahedrons. The next step is to approximate
the channel centerline by a natural cubic spline of the
circumsphere centers of the tetrahedrons. Additionally, a
“radius spline” is computed that determines the centerline
distance to the closest atom van der Waals sphere.
Step vii: filtering of channels
The above-described steps usually generate a large number
of channels. However, many of these channels are either
too narrow (i.e., have a bottleneck with a small
radius) to be considered relevant or are duplicated (i.e.,
too similar to each other). To obtain the most relevant
channels, the algorithm contains a filter with two
criteria.
The first criterion deals with bottlenecks using parameters
that define the maximum bottleneck length and
minimum bottleneck radius. These two parameters ensure
that there is enough room for a ligand to pass
through each region of the tunnel.
The second criterion is necessary because channels
generated using steps (i-vi) of the algorithm often have
very similar centerlines that only deviate towards the
ends of the channels near the molecular surface. Therefore,
for practical purposes, these channels can be considered
identical. To remove duplicate channels, a
parameter called the cutoff ratio is introduced. The centerlines
of each pair of tunnels are compared, and if two
channels “share” at least the cutoff ratio percentage of
the centerline, the longer one is removed.
Lining and physicochemical properties of identified
channels
The channel lining amino acids residues are the residues
that surround the centerline of the channel. The centerline
is uniformly divided into layers, and each layer is defined by
the residues lining it. A new layer starts whenever there is a
change in the list of residues lining the tunnel along its
length. The lining of the channel is then described as a sequence
of layer lining residues. For each layer, the length
(distance between the first and last atom of the layer
projected to the tunnel centerline) and radius (bottleneck)
are computed. Additionally, the orientation of each residue
is determined to check whether the residue faces the tunnel
with its backbone or side-chain moiety.
Basic physicochemical properties of protein channels are
computed from the set of lining amino acids residues. In
MOLE 2.0, the charge according to the amino acid sidechain
type (Arg, Lys +1e; Glu, Asp −1e), hydropathy [43],
hydrophobicity [44], mutability [45] and polarity [46] are
computed. The properties are calculated for the unique residues
surrounding the channel by averaging tabulated values
(Additional file 1: Table S1) for every amino acid residue
that has a side chain oriented towards the tunnel. The only
exception is charge, which is calculated as the sum of the
charges of individual amino acid side chains. For amino
acids that have their main chains oriented towards the tunnel,
tabulated values for glycine (Gly) are used to compute
the hydrophobicity and hydropathy, and the value for asparagine
(Asn) is used to evaluate polarity. Amino acids residues
that have their main chains lining the channel are not
considered when computing mutability. MOLE 2.0 also enables
calculation of the weighted physicochemical properties
(except the charge) of the channel. The weighted properties
are evaluated by applying the above methods separately for
each layer and then computing the weighted average, where
the weight is given by the length of the layer. We note that
the calculated physicochemical properties should be
interpreted with care, because the used calculation comes
from an assumption that the side chains making the channel
wall determine the internal environment of the channel.
Merging channels to pores
The MOLE 2.0 algorithm can compute pores by merging
channels. There are three modes for computing pores.
The first automatic mode evaluates pores as “channels”
between all pairs of end points in a given cavity. In the
second mode channels are computed among a set of
user-selected end points. Finally, the third mode first
computes channels from a user-defined start point and
then merges them to form a pore. This mode also imposes
a so called “pore criterion” that stipulates that the
end points of the pore must be further away than the
average length of the channels that formed the pore. In
all modes, pores that are too similar are removed using
the same criteria as for channels.
Complexity of the algorithm
The worst-case complexity of the algorithm is (N2
log
N), where N is the number of atoms in the molecule.
However, in most practical cases, the complexity is O(M
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log M), where M is the number of vertices in the
Voronoi diagram. In the worst case, M = N2
. However,
as shown by Dwyer et al. [47], in most cases M = O(N).
Thus, as a result of the use of the incremental algorithm
and Hilbert curve ordering, the complexity of calculating
the Delaunay triangulation of most molecular structures
is O(N log N). Finally, the complexity of all the
remaining steps of the algorithm is at most O(M log M).
MOLE 2.0 (Figure 3) supports protein files in PDB format.
Once the protein is loaded, the GUI provides a full
interactive 3D rendering of the protein and the option to
tune individual parameters of the channel computation.
The GUI displays information about the identified cavities
and once channels or pores are computed, a detailed
view of them can be displayed that provides
information about the channel’s profile, lining and physicochemical
properties (Figure 4). Information on the
channels can be exported in several formats, including
XML, CSV, PDB and PyMOL for enhanced visualization.
The command line version of MOLE 2.0 requires the
user to specify the input parameters in an XML file. The
output can be obtained in XML format as well as a PDB
or PyMOL script together with 3D representations of
channels that can be loaded to Jmol [48] (http://www.
jmol.org). The complete documentation can be found on
the web page http://mole.chemi.muni.cz.
Case study: properties of channels of cytochrome P450s
BM3 and P450cam
Channels were calculated using MOLE 2.0 with parameters
set as follows: minimal bottleneck radius 1.25 Å,
probe radius 3 Å, surface cover radius 10 Å and origin
radius 5 Å. The heme cofactor was used as the start
point in all structures, while all other non-protein
(“HETATM”) groups were ignored. The PDB database
contains a relatively large number of X-ray structures of
the two selected cytochrome P450s: 43 structures with
54 chains for P450cam (CAM) and 37 structures with 80
chains for P450BM3 (BM3). All crystal structures were
divided into monomers and superimposed using the
PyMOL 0.99rc program [40]. The identified channels
were sorted into specific families according to the nomenclature
of Wade and coworkers [15]: channels were
included in a particular family if they had at least one
point that trespassed a 4 Å wide cube in space assigned
to a specific area for that channel family (i.e., through
the B/C loop for channel 2e). Only the shortest channel
in each channel family was selected for each protein
Figure 3 MOLE 2.0 graphical user interface. The left side of the window contains an interactive visualization of the molecule, cavities and
computed tunnels. The panel on the right allows the user to tune the computation parameters, select which results are visualized and
export them.
Sehnal et al. Journal of Cheminformatics 2013, 5:39 Page 5 of 13
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structure. Other similar channels were designated as duplicates.
The remaining channels were visually checked
and meandering channels were also removed. Duplicates
were also excluded from the comparison of physicochemical
properties.
Results and discussion
Benchmarking study
MOLE 2.0 was compared with four other software tools:
MOLE 1.4 [19], MolAxis [36], CAVER 2.0 [38] and CAVER
3.0 [39] (beta version). The main features of the software
tools are listed in Table 1. By comparison, MOLE 2.0 provides
the richest set of input and output features and has
the advantage that both command line and graphical user
interfaces are available. The need for a start point is made
easier by the fact that MOLE 2.0 enables active sites annotated
in the Catalytic Site Atlas (CSA, http://www.ebi.ac.uk/
thornton-srv/databases/CSA/) [49] to be used as well as
automatic identification of start points in a given structure.
Data generated by MOLE 2.0 can be exported to PyMOL
[40], which is a popular visualization software, and conveniently,
MOLE 2.0 can also be called directly from PyMOL via
a plug-in module. In the MOLE 2.0 GUI, a user can select
and change the channel end points, which may facilitate the
detection of complex channels and pores. The calculation of
channels can be customized through nine parameters,
whose default values enable automatic identification of
channels in many common protein structures. Hence,
MOLE 2.0 can be readily used by a new user but provides
sufficient flexibility for an advanced user. Besides setup of
these parameters, users can adjust the surface of a molecule
and filtering of detected channels. It should be noted that
MOLE 2.0 is the only software currently available that allows
a user to compute cavities and estimate physicochemical
properties of identified channels.
The performance of all the considered software tools was
compared on a set of thirteen diverse biomacromolecules
containing several channels or pores: two RNAs, three
Figure 4 MOLE 2.0 channel details. Channel profile, i.e., plot of radius vs. distance from the start point (left), together with a list of lining amino
acid residues and physicochemical properties (right).
Table 1 Basic features of software tools for channel identification
Features Software
MOLE 2.0 MOLE 1.4 MolAxis CAVER 2.0 CAVER 3.0
Input and output Command line interface Yes Yes Yes Yes Yes
GUI Yes Web Web No No
Suggested start points from CSA Yes Yes No No No
Automatic suggestion of start points Yes No Yes No No
Possibility to set end point Yes No No No No
PyMOL export Yes Yes No Yes Yes
PyMOL plugin Yes Yes No Yes Yes
Settings of calculation Number of parameters 9 9 11 8 35
Adjustable surface of a molecule Yes No Limited No Yes
Channel filtering Yes No Limited No Yes
Cavity computation Yes No No No No
Computation of physicochemical properties Yes No No No No
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membrane proteins, the photosystem II oxygen evolving
center and seven representatives of enzymatic groups, which
have all been targeted in research studies dealing with molecular
channels (Figure 5). This comparison was carried out
on the laptop with CPU Intel Core i5-430 M 2.26 GHz and
4GB RAM, running native Windows 7. For MolAxis, the
webserver (http://bioinfo3d.cs.tau.ac.il/MolAxis/) was used.
The software tools were used to identify channels with a radius
of at least 1.25 Å along most of their length. Because
some channels may be “partially closed” by an amino acid
side chain, we also considered channels with a radius less
than 1.25 Å provided this narrowing was not longer than
3 Å. Such channels may still be biologically active because
they allow at least adaptive penetration of a water molecule
(radius ~1.4 Å) upon dynamical changes. If two channels
shared more than 70% of their length, only the shortest one
was reported. This feature eliminated very similar (duplicate)
channels. Full details of the setup of all the software tools
and post-processing of results are provided in the Additional
file 1. We used the same start points for all the software
tools (in Additional file 1: Table S2).
Both versions of MOLE (2.0 and 1.4) together with
MolAxis were able to process the largest molecular system
considered in the benchmarking, i.e., the large ribosomal
subunit containing almost 100,000 atoms.
Consistently, MOLE 2.0 displayed the shortest processing
times for both small and large systems. For small
systems, MOLE 2.0 gave similar processing times to
Figure 5 Channels found in the analyzed molecules.
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those of MolAxis (one order of magnitude faster than
the CAVER tools), whereas for large systems, MOLE 2.0
was one order of magnitude faster than MolAxis and
the CAVER tools were not able to calculate the largest
system (large ribosomal subunit 1JJ2) (Figure 6 and
Additional file 1: Table S3). Such enhancement of
processing times may be a considerable advantage if a
large number of structures need to be processed (e.g., in
analyses of structures from molecular dynamics
simulations).
MOLE 2.0 found channels in all the tested molecules,
whereas the other software tools did not detect any
channels in some cases: MOLE 1.4 and MolAxis in three
cases, CAVER 2.0 in six cases and CAVER 3.0 in five
cases (Figure 5 and Additional file 1: Table S4). All software
tools predicted a rather similar set of channels. The
software tools that had end points localized directly on
the convex hull (e.g., MOLE 1.4, CAVER 2.0) predicted
longer channels with large radii where the probe left the
biomacromolecular surface (this behavior could be easily
recognized from the “bulky ends” of the identified channels
outside the structure). In the case of gramicidin D,
which forms a transmembrane pore, MolAxis and
CAVER 2.0 predicted a clearly incorrect set of channels,
whereas the other tools identified appropriate channels
inside the pore. It should be noted that MOLE 2.0 has a
new feature of automatic identification of pores in a
biomacromolecular structure, which makes it easier to
characterize pores and avoids the need for manually
merging two (or more) channels into a single pore (a
process that cannot be overlooked if one wants to
analyze pores with software tools primarily designed for
the analysis of channels rather than pores).
For several of the molecules containing biologically
important channels/pores with known functionality and
properties, we evaluated the physicochemical properties
by MOLE 2.0 and related them to the known function of
the channel/pore (Figure 7 and Table 2).
 Gramicidin D (1GRM) is known to form a polar
pore in membranes (Figure 7A), [50] which was also
reflected in the physicochemical properties identified
using MOLE 2.0 as the polar part of the pore
surface was predicted to be 100%. However, the
predicted polarity of the pore was not high.
 The ribosomal polypeptide (1JJ2) exit channel
directs a nascent protein from the proteosynthetic
center to the outside of the ribosome [9]. MOLE 2.0
showed that the channel (Figure 7B) is highly polar
and lined by amino acids side chains bearing positive
charges (7 arginines). In addition, the channel is also
lined by 16 RNA backbone phosphate groups. This
clearly suggests a fragmental charge along the
channels, which is necessary to prevent the nascent
peptide from sticking to the channel wall inside the
ribosome.
 In the cytochrome c oxidase (1M56), MOLE 2.0
identified two channels with different polarities
(Figure 7C), which may be involved in the transfer
process required for the proper functioning of this
enzyme [51].
 The central pore (Figure 7D) of the nicotinic
acetycholine receptor (2BG9) was suggested to be
lined by 18 negatively charged amino acids, which
explains the experimentally observed selectivity for
cation permeation [52].
 The final analyzed channel was present in carbonic
anhydrase (3EYX), which can utilize inorganic
carbon sources CO2 and HCO3
−
[53]. MOLE 2.0
predicted that the channel (Figure 7E) is highly
polar, in agreement with expectations.
Taken together, the above findings indicate that physicochemical
properties may provide useful information
about the nature of the channel and its biological function.
However, the predicted physicochemical properties
may be highly sensitive to the choice of X-ray structure,
as discussed later.
Case study: properties of channels in cytochrome P450
BM3 and P450cam
Cytochrome P450s (P450) are heme-containing monoxygenases
the active sites of which are deeply buried inside
their structures [11,54] and are connected to the
exterior by access channels [15]. Hence, channels are
considered to play an important role in the metabolism
of P450 substrates [12]. Two bacterial cytochrome P450
enzymes - P450cam (CAM, which is also known as
CYP101) [55] and P450 BM3 (BM3, which is also known
Figure 6 Performance of software tools. Time taken for the
channel calculation with respect of the number of atoms in a
biomacromolecule (cf. Additional file 1: Table S3).
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as CYP102) [56]-have been extensively studied by X-ray
diffraction in both ligand-free and ligand-bound states;
to date, more than 80 structures have been published.
Thus, both cytochrome P450s are suitable systems for
testing the performance of MOLE 2.0 in predicting the
physicochemical properties of channels.
Channel families
More channels were identified in BM3 than in CAM
structures. As each independent chain within an asymmetric
unit can have different channels [57], it is worthwhile
testing all chains within a crystal structure for
channel identification. Therefore, we analyzed all 80
chains within the 37 BM3 crystal structures and 54
chains within the 43 CAM crystal structures. It should
be noted that CAM can be found in either closed or
open states, which differ in the conformation of the F/G
loop. Channels were found (using the setup described in
the Methods section) only in the open CAM structures
(i.e., only in 5 crystal structures: 1K2O, 1PHA, 1QMQ,
1RE9 and 1RF9).
CYP structures contain several different types of active
site access channels, which have been classified
according to their position in relation to conserved secondary
structures in the cytochrome P450 fold by Wade
and coworkers [15]. There are two specifically named
channels, which are considered to enable the exchange
of water molecules between the active site and the enzyme
exterior, i.e., the water channel neighboring the Bhelix,
which is the only channel leading to the CYP
proximal side [12], and the solvent channel between the
β4 sheet, F and I helices. Other channels are labeled by
numerals and only those that are present either in CAM
or BM3 structures are noted here. Channels close to the
B/C and F/G loops belong to the 2× family–channel 2a
is located close to the β1 sheet, F/G and B/B’ loops and
it has been suggested to be the main access channel of
CAM [58,59]; channel 2f neighbors channel 2a and the
solvent channel and it is located between the β5 sheet
and F/G loop; channel 2b also neighbors channel 2a and
is located between the B/C loop, β1 and β3 sheets; channel
2c neighbors channel 2a and is located close to the
B/C loop, G and I helices; channel 2ac connects channels
2a and 2c and is located between the B/C and F/G
loops; channel 2d is located between the N-terminus
and A helix (Figure 8).
Figure 7 Found channels. A–gramicidin D (1GRM), B–large ribosomal
subunit (1JJ2), C–cytochrome c oxidase (1M56), D–nicotinic acetylcholine
receptor (2BG9), E–carbonic anhydrase (3EYX) by MOLE 2.0. Nonpolar
channel in cytochrome c oxidase structure is shown in blue, polar
channel is shown in red.
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Variability of results
We identified 209 channels along with 73 duplicates
within the 80 BM3 chains. Such a large number of channels
allowed us to analyze the variability in geometrical
or physicochemical properties of the identified channels
between individual X-ray structures of a specific protein.
The variability was evaluated as the standard deviation
calculated for each channel type (W, S, 2a, 2b, 2c, 2ac,
2d, 2f). Then, the total standard deviation of a given
property was calculated as a channel-number weighted
average of the channels’ individual standard deviations.
We also calculated the relative variability as the total
standard deviation divided by the channel-number
weighted mean value of a given property.
Table 2 Physicochemical properties of the studied biologically important channels/pores
PDB Length (Å) Hydropathy Hydrophobicity Polarity Charge Mutability Polar length Nonpolar length
1GRM 25.2 −0.4 −0.8 3.38 0 (0–0) - 100% 0%
1JJ2 79.8 −1.7 −0.6 20.8 4 (6–2)c
68 92% 8%
1M56a
36.2 3.0 1.0 0.6 0 83 4% 96%
1M56b
41.9 1.3 0.8 12.3 0 84 48% 52%
2BG9 143.7 −1.1 −0.2 22.3 −8 (10–18) 85 81% 19%
3EYX 11.5 0.1 0.1 17.0 1 (2–1) 73 100% 0%
a
the nonpolar channel in Figure 7C (blue), b
the polar channel in Figure 7C (red), c
MOLE 2.0 counts the charge on amino acids only, whereas the ribosome
channel is also lined by 16 phosphates.
Figure 8 Cytochrome P450 access and egress channels calculated by MOLE 2.0. Channels were imposed on a cartoon representation of
structures of cytochrome P450 BM3 (in views A and B; PDB structure 1BU7 was used) and cytochrome P450 CAM (in views C and D; PDB 1RE9
was used). Important secondary structures are colored as follows: the I helix is yellow, the F/G-loop is orange, the B/C-loop is red and the heme
cofactor is shown as black balls. The images on the left (A and C) show views from the side in a plane horizontal to the plane of the heme; the
images on the right (B and D) show views from above the distal side. Arrows indicate the viewpoints of the respective images. Channels are
shown as connected spheres colored as follows: on the proximal side, channel W is colored in cyan; on the distal side channel S is shown in red;
2a–blue; 2ac–brown; 2b–light green; 2c–green; 2d–pink; 2f–magenta.
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 The channel length variation was usually between
10% and 20% of the average channel length, i.e.,
around 5 Å in the case of BM3.
 The bottleneck radius showed a deviation of about
± 0.23 Å (less than 15%).
 The variability in the distance of bottlenecks from
the start point was rather large, i.e., up to 8 Å (53%).
This is not surprising because the position of
bottlenecks is sensitive to the actual structure of the
channel (and conformation of the lining amino acids
side chains), i.e., it depends on the choice of X-ray
structure [14]. The large variability in the position of
bottlenecks has been also identified in molecular
dynamics simulations [60]. Based on the large
variability of this parameter, we do not recommend
that this parameter is viewed as a robust feature of
any channel found in only one crystal structure.
 The charge along a channel exhibited a deviation in
the order of 0.6 e (about 21%).
 The hydropathy index of amino acids ranges
between hydrophilic (−4.5) and hydrophobic (4.5).
The variation of this value was in the order of 0.5
(less than 9%).
 The hydrophobicity index is a similar measure to
the hydropathy index but has a smaller range of
values between hydrophilic (−1.14) and hydrophobic
amino acids (1.81). It exhibited a lower variation
than the hydropathy index of about 0.14. However,
its relative error was similar (less than 9%). It also
seemed to be more consistent between systems as
values for the same types of channels did not differ
much between both proteins.
 Polarity values range from 0 for nonpolar amino
acids through values of about 2 for polar amino
acids towards values around 50 for charged amino
acids. Polarity can therefore easily distinguish
between polar channels and channels lined with
charged amino acids. For instance, the solvent
channel in BM3 was predicted to have a similar
charge to that of channel 2f (−0.7 vs. -0.4). However,
the solvent channel showed a significantly higher
polarity index (9.4 vs. 2.0 for channel 2f). This
indicates that the solvent channel is lined with more
highly charged residues that cancel each other out,
whereas channel 2f is mostly lined with nonpolar
and polar residues. The variation of the polarity was
in the order of ± 2.5. The relative error was about
47%. However, this value should be interpreted with
care owing to the low polarity of the analyzed
channels (the channel number weighted mean value
was only 6.4 out of a possible range of 0–50).
 Mutability values range from the lowest mutability
of 44 for Cys to a value of 177 for the most easily
interchangeable Ser. The variation of mutability was
in the order of ±3 and the relative error was the
lowest of all the indices mentioned (less than 4%).
The results showed that the geometrical properties
and physicochemical properties of the found channels
typically varied by less than 20% except for the distance
of bottlenecks from the starting point.
Properties of CAM and BM3 channels
From a geometrical perspective, the most open channels
were usually found within the open CAM structures,
particularly 2a channels, which have a bottleneck radius
larger than 2.6 Å. Channels belonging to the 2× family
(mainly channels 2a, 2f, and in the case of BM3, channel
2b) were predicted to have bottleneck radii large enough
to allow substrates/products to pass (> 2 Å) in both the
CAM and BM3 structures, i.e., comparable or even larger
than the solvent channel bottleneck radius (> 1.4 Å,
radius of water molecule). The most closed channel was
the water channel. However this does not necessarily
mean that small molecules cannot pass through it as it
might partially open to allow molecules to enter due to
bottleneck fluctuations, as shown previously for the 2b
channel within the structure of mammalian cytochrome
P450 2A6 [14]. It is also worth noting that the solvent
channel was predicted to be ~7 Å longer in CAM than
in BM3, whereas other channels were typically longer in
BM3. In contrast, the most open channels 2a and 2f in
CAM were ~12 Å shorter than in BM3. However, this
was partly because we used a probe radius of 3 Å to
construct the overall shape of the protein, and therefore
we only detected channels below this radius.
The water and solvent channels were clearly the most
hydrophilic. The hydrophilicity also appeared to correlate
with the polarity of the channels because the water
and solvent channels were also predicted to be the most
polar channels. The higher polarity index indicates that
polar and charged amino acid residues line the solvent
and water channels. On the other hand, the mutability
index did not differ significantly between the individual
channels. The mutability was also relatively high, which
may indicate that the channels are lined with amino
acids that can be relatively easily interchanged. This
finding is in accord with the relatively low sequence
homology between individual members of CYP family
[60].
Ranking the channels according to their average
hydrophobicity supported the hypothesis that the water
and solvent channels are involved in water transfer into
the active site [61], as the water channel was the most
hydrophilic channel in both the CAM and BM3 structures,
followed by the solvent channel (according to the
hydropathy and hydrophobicity indices). BM3 was also
predicted to contain the rather polar channel 2b. The
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more hydrophobic channels 2f and 2a were present in
both the CAM and BM3 structures. Channels 2ac and
2d were more hydrophobic still. Finally, the most hydrophobic
channel was channel 2c. However, the last three
channels were found rather infrequently, i.e., only
present in some BM3 structures (Additional file 1:
Tables S5 and S6).
Conclusions
We present the advanced software tool MOLE 2.0
designed to analyze molecular channels and pores. We
benchmarked MOLE 2.0 against similar software tools
and showed that by comparison it is faster and capable
of analyzing large and complex systems containing up to
hundreds of thousands of atoms. As a new feature,
MOLE 2.0 estimates physicochemical properties of the
identified channels. We compared the estimated physicochemical
properties with the known functions of selected
biomacromolecular channels and concluded that
the properties correlated with the functions. We also
assessed the variability of physicochemical properties by
analyzing a large number of X-ray structures of two
members of the cytochrome P450 superfamily. We
propose that the physicochemical properties may provide
useful clues about the potential functions of identified
channels. The software is available free of charge at
http://mole.chemi.muni.cz.
Availability and requirements
Project name: MOLE 2.0
Project home page: http://mole.chemi.muni.cz
Operating systems: Mac OS, Linux, Windows
Programming language: C#
Other requirements: NET 4.0 for Windows based systems,
Mono framework 2.10. or newer (http://www.
mono-project.com) for other OS.
License: MOLE 2.0 license
Restrictions: free of charge
Additional file
Additional file 1: Table S1. Physicochemical properties of amino acids
residues, setup of all software tools used for the benchmarking study.
Table S2. Channel starting points used in the benchmarking study.
Table S3. Duration of channel calculations for all biomacromolecules
used in the benchmarking study. Table S4. Numbers of channels found
in the analyzed molecules in the benchmarking study. Table S5.
Comparison of geometrical and physicochemical properties of channels
detected in CAM structures. Table S6. Comparison of geometrical and
physicochemical properties of channels detected in BM3 structures.
Abbreviations
BM3 Cytochrome P450 BM3; CAM Cytochrome P450cam; all amino acids are
represented by their respective three-letter abbreviations.
Competing interests
The authors declare that they have no competing interests.
Authors’ contributions
All authors contributed extensively to the work presented in this paper.
DS wrote MOLE 2.0 application. All authors read and approved the final
manuscript.
Acknowledgement
This work was supported by the Czech Science Foundation (GD301/09/H004
to CMI, P208/12/G016 to MO, P303/12/P019 to KB) and the Operational
Program Research and Development for Innovations–European Regional
Development Fund (CZ.1.05/2.1.00/03.0058 to MO, KB, PB and CZ.1.05/1.1.00/
02.0068 to JK and RSV), European Social Fund (CZ.1.07/2.3.00/20.0017 to KB,
PB) and a student project of Palacký University (PrF_2013_028 to VN). C.M.I.
and D.S. thank Brno City Municipality for financial support provided through
the program Brno Ph.D. Talent. Access to the MetaCentrum supercomputing
facilities provided under the research intent MSM6383917201 is gratefully
acknowledged.
Author details
1
National Centre for Biomolecular Research, Faculty of Science and CEITECCentral
European Institute of Technology, Masaryk University Brno, Kamenice
5, 625 00 Brno-Bohunice, Czech Republic. 2
Faculty of Informatics, Masaryk
University Brno, Botanická 68a, 602 00 Brno, Czech Republic. 3
Department of
Physical Chemistry, Regional Centre of Advanced Technologies and Materials,
Faculty of Science, Palacký University Olomouc, tř. 17. listopadu 12, 771 46
Olomouc, Czech Republic.
Received: 4 April 2013 Accepted: 13 August 2013
Published: 16 August 2013
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doi:10.1186/1758-2946-5-39
Cite this article as: Sehnal et al.: MOLE 2.0: advanced approach for
analysis of biomacromolecular channels. Journal of Cheminformatics
2013 5:39.
Sehnal et al. Journal of Cheminformatics 2013, 5:39 Page 13 of 13
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Predicting pKa values from EEM atomic
charges
150
Svobodov´a Vaˇrekov´a et al. Journal of Cheminformatics 2013, 5:18
http://www.jcheminf.com/content/5/18
RESEARCH ARTICLE Open Access
Predicting pKa values from EEM atomic
charges
Radka Svobodov´a Vaˇrekov´a1, Stanislav Geidl1, Crina-Maria Ionescu1, Ondˇrej Skˇrehota1,
Tom´aˇs Bouchal1, David Sehnal1, Ruben Abagyan2 and Jaroslav Koˇca1*
Abstract
The acid dissociation constant pKa is a very important molecular property, and there is a strong interest in the
development of reliable and fast methods for pKa prediction. We have evaluated the pKa prediction capabilities of
QSPR models based on empirical atomic charges calculated by the Electronegativity Equalization Method (EEM).
Speciﬁcally, we collected 18 EEM parameter sets created for 8 diﬀerent quantum mechanical (QM) charge calculation
schemes. Afterwards, we prepared a training set of 74 substituted phenols. Additionally, for each molecule we
generated its dissociated form by removing the phenolic hydrogen. For all the molecules in the training set, we then
calculated EEM charges using the 18 parameter sets, and the QM charges using the 8 above mentioned charge
calculation schemes. For each type of QM and EEM charges, we created one QSPR model employing charges from the
non-dissociated molecules (three descriptor QSPR models), and one QSPR model based on charges from both
dissociated and non-dissociated molecules (QSPR models with ﬁve descriptors). Afterwards, we calculated the quality
criteria and evaluated all the QSPR models obtained. We found that QSPR models employing the EEM charges proved
as a good approach for the prediction of pKa (63% of these models had R2 > 0.9, while the best had R2 = 0.924). As
expected, QM QSPR models provided more accurate pKa predictions than the EEM QSPR models but the diﬀerences
were not signiﬁcant. Furthermore, a big advantage of the EEM QSPR models is that their descriptors (i.e., EEM atomic
charges) can be calculated markedly faster than the QM charge descriptors. Moreover, we found that the EEM QSPR
models are not so strongly inﬂuenced by the selection of the charge calculation approach as the QM QSPR models.
The robustness of the EEM QSPR models was subsequently conﬁrmed by cross-validation. The applicability of EEM
QSPR models for other chemical classes was illustrated by a case study focused on carboxylic acids. In summary, EEM
QSPR models constitute a fast and accurate pKa prediction approach that can be used in virtual screening.
Keywords: Dissociation constant, Quantitative structure-property relationship, QSPR, Partial atomic charges,
Electronegativity equalization method, EEM, Quantum mechanics, QM
Background
The acid dissociation constant pKa is an important molecular
property, and its values are of interest in pharmaceutical,
chemical, biological and environmental research.
The pKa values have found application in many areas,
such as the evaluation and optimization of candidate
drug molecules [1-3], ADME proﬁling [4,5], pharmacokinetics
[6], understanding of protein-ligand interactions
[7,8], etc.. Moreover, the key physicochemical properties
*Correspondence: jkoca@chemi.muni.cz
1National Centre for Biomolecular Research, Faculty of Science and CEITEC Central
European Institute of Technology, Masaryk University Brno, Kamenice
5, 625 00 Brno-Bohunice, Czech Republic
Full list of author information is available at the end of the article
like lipophilicity, solubility, and permeability are all pKa
dependent. For these reasons, pKa values are important
for virtual screening. Therefore, both the research community
and pharmaceutical companies are interested in
the development of reliable and above all fast methods for
pKa prediction.
Several approaches for pKa prediction have been developed
[8-11], namely LFER (Linear Free Energy Relationships)
methods [12,13], database methods, decision tree
methods [14], ab initio quantum mechanical calculations
[15,16], ANN (artiﬁcial neural networks) methods [17] or
QSPR (quantitative structure-property relationship) modelling
[18-20]. However, pKa values remain one of the
most challenging physicochemical properties to predict.
© 2013 Svobodov´a Vaˇrekov´a et al.; licensee Chemistry Central Ltd. This is an Open Access article distributed under the terms of
the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use,
distribution, and reproduction in any medium, provided the original work is properly cited.
Svobodov´a Vaˇrekov´a et al. Journal of Cheminformatics 2013, 5:18 Page 2 of 16
http://www.jcheminf.com/content/5/18
A promising approach for pKa prediction is to use QSPR
models which employ partial atomic charges as descriptors
[21-24].
The partial atomic charges cannot be determined experimentally
and they are also not quantum mechanical
observables. For this reason, the rules for determining
partial atomic charges depend on their application (e.g.
molecular mechanics energy, pKa etc.), and many diﬀerent
methods have been developed for their calculation. The
charge calculation methods can be divided into two main
groups, namely quantum mechanical (QM) approaches
and empirical approaches.
The quantum mechanical approaches ﬁrst calculate a
molecular wave function by a combination of some theory
level (e.g., HF, B3LYP, MP2) and basis set (e.g., STO-3G,
6–31G*), and then partition this wave function among the
atoms (i.e., the assignment of a speciﬁc part of the molecular
electron density to each atom). This partitioning can be
done using an orbital-based population analysis, such as
MPA (Mulliken population analysis) [25,26], L¨owdin population
analysis [27] or NPA (natural population analysis)
[28]. Other partitioning approaches are based on a wavefunction-dependent
physical observable. Such approaches
are, for example, AIM (atoms in molecules) [29], Hirshfeld
population analysis [30] and electrostatic potential ﬁtting
methods like CHELPG [31] or MK (Merz-Singh-Kollman)
[32]. Another partitioning method is the mapping of QM
atomic charges to reproduce charge-dependent observables
(e.g., CM1, CM2, CM3 and CM4) [33].
Empirical approaches determine partial atomic charges
without calculating a quantum mechanical wave function
for the given molecule. Therefore they are markedly
faster than QM approaches. One of the ﬁrst empirical
approaches developed, CHARGE [34], performs a breakdown
of the charge transmission by polar atoms into
one-bond, two-bond, and three-bond additive contributions.
Most of the other empirical approaches have been
derived on the basis of the electronegativity equalization
principle. One group of these empirical approaches invoke
the Laplacian matrix formalism, and result in a redistribution
of electronegativity. Such methods are PEOE (partial
equalization of orbital electronegativity) [35], GDAC
(geometry-dependent atomic charge) [36], KCM (Kirchhoﬀ
charge model) [37], DENR (dynamic electronegativity
relaxation) [38] or TSEF (topologically symmetric
energy function) [38]. The second group of approaches
use full equalization of orbital electronegativity, and
such approaches are, for example, EEM (electronegativity
equalization method) [39], QEq (charge equilibration)
[40] or SQE (split charge equilibration) [41]. The empirical
atomic charge calculation approaches can also be divided
into ’topological’ and ’geometrical’. Topological charges
are calculated using the 2D structure of the molecule, and
they are conformationally independent (i.e., CHARGE,
PEOE, KCM, DENR, and TSEF). Geometrical charges are
computed from the 3D structure of the molecule and they
consider the inﬂuence of conformation (i.e., GDAC, EEM,
Qeq, and SQE).
The prediction of pKa using QSPR models which
employ QM atomic charges was described in several
studies [21-24], which have analyzed the precision of
this approach and compared the quality of QSPR models
based on diﬀerent QM charge calculation schemes.
All these studies show that QM charges are successful
descriptors for pKa prediction, as the QSPR models based
on QM atomic charges are able to calculate pKa with high
accuracy. The weak point of QM charges is that their
calculation is very slow, as the computational complexity
is at least θ(E4), where E is the number of electrons in
the molecule. Therefore, pKa prediction by QSPR models
based on QM charges cannot be applied in virtual screening,
as it is not feasible to compute QM atomic charges
for hundreds of thousands of compounds in a reasonable
time. This issue can be avoided if empirical charges are
used instead of QM charges. A few studies were published,
which give QSPR models for predicting pKa using topological
empirical charges as descriptors (speciﬁcally PEOE
charges) [22,42,43]. But these models provided relatively
weak predictions.
The geometrical charges seem to be more promissing
descriptors, because they are able to take into consideration
the inﬂuence of the molecule’s conformation on
the atomic charges. The conformation of the atoms surrounding
the dissociating hydrogens strongly inﬂuences
the dissociation process, and also the atomic charges.
The EEM method is a geometrical empirical charge
calculation approach which can be useful for pKa prediction
by QSPR. This approach calculates charges using the
following equation system:
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
B1
κ
R1,2
. . . κ
R1,N
−1
κ
R2,1
B2 . . . κ
R2,N
−1
...
...
...
...
...
κ
RN,1
κ
RN,2
. . . BN −1
1 1 . . . 1 0
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
q1
q2
...
qN
χ
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
=
⎛
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎝
−A1
−A2
...
−AN
Q
⎞
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎠
(1)
where qi is the charge of atom i; Ri,j is the distance between
atoms i and j; Q is the total charge of the molecule; N is
the number of atoms in the molecule; χ is the molecular
electronegativity, and Ai, Bi and κ are empirical parameters.
These parameters are obtained by a parameterization
process, which uses QM atomic charges to calculate a
set of parameters for which EEM best reproduces these
QM charges. EEM is very popular, and despite the fact
that it was developed more than twenty years ago, new
Svobodov´a Vaˇrekov´a et al. Journal of Cheminformatics 2013, 5:18 Page 3 of 16
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parameterizations [39,44-50] and modiﬁcations [47,51,52]
of EEM are still under development. Its accuracy is comparable
to the QM charge calculation approach for which
it was parameterized. Additionally, EEM is very fast, as
its computational complexity is θ(N3), where N is the
number of atoms in the molecule.
Therefore, in the present study, we focus on pKa prediction
using QSPR models which employ EEM charges.
Speciﬁcally, we created and evaluated QSPR models based
on EEM charges computed using 18 EEM parameter sets.
We also compared these QSPR models with corresponding
QSPR models which employ QM charges computed
by the same charge calculation schemes used for EEM
parameterization.
Methods
EEM parameter sets
In our study, we used all EEM parameters published till
now. Speciﬁcally, we found 18 diﬀerent EEM parameters
sets, published in 8 diﬀerent articles [39,44-50]. The
parameters cover two QM theory levels (HF and B3LYP),
two basis sets (STO-3G and 6–31G*) and six population
analyses (MPA, NPA, Hirshfeld, MK, CHELPG, AIM).
Unfortunately, only some combinations of QM theory levels,
basis sets and population analyses are available. On
the other hand, more parameter sets were published for
some combinations (i.e., 6 parameter sets for HF/STO-
3G/MPA). All the parameter sets include parameters for
C, O, N and H. Some sets include also parameters for S,
P, halogens and metals. Most of the sets do not include
parameters for C and N bonded by triple bond. Summary
information about all these parameter sets is given
in Table 1.
EEM charge calculation
The EEM charges were calculated by the program EEM
SOLVER [53] using each of the 18 EEM parameter sets.
QM charge calculation
We calculated QM atomic charges for all the combinations
of QM theory level, basis set and population analysis
for which we have EEM parameters (see Table 1).
Speciﬁcally, atomic charges were calculated for these eight
QM approaches: HF/STO-3G/MPA, HF/6–31G*/MK,
and B3LYP/6–31G* with MPA, NPA, Hirshfeld, MK,
CHELPG and AIM). The QM charge calculations were
carried out using Gaussian09 [54]. In the case of AIM population
analysis, the output from Gaussian09 was further
processed by the software package AIMAll [55].
Data set for phenols
There are two main ways to create a QSPR model for a
feature to be predicted. The ﬁrst is to create as general
a model as possible, with the risk that the accuracy of
such a model may not be high. The second approach
is to develop more models, each of them being dedicated
to a certain class of compounds. Here we took the
second approach, following a similar methodology as in
previous studies [21-24]. Speciﬁcally, we focus on substituted
phenols, because they are the most common test set
molecules employed in the evaluation of novel pKa prediction
approaches [21-24,56-58]. Our data set contains the
3D structures of 74 distinct phenol molecules. This data
set is of high structural diversity and it covers molecules
with pKa values from 0.38 to 11.1. The molecules were
obtained from the NCI Open Database Compounds [59]
and their 3D structures were generated by CORINA 2.6
[60], without any further geometry optimization. Our data
set is a subset of the phenol data set used in our previous
work related to pKa prediction from QM atomic
charges [24]. The subset is made up of phenols which
contain only C, O, N and H, and none of the molecules
contain triple bonds. This limitation is necessary, because
the EEM parameters of all 18 studied EEM parameter sets
are available only for such molecules (see Table 1). For
each phenol molecule from our data set, we also prepared
the structure of the dissociated form, where the hydrogen
is missing from the phenolic OH group. This dissociated
molecule was created by removing the hydrogen from
the original structure without subsequent geometry optimization.
The list of the molecules, including their names,
NCS numbers, CAS numbers and experimental pKa values,
can be found in the (Additional ﬁle 1: Table S1a).
The SDF ﬁles with the 3D structures of molecules and
their dissociated forms are also in the (Additional ﬁle 2:
Molecules).
Data set for carboxylic acids
An aspect which is very important for the applicability of
the pKa prediction approach is its transferability to other
chemical classes. In this work, we provide a case study
showing the performance of the approach on carboxylic
acids, which are also very common testing molecules for
pKa prediction approaches [19-21,43]. The data set contains
71 distinct molecules of carboxylic acids and their
dissociated forms. The 3D structures of these molecules
were obtained in the same way as for the phenols. The list
of the molecules, including their names, NCS numbers,
CAS numbers and experimental pKa values can be found
in the (Additional ﬁle 3: Table S1b). The SDF ﬁles with the
3D structures of the molecules and their dissociated forms
are also included in the (Additional ﬁle 2: Molecules).
pKa values
The experimental pKa values were taken from the
Physprop database [61].
Svobodov´a Vaˇrekov´a et al. Journal of Cheminformatics 2013, 5:18 Page 4 of 16
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Table 1 Summary information about the EEM parameter sets used in the present study
QM theory level PA EEM parameter Published by Year of Elements included
+ basis set set name publication
HF/STO-3G MPA Svob2007 cbeg2 Svobodova et al. [44] 2007 C, O, N, H, S
Svob2007 cmet2 Svobodova et al. [44] 2007 C, O, N, H, S, Fe, Zn
Svob2007 chal2 Svobodova et al. [44] 2007 C, O, N, H, S, Br, Cl, F, I
Svob2007 hm2 Svobodova et al. [44] 2007 C, O, N, H, S, F, Cl, Br, I, Fe, Zn
Baek1991 Baekelandt et al. [45] 1991 C, O, N, H, P, Al, Si
Mort1986 Mortier et al. [39] 1986 C, O, N, H
HF/6–31G* MK Jir2008 hf Jirouskova et al. [46] 2008 C, O, N, H, S, F, Cl, Br, I, Zn
B3LYP/6–31G* MPA Chaves2006 Chaves et al. [47] 2006 C, O, N, H, F
Bult2002 mul Bultinck et al. [48] 2002 C, O, N, H, F
NPA Ouy2009 Ouyang et al. [49] 2009 C, O, N, H, F
Ouy2009 elem Ouyang et al. [49] 2009 C, O, N, H, F
Ouy2009 elemF Ouyang et al. [49] 2009 C, O, N, H, F
Bult2002 npa Bultinck et al. [48] 2002 C, O, N, H, F
Hir. Bult2002 hir Bultinck et al. [48] 2002 C, O, N, H, F
MK Jir2008 mk Jirouskova et al. [46] 2008 C, O, N, H, S, F, Cl, Br, I, Zn
Bult2002 mk Bultinck et al. [48] 2002 C, O, N, H, F
CHELPG Bult2002 che Bultinck et al. [48] 2002 C, O, N, H, F
AIM Bult2004 aim Bultinck et al. [50] 2004 C, O, N, H, F
Descriptors and QSPR models for phenols
Our descriptors were atomic charges. We analyzed two
types of QSPR models, namely QSPR models with three
descriptors (3d QSPR models) and QSPR models with ﬁve
descriptors (5d QSPR models).
The 3d QSPR models used those descriptors which
proved to be the most relevant for pKa prediction in our
previous study [24]. Therefore these descriptors were the
atomic charge of the hydrogen atom from the phenolic
OH group (qH), the charge on the oxygen atom from
the phenolic OH group (qO), and the charge on the carbon
atom binding the phenolic OH group (qC1). These
descriptors were used to establish the QSPR models by the
general equation:
pKa = pH · qH + pO · qO + pC1 · qC1 + p (2)
where pH, pO, pC1 and p are parameters of the QSPR
model (i.e., constants derived by multiple linear regression).
The 5d QSPR models employ the above mentioned
descriptors qH, qO and qC1 and additionally also
the charge on the phenoxide O− from the dissociated
molecule (qOD), and the charge on the carbon atom binding
this oxygen (qC1D). Using the charges from the dissociated
molecules for pKa prediction was inspired by the
work of Dixon et al. [19]. The equation of the 5d QSPR
models is therefore:
pKa =pH·qH+pO·qO+pC1·qC1+pOD·qOD+pC1D·qC1D+p
(3)
where pH, pO, pC1, pOD, pC1D and p are parameters of the
QSPR model.
Descriptors and QSPR models for carboxylic acids
The descriptors were again atomic charges and, similarly
as for phenols, two types of QSPR models were developed
and evaluated. Speciﬁcally, QSPR models with four
descriptors (4d QSPR models) and QSPR models with
seven descriptors (7d QSPR models). The 4d QSPR models
used similar descriptors as the 3d models for phenols the
atomic charge of the hydrogen atom from the COOH
group (qH), the charge on the hydrogen bound oxygen
atom from the COOH group (qO), and the charge on the
carbon atom binding the COOH group (qC1). Additionally,
also the charge of the second carboxyl oxygen (qO2) is
included. These 4d QSPR models are represented by the
equation:
pKa = pH · qH + pO · qO + pO2 · qO2 + pC1 · qC1 + p (4)
where pH, pO, pO2, pC1 and p are parameters of the QSPR
model. The 7d QSPR models employ also charges from
the dissociated forms, namely the charge on the carboxyl
oxygens (qOD, qO2D) and the charge on the carboxylic carbon
atom (qC1D). The equation of the 7d QSPR models is
therefore:
pKa = pH · qH + pO · qO + pO2 · qO2 + pC1 · qC1
+ pOD · qOD + pO2D · qO2D + pC1D · qC1D + p
(5)
Svobodov´a Vaˇrekov´a et al. Journal of Cheminformatics 2013, 5:18 Page 5 of 16
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where pH, pO, pO2, pC1, pOD, pO2D, pC1D and p are
parameters of the QSPR model.
QSPR model parameterization
The parameterization of the QSPR models was done by
multiple linear regression (MLR) using the software tool
QSPR Designer [62].
Results and discussion
QM and EEM QSPR models for phenols
We prepared one 3d QSPR model and one 5d QSPR model
using atomic charges calculated by each of the above mentioned
18 EEM parameter sets. These models are denoted
3d or 5d EEM QSPR models. Additionally, we created
one 3d and one 5d QSPR model using atomic charges
calculated by each of the corresponding 8 QM charge
calculation approaches (denoted as 3d or 5d QM QSPR
models). The data set of 74 phenol molecules was used
for the parameterization of the QSPR models, and the
obtained models were validated for all molecules in the
data set.
The parameterization of the 3d EEM QSPR models
showed that several molecules in the data set perform
as outliers. For this reason, we created also EEM QSPR
models without outliers (i.e., EEM QSPR models for
which parameterization was done using a data set that
excluded the previously observed outliers). These models
are denoted 3d EEM QSPR WO models. We classiﬁed
as outliers 10% of the molecules from our data set, which
had the highest Cook’s square distance. Therefore the 3d
EEM QSPR WO models were parameterized using 67
molecules, and their validation was also done on the data
set excluding outliers.
The quality of the QSPR models, i.e. the correlation
between experimental pKa and the pKa calculated by each
model, was evaluated using the squared Pearson correlation
coeﬃcient (R2), root mean square error (RMSE), and
average absolute pKa error ( ), while the statistical criteria
were the standard deviation of the estimation (s) and
Fisher’s statistics of the regression (F).
Table 2 contains the quality criteria (R2, RMSE, ) and
statistical criteria (s and F) for all the QSPR models analyzed.
All these models are statistically signiﬁcant at p =
0.01. Since our data sets contained 74 and 67 molecules,
respectively, the appropriate F value to consider was that
for 60 samples. Thus, the 3d QSPR models are statistically
signiﬁcant (at p = 0.01) when F > 4.126 and the 5d
QSPR models when F > 3.339. Figure 1 summarizes the
R2 of all QSPR models for ease of visual comparison, and
Tables 3 and 4 provide a comparison of the models from
speciﬁc points of view. The parameters of the QSPR models
are summarized in the (Additional ﬁle 4: Table S2) and
all charge descriptors and pKa values are contained in the
(Additional ﬁle 5: Table S6). The most relevant graphs of
correlation between experimental and calculated pKa are
visualized in Figure 2.
Prediction of pKa using EEM charges
The key question we wanted to answer in this paper
is whether EEM QSPR models are applicable for pKa
prediction. For this purpose we selected a set of phenol
molecules and generated QSPR models which used
EEM atomic charges as descriptors. We then evaluated
the accuracy of these models by comparing the predicted
pKa values with the experimental ones. The results (see
Tables 2 and 3, Figure 1) clearly show that QSPR models
based on EEM charges are indeed able to predict the
pKa of phenols with very good accuracy. Namely, 63% of
the EEM QSPR models evaluated in this study were able
to predict pKa with R2 > 0.9. The average R2 for all 54
EEM QSPR models considered was 0.9, while the best
EEM QSPR model reached R2 = 0.924. Our ﬁndings thus
suggest that EEM atomic charges may prove as eﬃcient
QSPR descriptors for pKa prediction. The only drawback
of EEM is that EEM parameters are currently not available
for some types of atoms. Nevertheless, EEM parameterization
is still a topic of research, therefore more general
parameter sets are being developed.
Improvement of EEM QSPR models by removing outliers
The quality of 3d EEM QSPR models can be markedly
increased by removing the outliers. In this case, the models
have average R2 = 0.911 and 83% of them have R2 >
0.9. The disadvantage of these models is that they are not
able to cover the complete data set (i.e., 10% of molecules
must be excluded as outliers).
On the other hand, the outliers are similar for all EEM
QSPR models. For example, while 16 molecules from our
data set are outliers for at least one parameter set, 10 out of
these 16 molecules are outliers for ﬁve or more parameter
sets. From the chemical point of view, most of the outliers
contain one or more nitro groups. This may be related
to reported lower accuracy of EEM for these groups [48].
In general one limitation of the 3d EEM QSPR models is
that they are very sensitive to the quality of EEM charges.
Therefore, if the EEM charges are inaccurate for certain
compounds or class of compounds, the 3d QSPR models
based on these EEM charges will have lower performance
for these compounds or class of compounds. In addition, a
lower experimental accuracy of these pKa values may also
be a reason for low performance in some cases. A table
containing information about outlier molecules is given in
the (Additional ﬁle 6: Table S3).
Improvement of EEM QSPR models by adding descriptors
Our ﬁrst EEM QSPR models contained three descriptors
(3d), namely atomic charges originating from the nondissociated
molecule. Nonetheless, in our study we found
Svobodov´a Vaˇrekov´a et al. Journal of Cheminformatics 2013, 5:18 Page 6 of 16
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Table 2 Quality criteria and statistical criteria for all the QSPR models analyzed in the present study and focused on
phenols
QM theory level PA EEM parameter QSPR model R2 RMSE s F
+ basis set set name
HF/STO-3G MPA - 3d QM 0.9515 0.490 0.388 0.504 458
- 5d QM 0.9657 0.412 0.310 0.430 358
Svob2007 cbeg2 3d EEM 0.8671 0.812 0.571 0.835 152
3d EEM WO 0.9239 0.482 0.382 0.497 255
5d EEM 0.9179 0.638 0.481 0.666 152
Svob2007 cmet2 3d EEM 0.8663 0.814 0.577 0.837 151
3d EEM WO 0.9239 0.482 0.386 0.497 255
5d EEM 0.9189 0.634 0.476 0.661 154
Svob2007 chal2 3d EEM 0.8737 0.792 0.554 0.814 161
3d EEM WO 0.9127 0.483 0.387 0.498 220
5d EEM 0.9203 0.629 0.473 0.656 157
Svob2007 hm2 3d EEM 0.8671 0.812 0.578 0.835 152
3d EEM WO 0.9241 0.481 0.387 0.496 256
5d EEM 0.9179 0.638 0.478 0.666 152
Baek1991 3d EEM 0.9099 0.669 0.531 0.688 236
3d EEM WO 0.9166 0.531 0.423 0.548 231
5d EEM 0.9195 0.632 0.493 0.659 155
Mort1986 3d EEM 0.8860 0.752 0.577 0.773 181
3d EEM WO 0.9151 0.520 0.405 0.536 226
5d EEM 0.9142 0.652 0.524 0.680 145
HF/6–31G* MK - 3d QM 0.8405 0.890 0.727 0.915 123
- 5d QM 0.8865 0.750 0.641 0.782 106
Jir2008 hf 3d EEM 0.8612 0.830 0.582 0.853 145
3d EEM WO 0.9182 0.500 0.394 0.516 236
5d EEM 0.9154 0.648 0.488 0.676 147
B3LYP/6–31G* MPA - 3d QM 0.9671 0.404 0.317 0.415 686
- 5d QM 0.9724 0.370 0.274 0.386 479
Chaves2006 3d EEM 0.891 0.735 0.570 0.756 191
3d EEM WO 0.9198 0.505 0.398 0.521 241
5d EEM 0.9192 0.633 0.489 0.660 155
Bult2002 mul 3d EEM 0.8876 0.747 0.589 0.768 184
3d EEM WO 0.9151 0.520 0.416 0.536 226
5d EEM 0.9158 0.646 0.504 0.674 148
B3LYP/6–31G* NPA - 3d QM 0.9590 0.451 0.349 0.464 546
- 5d QM 0.9680 0.399 0.295 0.416 411
Ouy2009 3d EEM 0.8731 0.793 0.541 0.815 161
3d EEM WO 0.9043 0.505 0.379 0.521 198
5d EEM 0.9094 0.670 0.503 0.699 137
Ouy2009 elem 3d EEM 0.8727 0.795 0.546 0.817 160
3d EEM WO 0.9113 0.487 0.382 0.502 216
5d EEM 0.9132 0.656 0.495 0.684 143
Ouy2009 elemF 3d EEM 0.8848 0.756 0.519 0.777 179
3d EEM WO 0.9012 0.512 0.386 0.528 192
5d EEM 0.8866 0.750 0.520 0.782 106
Svobodov´a Vaˇrekov´a et al. Journal of Cheminformatics 2013, 5:18 Page 7 of 16
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Table 2 Quality criteria and statistical criteria for all the QSPR models analyzed in the present study and focused on
phenols (continued)
Bult2002 npa 3d EEM 0.9044 0.689 0.532 0.708 221
3d EEM WO 0.9098 0.523 0.405 0.539 212
5d EEM 0.9180 0.638 0.488 0.666 152
Hir. - 3d QM 0.9042 0.689 0.503 0.708 220
- 5d QM 0.9477 0.509 0.356 0.531 246
Bult2002 hir 3d EEM 0.8415 0.887 0.636 0.912 124
3d EEM WO 0.8838 0.579 0.414 0.597 160
5d EEM 0.9050 0.687 0.522 0.717 130
MK - 3d QM 0.8447 0.878 0.705 0.903 127
- 5d QM 0.8960 0.718 0.594 0.749 117
Jir2008 dft 3d EEM 0.8696 0.804 0.555 0.827 156
3d EEM WO 0.9224 0.487 0.371 0.502 250
5d EEM 0.9148 0.650 0.489 0.678 146
Bult2002 mk 3d EEM 0.8639 0.822 0.610 0.845 148
3d EEM WO 0.9053 0.519 0.384 0.535 201
5d EEM 0.9131 0.657 0.508 0.685 143
Chel. - 3d QM 0.8528 0.854 0.712 0.878 135
- 5d QM 0.9087 0.673 0.552 0.702 135
Bult2002 che 3d EEM 0.8695 0.805 0.597 0.828 155
3d EEM WO 0.8863 0.588 0.436 0.606 164
5d EEM 0.9057 0.684 0.540 0.714 131
AIM - 3d QM 0.9609 0.440 0.332 0.452 573
- 5d QM 0.9677 0.400 0.285 0.417 407
Bult2004 aim 3d EEM 0.8646 0.819 0.619 0.842 149
3d EEM WO 0.8972 0.590 0.438 0.608 183
5d EEM 0.9017 0.698 0.571 0.728 125
that using two additional charge descriptors from the dissociated
molecule can markedly improve the predictive
power of the EEM QSPR models. Tables 2 and 3, Figure 1
show that these new 5d EEM QSPR models provide better
pKa prediction than their corresponding 3d EEM QSPR
models. Speciﬁcally, adding the descriptors derived from
the dissociated molecules increased the average R2 value
for the EEM QSPR models from 0.876 to 0.913.
Comparison of EEM QSPR models and QM QSPR models
Another important question is how accurate the EEM
QSPR models are in comparison with QM QSPR models.
Table 2 and Figure 1 show that QM QSPR models
provide, in most cases, more precise predictions. This is
conﬁrmed also by the average R2 values from Table 3. This
is not surprising, since EEM is an empirical method which
just mimics the QM approach for which it was parameterized.
An interesting fact is that the diﬀerences in accuracy
between QM QSPR models and EEM QSPR models
are not substantial. For example, 5d EEM QSPR models
have average R2 = 0.913, while 5d QM QSPR models
have average R2 = 0.951. We also note that adding more
descriptors to a QM QSPR model brings less improvement
than adding more descriptors to an EEM QSPR
model.
Inﬂuence of theory level and basis set
EEM parameters are available only for a relatively small
number of theory levels (HF and B3LYP) and basis sets
(STO-3G and 6–31G*). Therefore we can not perform
such a deep analysis of theory level and basis set inﬂuence
on pKa prediction capability from EEM atomic charges,
as was done for QM QSPR models by Gross et al. [22]
or Svobodova et al. [24]. We can only compare the models
employing HF/STO-3G and B3LYP/6–31G* charges,
as these are the only combinations for which EEM parameters
are available for the same population analysis (MPA).
Therefore we can study only the inﬂuence of the combination
of theory level / basis set, and not the isolated inﬂuence
of the theory level or basis set. Our analysis revealed
that B3LYP/6–31G* charges provide slightly more accurate
QM QSPR models than HF/STO-3G charges (see
Svobodov´a Vaˇrekov´a et al. Journal of Cheminformatics 2013, 5:18 Page 8 of 16
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QM theory level PA EEM parameter R2
of QSPR model
+ basis set set name 3d EEM 3d EEM WO 5d EEM 3d QM 5d QM
HF/STO-3G MPA Svob2007 cbeg2 0.8671 0.9239 0.9179 0.9515 0.9657
Svob2007 cmet2 0.8663 0.9239 0.9189
Svob2007 chal2 0.8737 0.9127 0.9203
Svob2007 hm2 0.8671 0.9241 0.9179
Baek1991 0.9099 0.9166 0.9195
Mort1986 0.8860 0.9151 0.9142
HF/6-31G* MK Jir2008 hf 0.8696 0.9182 0.9154 0.8405 0.8865
B3LYP/6-31G* MPA Chaves 2006 0.8910 0.9198 0.9192 0.9671 0.9724
Bult2002 mul 0.8876 0.9151 0.9158
NPA Ouy2009 0.8731 0.9043 0.9094 0.9590 0.9680
Ouy2009 elem 0.8727 0.9113 0.9132
Ouy2009 elemF 0.8848 0.9012 0.8866
Bult2002 npa 0.9044 0.9098 0.9180
Hir. Bult2002 hir 0.8415 0.8838 0.9050 0.9042 0.9477
MK Jir2008 mk 0.8696 0.9224 0.9148 0.8447 0.8960
Bult2002 mk 0.8639 0.9053 0.9131
Chel. Bult2002 che 0.8695 0.8863 0.9057 0.8528 0.9087
AIM Bult2004 aim 0.8646 0.8972 0.9017 0.9609 0.9677
Legend excellent very good good satisfactory acceptable weak
R2
0.95– 0.97 0.92– 0.95 0.91– 0.92 0.9 – 0.91 0.85– 0.9 0.8 – 0.85
Figure 1 R2 for the correlation between calculated and experimental pKa.
Table 3 Average R2 between experimental and predicted pKa for all QSPR models of a certain type and percentages of
QSPR models whose R2 values are in a certain interval
QSPR model 3d EEM 3d EEM WO 5d EEM 3d QM 5d QM
Average R2 0.876 0.911 0.913 0.929 0.951
Interval of R2 R2 > 0.9 11% 83% 94% 78% 83%
0.9 ≥ R2 > 0.85 83% 17% 6% 6% 17%
0.85 ≥ R2 > 0.8 6% 0% 0% 17% 0%
QSPR model EEM based models QM based models
Average R2 0.900 0.940
Interval of R2 R2 > 0.9 63% 81%
0.9 ≥ R2 > 0.85 35% 13%
0.85 ≥ R2 > 0.8 2% 6%
Table 4 Average R2 between experimental and predicted pKa for all QSPR models using atomic charges calculated by a
speciﬁc combination of theory level and basis set, or by a speciﬁc population analysis
QSPR model 3d EEM 3d EEM WO 5d EEM 3d QM 5d QM
Theory level HF/STO-3G 0.878 0.919 0.918 0.952 0.966
and basis set * B3LYP/6–31G* 0.889 0.917 0.918 0.967 0.972
Population MPA 0.889 0.917 0.918 0.967 0.972
analysis ** NPA 0.884 0.907 0.907 0.959 0.968
Hirshfeld 0.842 0.884 0.905 0.904 0.948
MK 0.867 0.914 0.914 0.845 0.896
CHELPG 0.870 0.886 0.906 0.853 0.909
AIM 0.865 0.897 0.902 0.961 0.968
*
Only QSPR models employing MPA were included in this analysis.
**
Only QSPR models using B3LYP/6–31G* were included in this analysis.
Svobodov´a Vaˇrekov´a et al. Journal of Cheminformatics 2013, 5:18 Page 9 of 16
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0
2
4
6
8
10
12
0 2 4 6 8 10 12
calculatedpKa
experimental pKa
HF/STO-3G/MPA/3d
0
2
4
6
8
10
12
0 2 4 6 8 10 12
calculatedpKa
experimental pKa
B3LYP/6-31G*/MPA/3d
0
2
4
6
8
10
12
0 2 4 6 8 10 12
calculatedpKa
experimental pKa
B3LYP/6-31G*/NPA/3d
0
2
4
6
8
10
12
0 2 4 6 8 10 12
calculatedpKa
experimental pKa
B3LYP/6-31G*/MK/3d
0
2
4
6
8
10
12
0 2 4 6 8 10 12
calculatedpKa
experimental pKa
HF/STO-3G/MPA/5d
0
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6
8
10
12
0 2 4 6 8 10 12
calculatedpKa
experimental pKa
B3LYP/6-31G*/MPA/5d
0
2
4
6
8
10
12
0 2 4 6 8 10 12
calculatedpKa experimental pKa
B3LYP/6-31G*/NPA/5d
0
2
4
6
8
10
12
0 2 4 6 8 10 12
calculatedpKa
experimental pKa
B3LYP/6-31G*/MK/5d
0
2
4
6
8
10
12
0 2 4 6 8 10 12
calculatedpKa
experimental pKa
Svob2007_chal2/3d
0
2
4
6
8
10
12
0 2 4 6 8 10 12
calculatedpKa
experimental pKa
Chaves2006/3d
0
2
4
6
8
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12
0 2 4 6 8 10 12
calculatedpKa
experimental pKa
Bult2002_npa/3d
0
2
4
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8
10
12
0 2 4 6 8 10 12
calculatedpKa
experimental pKa
Bult2002_mk/3d
0
2
4
6
8
10
12
0 2 4 6 8 10 12
calculatedpKa
experimental pKa
Svob2007_chal2/3d WO
0
2
4
6
8
10
12
0 2 4 6 8 10 12
calculatedpKa
experimental pKa
Chaves2006/3d WO
0
2
4
6
8
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12
0 2 4 6 8 10 12
calculatedpKa
experimental pKa
Bult2002_npa/3d WO
0
2
4
6
8
10
12
0 2 4 6 8 10 12
calculatedpKa
experimental pKa
Bult2002_mk/3d WO
0
2
4
6
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12
0 2 4 6 8 10 12
calculatedpKa
experimental pKa
Svob2007_chal2/5d
0
2
4
6
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0 2 4 6 8 10 12
calculatedpKa
experimental pKa
Chaves2006/5d
0
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4
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calculatedpKa
experimental pKa
Bult2002_npa/5d
0
2
4
6
8
10
12
0 2 4 6 8 10 12
calculatedpKa
experimental pKa
Bult2002_mk/5d
Figure 2 Correlation graphs. Graphs showing the correlation between experimental and calculated pKa for selected QSPR models.
Table 4). This is in agreement with our previous ﬁndings
[24], and it can be explained by the fact that 6–31G*
is a more robust basis set than STO-3G. However, the
diﬀerence is not marked in the case of EEM QSPR models.
Inﬂuence of population analysis
Eleven EEM parameter sets were published for B3LYP/6–
31G* with six diﬀerent population analyses (see Table 1).
Therefore it is straightforward to analyze the inﬂuence
of the population analysis on the predictive power of the
resulting QSPR models (see Table 4). We found that MPA
and NPA provide the best QM models, while MK and
CHELPG (PAs based on ﬁtting the atomic charges to the
molecular electrostatic potential) provide weak QM models.
Our results are in agreement with previous studies
[22,24]. QM QSPR models based on AIM predict pKa
with accuracy comparable to MPA and NPA. In the case
of EEM QSPR models, we did indeed ﬁnd that MPA provided
the best models, but most of the other population
analyses gave comparable results. This conﬁrms previous
observations that the EEM approach is not able to
faithfully mimic MK charges [63]. On the other hand,
Svobodov´a Vaˇrekov´a et al. Journal of Cheminformatics 2013, 5:18 Page 10 of 16
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Table 5 Comparison between the performance of the QSPR models developed here, and previously developed models
Theory Number of
Method level PA Basis set Descriptors R2 s F molecules Source
QM B3LYP NPA 6–311G** qOH 0.789 1.300 48 15 Kreye and Seybold [23]a
B3LYP NPA 6–311G** qO 0.731 1.500 38 15 Kreye and Seybold [23]a
B3LYP NPA 6–31+G* qOH 0.880 0.970 95 15 Kreye and Seybold [23]b
B3LYP NPA 6–31+G* qO 0.865 1.000 38 15 Kreye and Seybold [23]b
B3LYP NPA 6–311G(d,p) qO− 0.911 0.252 173 19 Gross and Seybold [22]
B3LYP NPA 6–311G(d,p) qH 0.887 0.283 134 19 Gross and Seybold [22]
B3LYP NPA 6–31G* qH, qO, qC1 0.961 0.440 986 124 Svobodova and Geidl [24]
B3LYP NPA 6–311G qH, qO, qC1 0.962 0.435 1013 124 Svobodova and Geidl [24]
B3LYP NPA 6–31G* qH, qO, qC1 0.959 0.464 545 74 This work
B3LYP NPA 6–31G* qH, qO, qC1, 0.968 0.410 705 74 This work
qOD, qC1D
EEM B3LYP NPA 6–31G* qH, qO, qC1, 0.918 0.656 261 74 This workc
qOD, qC1D
QM B3LYP MPA 6–311G(d,p) qH 0.913 0.248 179 19 Gross and Seybold [22]
B3LYP MPA 6–311G(d,p) qO− 0.894 0.274 144 19 Gross and Seybold [22]
B3LYP MPA 6–311G qH, qO, qC1 0.938 0.556 605 124 Svobodova and Geidl [24]
B3LYP MPA 6–31G* qH, qO, qC1 0.959 0.450 936 124 Svobodova and Geidl [24]
B3LYP MPA 6–31G* qH, qO, qC1 0.967 0.415 685 74 This work
B3LYP MPA 6–31G* qH, qO, qC1, 0.972 0.380 822 74 This work
qOD, qC1D
EEM B3LYP MPA 6–31G* qH, qO, qC1, 0.919 0.651 265 74 This workd
qOD, qC1D
QM B3LYP MK 6–311G(d,p) qH 0.344 0.682 9 19 Gross and Seybold [22]
B3LYP MK 6–311G(d,p) qO− 0.692 0.467 38 19 Gross and Seybold [22]
B3LYP MK 6–311G qH, qO, qC1 0.822 0.941 185 124 Svobodova and Geidl [24]
B3LYP MK 6–31G* qH, qO, qC1 0.808 0.978 168 124 Svobodova and Geidl [24]
B3LYP MK 6–31G* qH, qO, qC1 0.845 0.902 126 74 This work
B3LYP MK 6–31G* qH, qO, qC1 0.896 0.739 201 74 This work
qOD, qC1D
EEM B3LYP MK 6–31G* qH, qO, qC1 0.915 0.669 250 74 This worke
qOD, qC1D
a
With solvent model SM5.4.
b
With solvent model SM8.
c
EEM parameter set Bult2002 npa.
d
EEM parameter set Chaves2006.
e
EEM parameter set Jir2008 mk.
this drawback of EEM allowed the EEM QSPR models
employing MK charges to predict pKa more accurately
than the corresponding QM QSPR models.
Inﬂuence of the EEM parameter set
Two or more EEM parameter sets are available in literature
for four combinations of theory level, basis set and
population analysis (see Table 1). We found that the quality
of EEM QSPR models employing the same types of
charges slightly varies when using EEM parameters coming
from diﬀerent studies (see Table 2 and Figure 1). Even
EEM parameters from the same study, but obtained by
diﬀerent approaches, lead to QSPR models of slightly different
quality. In any case, these diﬀerences are minimal.
Comparison with previous work
QM QSPR models for pKa prediction in phenols, similar
to those presented in this paper (i.e., employing similar
Svobodov´a Vaˇrekov´a et al. Journal of Cheminformatics 2013, 5:18 Page 11 of 16
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Table 6 Comparison of the quality criteria and statistical criteria for the training set, test set and complete set for some
selected charge calculation approaches
5d EEM QSPR model employing Svob2007 chal2 EEM parameters:
Complete set:
R2 RMSE s F Number of molecules
0.920 0.629 0.647 269 74
Cross-validation:
Cross- Training set Test set
validation Number of Number of
step R2 RMSE s F molecules R2 RMSE s F molecules
1 0.9283 0.5211 0.5498 137 59 0.9202 1.0754 1.3884 21 15
2 0.9210 0.6538 0.6899 124 59 0.9029 0.5394 0.6963 17 15
3 0.9191 0.6442 0.6796 120 59 0.9275 0.5823 0.7517 23 15
4 0.9207 0.6244 0.6588 123 59 0.9271 0.6878 0.8880 23 15
5 0.9274 0.6302 0.6643 138 60 0.9008 0.6678 0.8834 15 14
5d EEM QSPR model employing Ouy2009 elemF EEM parameters:
Complete set:
R2 RMSE s F Number of molecules
0.8866 0.7501 0.7825 106 74
Cross-validation:
Cross- Training set Test set
validation Number of Number of
step R2 RMSE s F molecules R2 RMSE s F molecules
1 0.8936 0.6349 0.6698 89 59 0.8704 1.2857 1.6598 12 15
2 0.8953 0.7526 0.7940 91 59 0.8018 0.7802 1.0072 7 15
3 0.8908 0.7481 0.7893 86 59 0.8647 0.7983 1.0306 12 15
4 0.8821 0.7614 0.8033 79 59 0.9154 0.7481 0.9658 19 15
5 0.8956 0.7557 0.7966 93 60 0.8089 0.8396 1.1107 7 14
charges) were previously published by Gross and Seybold
[22], Kreye and Seybold [23] and Svobodova and Geidl
[24]. Table 5 shows a comparison between these models
and the models developed in this study. Our work is
the ﬁrst which presents QSPR models for pKa prediction
based on EEM charges. Therefore, we can not provide
a comparison between EEM QSPR models, but we can
compare against QSPR models based on QM charges only.
It is seen therein that our 3d QM QSPR models show
markedly higher R2 and F values than the models published
by Gross and Seybold and Kreye and Seybold (even
if some of these models employ higher basis sets) and
comparable R2 and F values as models published by Svobodova
and Geidl. Moreover, our 5d QM QSPR models
outperform the models from Svobodova and Geidl. Our
best EEM QSPR models (i.e., 5d EEM QSPR models) provide
even better results than QM QSPR models from
Gross and Seybold and Kreye and Seybold. These EEM
QSPR models are not as accurate as the QM QSPR models
published by Svobodova and Geidl or those developed
in this work, but the loss of accuracy is not too high (R2
values are still > 0.91).
Cross-validation
Our results show that 5d EEM QSPR models provide a
fast and accurate approach for pKa prediction. Nonetheless,
the robustness of these models should be proved.
Therefore, all the 5d EEM QSPR models (i.e., 18 models)
were tested by cross-validation. For comparison, also the
cross-validation of all 5d QM QSPR models (i.e., 8 models)
was done. The k-fold cross-validation procedure was
used [64,65], where k = 5. Speciﬁcally, the set of phenol
molecules was divided into ﬁve parts (each contained
20% of the molecules). The division was done randomly,
and included stratiﬁcation by pKa value. Afterwards, ﬁve
cross validation steps were performed. In the ﬁrst step,
the ﬁrst part was selected as a test set, and the remaining
four parts were taken together as the training set.
The test and training sets for the other steps were prepared
in a similar manner, by subsequently considering
Svobodov´a Vaˇrekov´a et al. Journal of Cheminformatics 2013, 5:18 Page 12 of 16
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QM theory level PA EEM parameter R2 of QSPR model
+ basis set set name 7d EEM 7d QM
HF/STO-3G MPA Svob2007 cbeg2 0.8831 0.9327
Svob2007 cmet2 0.8810
Svob2007 chal2 0.8822
Svob2007 hm2 0.8793
Baek1991 0.9211
Mort1986 0.9176
B3LYP/6-31G* MPA Chaves2006 0.9238 0.9059
Bult2002 mul 0.9248
NPA Ouy2009 0.8825 0.9169
Ouy2009 elem 0.8777
Ouy2009 elemF 0.8478
Bult2002 npa 0.9094
Legend very good good satisfactory acceptable weak
R2
0.92– 0.95 0.91– 0.92 0.9 – 0.91 0.85– 0.9 0.8 – 0.85
Figure 3 Correlation between calculated and experimental pKa for carboxylic acids.
one part as a test set, while the remaining parts served as
a training set. For each step, the QSPR model was parameterized
on the training set. Afterwards, the pKa values
of the respective test molecules were calculated via this
model, and compared with experimental pKa values. The
results are summarized in the (Additional ﬁle 7: Table
S4), while the cross-validation results for the best and the
worst performing 5d EEM QSPR models are shown in
Table 6. The cross-validation showed that the models are
stable and the values of R2 and RMSE are similar for the
test set, the training set and the complete set. The robustness
of EEM QSPR models and QM QSPR models is
comparable.
Case study for carboxylic acids
We have shown that QSPR models based on EEM atomic
charges can be used for predicting pKa in phenols. In
order to evaluate the general applicability of this approach
for pKa prediction, we tested the performance of such
models for carboxylic acids. This case study is done for
the charge schemes found to provide the best QM and
EEM QSPR models in the case of phenols. Speciﬁcally,
QM charges calculated by HF/STO-3G/MPA, B3LYP/6–
31G*/MPA and B3LYP/6–31G*/NPA, and EEM charges
calculated using the corresponding EEM parameters.
Because 5d QSPR models provide the most accurate prediction
for phenols, the case study is focused on their analogue
for carboxylic acids, i.e., 7d QSPR models. Squared
Pearson correlation coeﬃcients of the analysed QSPR
models are summarized in Figure 3, and all the quality
and statistical criteria can be found in (Additional ﬁle 8:
Table S5). The results show that 7d EEM QSPR models are
able to predict the pKa of carboxylic acids with very good
accuracy. Namely, 5 out of 12 analysed 7d EEM QSPR
models were able to predict pKa with R2 > 0.9, while the
best EEM QSPR model reached R2 = 0.925. Therefore, we
concluded that EEM QSPR models are indeed applicable
also for carboxylic acids. Again QM QSPR models perform
better than EEM QSPR models, but the diﬀerences
are not substantial.
Conclusions
We found that the QSPR models employing EEM charges
can be a suitable approach for pKa prediction. From our
54 EEM QSPR models focused on phenols, 63% show a
correlation of R2 > 0.9 between the experimental and predicted
pKa. The most successful type of these EEM QSPR
models employed 5 descriptors, namely the atomic charge
of the hydrogen atom from the phenolic OH group, the
charge on the oxygen atom from the phenolic OH group,
the charge on the carbon atom binding the phenolic OH
group, the charge on the oxygen from the phenoxide O−
from the dissociated molecule, and the charge on the carbon
atom binding this oxygen. Speciﬁcally, 94% of these
models have R2 > 0.9, and the best one has R2 = 0.920.
In general, including charge descriptors from dissociated
molecules, which was introduced in our work, always
increases the quality of a QSPR model. The only drawback
of EEM QSPR models is that the EEM parameters are currently
not available for all types of atoms. Therefore the
EEM parameter sets need to be expanded to larger sets of
molecules and further improved.
Svobodov´a Vaˇrekov´a et al. Journal of Cheminformatics 2013, 5:18 Page 13 of 16
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As expected, the QM QSPR models provided more
accurate pKa predictions than the EEM QSPR models.
Nevertheless, these diﬀerences are not substantial.
Furthermore, a big advantage of EEM QSPR models is
that one can calculate the EEM charges markedly faster
than the QM charges. Moreover, the EEM QSPR models
are not so strongly inﬂuenced by the charge calculation
approach as the QM QSPR models are. Speciﬁcally,
the QM QSPR models which use atomic charges
obtained from calculations with higher basis set perform
better, while the EEM QSPR models do not show
such marked diﬀerences. Similarly, the quality of QM
QSPR models depends a lot on population analysis,
but EEM QSPR models are not inﬂuenced so much.
Namely, QM QSPR models which use atomic charges calculated
from MPA, NPA and Hirshfeld PA performed
very well, while MK provides only weak models. In the
case of EEM QSPR models, MPA performs also the
best, but all other PAs (including MK) provide accurate
results as well. The source of the EEM parameters
also did not aﬀect the quality of the EEM QSPR models
signiﬁcantly.
The robustness of EEM QSPR models was successfully
conﬁrmed by cross-validation. Speciﬁcally, the accuracy
of pKa prediction for the test, training and complete
set were comparable. The applicability of EEM QSPR
models for other chemical classes was tested in a case
study focused on carboxylic acids. This case study
showed that EEM QSPR models are indeed applicable
for pKa prediction also for carboxylic acids. Namely,
5 from 12 of these models were able to predict pKa
with R2 > 0.9, while the best EEM QSPR model reached
R2 = 0.925.
Therefore, EEM QSPR models constitute a very promising
approach for the prediction of pKa. Their main advantages
are that they are accurate, and can predict pKa values
very quickly, since the atomic charge descriptors used in
the QSPR model can be obtained much faster by EEM
than by QM. Additionally, the quality of EEM QSPR models
is less dependent on the type of atomic charges used
(theory level, basis set, population analysis) than in the
case of QM QSPR models. Accordingly, EEM QSPR models
constitute a pKa prediction approach which is very
suitable for virtual screening.
Additional ﬁles
Additional ﬁle 1: Table S1a. The list of the phenol molecules, including
their names, NCS numbers, CAS numbers and experimental pKa values.
Additional ﬁle 2: Molecules. The SDF ﬁles with the structures of the
molecules and also their dissociated forms.
Additional ﬁle 3: Table S1b. The list of the carboxylic acid molecules,
including their names, NCS numbers, CAS numbers and experimental
pKa values.
Additional ﬁle 4: Table S2. The parameters of all the QSPR models for
phenols.
Additional ﬁle 5: Table S6. The table containing charge descriptors for
all charge calculation approaches and predicted pKa values for all QSPR
models (for phenols).
Additional ﬁle 6: Table S3. The information about outlier molecules for
phenols.
Additional ﬁle 7: Table S4. The table of cross-validation results for
phenols.
Additional ﬁle 8: Table S5. The quality and statistical criteria of QSPR
models for carboxylic acids.
Abbreviations
3d: 3 descriptors; 4d: 4 descriptors; 5d: 5 descriptors; 7d: 7 descriptors; AIM:
Atoms in Molecules; ANN: Artiﬁcial Neural Networks; B3LYP: Becke,
three-parameter, Lee-Yang-Parr; DENR: Dynamic Electronegativity Relaxation;
EEM: Electronegativity Equalization Method; GDAC: Geometry-Dependent
Atomic Charge; HF: Hartree-Fock; KCM: Kirchhoﬀ Charge Model; LFER: Linear
Free Energy Relationships; MK: Merz-Singh-Kollman; MLR: Multiple Linear
Regression; MP2: Møller-Plesset Perturbation Theory; MPA: Mulliken Population
Analysis; NPA: Natural Population Analysis; PA: Population Analysis; PEOE:
Partial Equalization of Orbital Electronegativity; QEq: Charge Equilibration; QM:
Quantum Mechanical; QSPR: Quantitative Structure-Property Relationship;
RMSE: Root Mean Square Error; SQE: Split Charge Equilibration; TSEF:
Topologically Symmetric Energy Function; WO: Without Outliers.
Competing interests
The authors declare that they have no competing interests.
Author’s contributions
The concept of the study originated from JK and was reviewed and extended
by RA, while the design was put together by RSV and SG and reviewed by JK
and RA. SG and CMI collected and prepared the input data. SG, OS, DS and TB
performed the acquisition and post-processing of data. The data were
analyzed and interpreted by RSV, SG, CMI and JK. The manuscript was written
by RSV and SG in cooperation with JK and CMI, and reviewed by all authors.
Authors’ information
Radka Svobodov´a Vaˇrekov´a and Stanislav Geidl wish it to be known that, in
their opinion, the ﬁrst two authors should be regarded as joint First Authors.
Acknowledgements
This work was supported by the Ministry of Education of the Czech Republic
(LH13055), by the European Community’s Seventh Framework Programme
(CZ.1.05/1.1.00/02.0068 to J.K. and R.S.V.) from the European Regional
Development Fund and by the EU Seventh Framework Programme under the
“Capacities” speciﬁc programme (Contract No. 286154 to J.K.). C.M.I. and D.S.
would like to thank Brno City Municipality for the ﬁnancial support provided to
them through the program Brno Ph.D. Talent. This work was also supported in
part by NIH grants R01 GM071872, U01 GM094612, and U54 GM094618 to R.A..
The access to computing and storage facilities owned by parties and projects
contributing to the National Grid Infrastructure MetaCentrum, provided under
the programme “Projects of Large Infrastructure for Research, Development,
and Innovations” (LM2010005) is highly appreciated. Also the access to the
CERIT-SC computing facilities provided under the programme Center CERIT
Scientiﬁc Cloud, part of the Operational Program Research and Development
for Innovations, reg. no. CZ. 1.05/3.2.00/08.0144 is acknowledged.
Author details
1National Centre for Biomolecular Research, Faculty of Science and CEITEC Central
European Institute of Technology, Masaryk University Brno, Kamenice
5, 625 00 Brno-Bohunice, Czech Republic. 2Skaggs School of Pharmacy and
Pharmaceutical Sciences, University of California, 9500 Gilman Drive, MC 0657,
San Diego, USA.
Svobodov´a Vaˇrekov´a et al. Journal of Cheminformatics 2013, 5:18 Page 14 of 16
http://www.jcheminf.com/content/5/18
Received: 16 November 2012 Accepted: 27 March 2013
Published: 10 April 2013
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Rapid calculation of accurate atomic charges
for proteins via the Electronegativity
Equalization Method
166
Rapid Calculation of Accurate Atomic Charges for Proteins via the
Electronegativity Equalization Method
Crina-Maria Ionescu, Stanislav Geidl, Radka Svobodová Vařeková,* and Jaroslav Koča*
CEITECCentral European Institute of Technology, and National Centre for Biomolecular Research, Faculty of Science,
Masaryk University Brno, Kamenice 5, 625 00, Brno-Bohunice, Czech Republic
*S Supporting Information
ABSTRACT: We focused on the parametrization and evaluation
of empirical models for fast and accurate calculation of
conformationally dependent atomic charges in proteins. The
models were based on the electronegativity equalization method
(EEM), and the parametrization procedure was tailored to
proteins. We used large protein fragments as reference structures
and ﬁtted the EEM model parameters using atomic
charges computed by three population analyses (Mulliken,
Natural, iterative Hirshfeld), at the Hartree−Fock level with
two basis sets (6-31G*, 6-31G**) and in two environments
(gas phase, implicit solvation). We parametrized and successfully validated 24 EEM models. When tested on insulin and
ubiquitin, all models reproduced quantum mechanics level charges well and were consistent with respect to population analysis
and basis set. Speciﬁcally, the models showed on average a correlation of 0.961, RMSD 0.097 e, and average absolute error per
atom 0.072 e. The EEM models can be used with the freely available EEM implementation EEM_SOLVER.
■ INTRODUCTION
The concept of atomic point charges is well established in theoretical
chemistry. Atomic point charges have played an important
role in understanding and modeling chemical behavior by
allowing the extraction and quantiﬁcation of information stored
in the molecular electron distribution of chemical compounds.
Thus, atomic point charges have been used to estimate reactivity
indices, dissociation constants, partition coeﬃcients, the electrostatic
contribution in molecular dynamics or docking studies,
etc.1−4
Virtual screening, the process by which potential drug
candidates or targets are identiﬁed by screening huge libraries of
compounds, employs atomic point charges, for instance, as
parameters in the docking stage. Absorbtion, distribution,
metabolism, and excretion proﬁling studies, involved in drug
discovery programs, employ atomic point charges as descriptors
useful in predicting various pharmacological properties. It is
therefore desirable to have knowledge of the values of atomic
charges.
While atomic charges are very intuitive, they are not physical
observables. Nevertheless, atomic partial charges can be derived
from physical observables, the values of which are most
commonly obtained by quantum mechanical (QM) calculations.
A remarkable fact is that a unique deﬁnition of atomic partial
charges has yet to be accepted. As such, a score of methods have
been developed to estimate the values of atomic charges, which is
another indication that atomic charges are of great interest.
Roughly, these methods can be classiﬁed as QM-based or
empirical.
QM-based approaches ﬁrst compute the wave function and
subsequently the molecular electron density. In further, various
population analyses can be performed in order to partition the
molecular electron density into its atomic contributions. Some
partitioning approaches are based on the wave function itself;5−8
others on a wave function-dependent physical observable.9−13
QM atomic charges can also be mapped to reproduce chargedependent
observables.14
Along with physical soundness, the
advantage of QM based approaches for charge calculation is their
general applicability.
Empirical approaches, on the other hand, do not need the
molecular wave function and instead employ a wide array of
principles and intuitive derivations, coupled with cost-eﬀective
algorithms. Empirical approaches for atomic charge calculation
can be divided into those which depend only on the 2D structure
of the molecule,15−18
and those which depend on the 3D structure
of the molecule.19−24
The majority of empirical approaches
are based on partial or complete equalization of the electronegativity.
Atomic charge calculation via empirical approaches is
an extremely cost-eﬀective alternative to QM-based methods,
though appropriate parametrizations need to be performed
before any empirical method can be used with conﬁdence. Unlike
QM based approaches, the applicability of empirical methods is
many times limited to certain kinds of systems, either because of
the intrinsic approximations that are made or by the parametrization
procedure.
Although these atomic charge deﬁnitions diﬀer in both the
principles and algorithms they employ, many such deﬁnitions
have already proven suitable for the prediction of relevant
Received: May 1, 2013
Published: August 22, 2013
Article
pubs.acs.org/jcim
© 2013 American Chemical Society 2548 dx.doi.org/10.1021/ci400448n | J. Chem. Inf. Model. 2013, 53, 2548−2558
chemical phenomena. Following a statistical analysis of 25 charge
deﬁnition schemes, Meister and Schwarz25
concluded that the
same physical principles govern all the schemes under study, and
therefore, all charge deﬁnition schemes are relevant, despite the
diﬀerences in scale.
In the present study, we focus on proteins, due to their capital
importance on all aspects of cellular life. Charge transfer was
found to be signiﬁcant in protein folding and many biomolecular
interactions,4,26−28
and functionally linked to protein structural
dynamics.29
Cho et al.4
have shown that using conformationally
dependent, QM-level atomic charges is critical to identifying the
correct binding partners in docking studies on various proteins.
Later, Cho and Rinaldo30
found that, especially in the case
of metalloproteins, it is necessary to compute QM charges
for as many atoms as possible close to the metal ion in order to
allow the correct prediction of ligand binding modes. Wallin
et al.31
emphasized the need to generalize and automatize the
charge assignment procedure and include this procedure in
the work ﬂow of ligand preparation for binding free energy
calculations.
In the light of the above-mentioned ﬁndings, it is clear that
there is a need for a fast, accurate, and accessible procedure to
calculate atomic charges in proteins. Nonetheless, an aﬀordable,
accurate, and highly available solution to handle large
biomolecular systems at the QM level has not yet been found.
Clearly, direct QM calculations are not yet a feasible option for
charge calculation in proteins, and one must rely on some
empirical method. In the present study, we focus on the
electronegativity equalization method (EEM) as a method for
rapid and accurate estimation of atomic partial charges.20,32−45
EEM is fast, has a straightforward implementation, and is
generally applicable and sensitive to a molecule’s 3D structure.
EEM has been successfully applied to zeolites, small organic
molecules, and polypeptides.46−50
A recent EEM investigation
proved useful in mapping the allosteric activation mechanism of
two apoptotic proteins.44
Before an empirical model can be used with conﬁdence,
appropriate parameters must be determined, i.e., the model must
be parametrized. EEM models are parametrized by ﬁtting the
model parameters to a set of reference data usually made up of
atomic charges obtained by various QM-based approaches. A
QM-based charge calculation approach is characterized by the
setup of the wave function calculation (theory level, basis set,
environment), as well as by the population analysis (PA) used to
partition the molecular electron density. We will refer to the
sum of these characteristics as the “type” of charge produced
by the QM approach. The maximum accuracy and potential
application of any EEM model is given by the type of charge
used during its parametrization. Previous works have parametrized
EEM mainly for inorganic or small organic molecules,
and especially for drug-like molecules,20,33−45
but very few
with speciﬁc focus on biomolecules. Some EEM models have
been successfully tested on peptides of various size,20,41
but
these models cover only two types of charges and contain no
parameters for sulfur, an element commonly found in
proteins. Some EEM models were successfully tested on
large protein fragments,44
but these models only cover one
type of charge.
Thus, the goal of the present study was to provide wider
coverage and evaluation of the EEM approach for proteins. In
this study, we have developed and validated 24 EEM models
speciﬁcally tailored to cover 12 types of charges in proteins.
Our reference data came from QM calculations at the HF level
with two basis sets (6-31G*, 6-31G**), in the gas-phase and
implicit solvent. Three atomic charge deﬁnitions were
considered (Mulliken, Natural, iterative Hirshfeld). The
accuracy of the proposed models was evaluated on insulin
and ubiquitin.
■ THEORY AND METHODS
Electronegativity Equalization Method. The electronegativity
equalization method (EEM)20
enables the determination
of atomic charges that are sensitive to the molecule’s
topology and three-dimensional structure. EEM is based on the
electronegativity equalization principle,51
which has received
theoretical grounding within the density functional theory,52,53
and which states that the electronegativity of all atoms is
equalized throughout a molecule:
= = = = ̅X X X X... ...i1 2 (1)
Within EEM, the electronegativity Xi of each atom i in a
molecule can be approximated as a linear function of several
terms:
∑η η= + Δ + + Δ +
≠
X X X q k
q
r
( ) 2( )i i i i i
i j
j
ij
1
0 0
(2)
The ﬁrst term is the electronegativity of the isolated atom Xi
0
,
empirically corrected for the presence of the molecular
environment (ΔXi). The second term is the product between
the charge of the atom qi and the hardness of the isolated atom ηi
0
,
empirically corrected for the presence of the molecular
environment (Δηi). The last term k∑i≠j(qj/rij) accounts for the
electrostatic interaction with every other charged atom j in the
molecule. k is an adjusting factor ﬁrst introduced by Yang and
Shen.54
Setting Ai = Xi
0
+ ΔXi and Bi = 2(ηi
0
+ Δηi), the molecular
electronegativity can be formally expressed as
∑̅ = + +
≠
X A B q k
q
r
i i i
i j
j
ij (3)
Additionally, the total molecular charge Q is the sum of all partial
atomic charges qi:
∑ =q Qi (4)
Taken all together, eqs 1, 3, and 4 can be expressed as a system
of equations from which the partial atomic charges qi and the
molecular electronegativity X̅ can be calculated, provided that the
rest of the terms (Q, rij, k, Ai, Bi) are known:
−
−
− ̅
=
−
−
⎛
⎝
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜
⎜⎜
⎞
⎠
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟
⎟⎟
⎛
⎝
⎜
⎜
⎜
⎜
⎜⎜
⎞
⎠
⎟
⎟
⎟
⎟
⎟⎟
⎛
⎝
⎜
⎜
⎜
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
⎟
⎟
⎟
B
k
r
k
r
k
r
B
k
r
k
r
k
r
B
q
q
q
X
A
A
A
Q
... 1
... 1
... ... ... ... ...
... 1
1 1 ... 1 0
... ...
N
N
N N
N
N N
1
1,2 1,
2,3
2
2,
,1 ,2
1
2
1
2
(5)
This formalism estimates atomic charges via a set of coupled
linear equations which can be eﬃciently solved by a Gaussian
elimination procedure.55
The computational complexity is
θ(N3
), where N is the number of atoms in the molecule.
Journal of Chemical Information and Modeling Article
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EEM Model Parameterization Theory. Given the threedimensional
structure of the molecule and its total charge, partial
charges for all atoms in the molecule can be calculated only if the
values of the EEM parameters (k, ⟨Ai, Bi⟩) are known. Otherwise,
the EEM model needs to be parametrized by ﬁtting against
reference data (training data set). We employed QM atomic
charges to ﬁt the EEM parameters given by the electronegativity
and hardness contributions Ai = Xi
0
+ ΔXi and Bi = 2(ηi
0
+ Δηi),
respectively, as well as the value of the parameter k present in this
formalism. The EEM parametrization methodology employed
here was described by Svobodová Vařeková et al.,37
and its
principles are given below.
For the purpose of EEM model parametrization, eq 3 can be
rearranged as a linear equation in Ai and Bi for each atom i in the
system:
∑+ = ̅ −
≠
A B q X k
q
r
i i i
i j
j
ij (6)
For a given value of the parameter k, sets of eqs 6 can be
grouped together according to the kind of atom they refer to. The
values of atomic charges qi and interatomic distances rij are taken
from the training data set, and the value of the molecular electronegativity
X̅ can be calculated as an average of the isolated atom
electronegativities Xi
0
. Under these circumstances, each
group of linear equations becomes an overdetermined system
of equations, enabling the determination of a set of parameters
(A, B)m for each atom type m by least-squares minimization.
The classiﬁcation of atoms into types can be done according
to various criteria, such as chemical element, hybridization,
binding partners, etc. Once a set of parameters (A, B)m
has been obtained for all M atom types, for all given values
of k, it is possible to determine the optimal EEM parameter
set k[(A, B)1, (A, B)2, ..., (A, B)M], in further denoted
simply as k[(A, B)m]1
M
, as the parameter set which produces
the best EEM model in the internal validation step (see
below).
EEM Model Validation Theory. The accuracy of an EEM
model in reproducing the reference data (here, QM atomic
charges) can be evaluated by internal and external validation.
In the internal validation step, the EEM model is evaluated for
its ability to reproduce the reference data which was used
during its parametrization. In other words, EEM is ﬁrst
validated on the training data set. Next, in the external
validation step, the EEM model is evaluated for its ability to
reproduce reference data which was not used during its
parametrization. In other words, EEM is also validated on test
molecules. The correlation between the reference QM charges
and predicted EEM charges can be assessed by various
indicators.
The ﬁrst indicator used in the present study was the average
correlation coeﬃcient (squared Pearson’s correlation coeﬃcient),
computed for each molecule, and averaged over all
molecules in the data set:
=
∑
σ σ=
∑ − −
−
=
⎛
⎝
⎜
⎞
⎠
⎟
R
N
I
N q q q q
n
avg
1
( )( )
( 1)
i
nI
i I i I
I I I
1
QM QM EEM EEM
QM EEM
(7)
where the index i = 1...nI described all atoms in molecule I, qI
QM
and qI
EEM
represented average atomic charges in molecule I, σI
QM
and σI
EEM
were standard deviations of the atomic charges in
molecule I, nI was the number of atoms in molecule I, and N was
the number of molecules in a given set.
The second indicator was the root-mean-square deviation,
computed for each molecule, and averaged over all molecules in
the data set:
=
∑ =
∑ −=
N
RMSD
I
N q q
n
avg
1
( )i
nI
i i
I
1
QM EEM 2
(8)
The third indicator was the average absolute diﬀerence,
computed for each molecule and averaged over all molecules in
the data set:
=
∑ =
∑ −=
D
N
I
N q q
n
avg
1
( )i
nI
i i
I
1
QM EEM 2
(9)
Reference StructuresTraining Data Set. The reference
molecules used in the model parametrization and internal
validation steps were 41 fragments of proteins from the Protein
Data Bank (PDB), whose structures had been determined by
X-ray crystallography or solution state NMR experiments.
Protein fragments, rather than small molecules, were chosen
as reference structures since they reﬂect the complex nature of
proteins as long, non-neutral molecular chains with complex
3D assembly.
The 41 reference structures consisted of amino acid chains,
water molecules, and calcium ions, and were obtained from
the 3D structure of their parent protein using the program
Triton.56
Hydrogen atoms were added for all crystal structures
to satisfy the missing valences. The protonation states of the
amino acid residues were +1 for Arg, Lys, and His and charged
amino ends of the polypeptide chains, −1 for Glu, Asp, and
charged carboxyl ends of the polypeptidic chains, 0 for the
rest. Only the ﬁrst structural model was used in the case of
NMR structures.
Reference StructuresTest Molecules. Two small
proteins were used in the external validation step, namely insulin
(PDB ID 3E7Y57
) and ubiquitin (PDB ID 1UBQ58
). The nature
of the calculations imposed some limitations to the size of the
systems used for testing. Thus, only one of the two insulin
monomers was kept, containing chains C and D, along with a few
water molecules cocrystallized with the protein. None of the Cl
and Zn ions found cocrystallized with insulin were kept, as no
EEM parameters were obtained for these ions. In the case of
ubiquitin, the ﬁrst 14 residues had to be removed in order to
reduce the system to a manageable size.
Table 1. Atomic Composition of the Data Sets Used in This Study
Nr molecules Nr atoms H C N O S Ca
training set 41 40142 19879 11912 3188 4954 148 61
insulin 1 802 397 248 63 88 6
ubiquitin 1 998 505 306 88 99
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An overview of the composition of all molecules used for EEM
model parametrization and validation is given in Table 1. The 3D
structures of these fragments are available as Supporting
Information in PDB format.
Reference QM Atomic Charges. For each reference
structure, QM atomic charges were obtained from the Mulliken
Population Analysis (MPA),5,6
Natural Population Analysis
(NPA),8
and iterative Hirshfeld analysis (HiI)11
performed at the
Hartree−Fock (HF) theory level with 6-31G* and 6-31G**
basis sets in the gas phase and polarizable continuum model
(PCM).59
These three population analyses were chosen because
they are known to work well with EEM.34,50
Moreover, these
population analyses can be performed by currently available
software tools for very large protein fragments that we used as
training and test molecules.
A total of 12 QM reference data sets were thus obtained:
MPA/6-31G*/gas, MPA/6-31G*/PCM, MPA/6-31G**/gas,
MPA/6-31G**/PCM, NPA/6-31G*/gas, NPA/6-31G*/PCM,
NPA/6-31G**/gas, NPA/6-31G**/PCM, HiI/6-31G*/gas,
HiI/6-31G*/PCM, HiI/6-31G**/gas, HiI/6-31G**/PCM. All
QM single point energy calculations and MPA were performed
using Gaussian 09,60
while NPA was performed using the NBO
program,61
and HiI was performed using the HiPart program.62
The values of all QM atomic charges obtained in this study are
included as Supporting Information in csv format.
EEM Models. Two classiﬁcations of atoms into atom types
were employed here. One classiﬁcation was based on chemical
elements (denoted “E”), and the other on chemical elements and
maximum bond multiplicity for each atom (denoted “EX”, so
that, for example, “O1” indicates sp3
hybridized oxygen and
“O2”, sp2
hybridized oxygen). Both atom classiﬁcation
approaches were applied to all 12 QM reference data sets.
Within a given atom classiﬁcation, the parameter k was
sampled as discrete values on several intervals. For each discrete
value of k, the set of parameters (A, B)m were obtained for all
atom types in the given classiﬁcation. For each atom type m, the
parameters (A, B)m were determined by least-squares minimization,
as the values of all other variables were known: the
interatomic distances were calculated from the 3D atomic
coordinates of the reference structures, the atomic charges were
calculated by the 12 QM schemes described above, and the value
of the average electronegativity for each molecule was calculated
as the harmonic average of the electronegativities of the
constituent atoms63
X̅ = n(∑i=1
n
(1/Xi
0
))−1
, where n is the
number of atoms in the molecule, and the values of Xi
0
correspond to Pauling electronegativities.64,65
Thus, within
each of the two atom type classiﬁcations, for each discrete
value of k, an EEM model described by the parameter set
k[(A, B)m]1
M
was obtained. Internal validation was then
performed for all such EEM models. Namely, each model
was used to predict the EEM charges of the reference
molecules in the training data set. The atomic charges
predicted by the EEM model were compared against the
reference QM atomic charges used during the model
parametrization. The EEM model which gave the highest
Ravg between the EEM predicted charges and the QM
reference charges for the whole training set was designated
as the ﬁnal EEM model within the given atom type
classiﬁcation.
Finally, 12 EEM models were obtained for the ﬁrst atom
classiﬁcation E, based on chemical elements: E-MPA/6-31G*/
gas, E-MPA/6-31G*/PCM, E-MPA/6-31G**/gas, E-MPA/
6-31G**/PCM, E-NPA/6-31G*/gas, E-NPA/6-31G*/PCM,
E-NPA/6-31G**/gas, E-NPA/6-31G**/PCM, E-HiI/
6-31G*/gas, E-HiI/6-31G*/PCM, E-HiI/6-31G**/gas, E-HiI/
Table 2. Overview of the 12 Types of QM Calculations Performed, and 24 EEM Models Obtained in This Study
EEM model characteristics
QM scheme training data sets
atom type classiﬁcation PA basis set environment Nr molecules Nr atoms EEM model
E MPA 6-31G* gas phase 41 40142 E-MPA/6-31G*/gas
PCM 41 40142 E-MPA/6-31G*/PCM
6-31G** gas phase 41 40142 E-MPA/6-31G**/gas
PCM 41 40142 E-MPA/6-31G**/PCM
NPA 6-31G* gas phase 41 40142 E-NPA/6-31G*/gas
PCM 40 39061 E-NPA/6-31G*/PCM
6-31G** gas phase 41 40142 E-NPA/6-31G**/gas
PCM 40 39061 E-NPA/6-31G**/PCM
HiI 6-31G* gas phase 41 40142 E-HiI/6-31G*/gas
PCM 38 36875 E-HiI/6-31G*/PCM
6-31G** gas phase 41 40142 E-HiI/6-31G**/gas
PCM 40 39061 E-HiI/6-31G**/PCM
EX MPA 6-31G* gas phase 41 40142 EX-MPA/6-31G*/gas
PCM 41 40142 EX-MPA/6-31G*/PCM
6-31G** gas phase 41 40142 EX-MPA/6-31G**/gas
PCM 41 40142 EX-MPA/6-31G**/PCM
NPA 6-31G* gas phase 41 40142 EX-NPA/6-31G*/gas
PCM 40 39061 EX-NPA/6-31G*/PCM
6-31G** gas phase 41 40142 EX-NPA/6-31G**/gas
PCM 40 39061 EX-NPA/6-31G**/PCM
HiI 6-31G* gas phase 41 40142 EX-HiI/6-31G*/gas
PCM 38 36875 EX-HiI/6-31G*/PCM
6-31G** gas phase 41 40142 EX-HiI/6-31G**/gas
PCM 40 39061 EX-HiI/6-31G**/PCM
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6-31G**/PCM. Additionally, 12 EEM models were obtained for
the second atom classiﬁcation EX, based on chemical elements
and maximum bond multiplicity: EX-MPA/6-31G*/gas,
EX-MPA/6-31G*/PCM, EX-MPA/6-31G**/gas, EX-MPA/
6-31G**/PCM, EX-NPA/6-31G*/gas, EX-NPA/6-31G*/
PCM, EX-NPA/6-31G**/gas, EX-NPA/6-31G**/PCM,
EX-HiI/6-31G*/gas, EX-HiI/6-31G*/PCM, EX-HiI/
6-31G**/gas, EX-HiI/6-31G**/PCM. All 24 EEM models
Figure 1. Flowchart of parametrization of EEM models for calculating partial atomic charges in proteins. (A) The reference data used in this study
consisted of QM atomic charges for one training data set of protein fragments, and two test molecules (insulin and ubiquitin). Due to the system size
limitations imposed by the QM calculation, only one insulin monomer was used, and the ﬁrst 14 residues were removed from the ubiquitin structure. In
total, 12 diﬀerent QM atomic charge calculation schemes were used. (B) For each of the 12 QM charge schemes, two atom type classiﬁcation approaches
were employed for EEM model parametrization. Parameters for 24 EEM models were ﬁtted onto the QM charges of the training data set. (C) Each EEM
model was subjected to internal and external validation by comparing the EEM charges against reference QM charges of the training and test molecules,
respectively. Performance was evaluated by 3 indicators, namely the average correlation coeﬃcient (Ravg), the average root-mean-square deviation
(RMSDavg), and the average absolute diﬀerence (Davg).
Journal of Chemical Information and Modeling Article
dx.doi.org/10.1021/ci400448n | J. Chem. Inf. Model. 2013, 53, 2548−25582552
were further subjected to external validation, whereby they were
evaluated for their ability to predict the atomic charges of the test
molecules insulin and ubiquitin.
An overview of all QM calculations performed, and all EEM
models obtained is given in Table 2. An overview of the entire
EEM model parametrization procedure employed in this study is
given in Figure 1. The parametrization and validation of the EEM
models were done using an in-house program. The visualization
of structural models in various representations was performed
using VMD.66
The values of all EEM atomic charges obtained in
this study are included as Supporting Information in csv format.
The parameters of all 24 EEM models developed in this study are
given in Table S1 of the Supporting Information.
■ RESULTS AND DISCUSSION
Performance of the EEM Models. In this study, we
obtained 24 EEM models (Figure 1, Table 2). Each EEM model
was validated with respect to Ravg, RMSDavg, and Davg between
reference QM charges and predicted EEM charges. The results of
the internal and external validation procedures are given in
Table 3 and Figure 2 (see also Supporting Information
Table S2).
Overall, there is good agreement between QM and EEM
charges, suggesting that these EEM models can be used reliably
for rapid atomic charge calculation in proteins. With respect to
internal validation (i.e., validation against the training data sets),
all 24 models have Ravg over 0.91, while 19 models have Ravg over
0.95, and 15 models have Ravg over 0.97. All models have
RMSDavg less than 0.17 e and Davg less than 0.12 e, while 16
models have RMSDavg less than 0.10 e and Davg less than 0.07 e.
With respect to external validation on insulin and ubiquitin, all
EEM models perform comparably as in the internal validation
step, suggesting high transferability. Speciﬁcally, all 24 models
have Ravg over 0.9, while 19 models have Ravg over 0.95, and
14 models have Ravg over 0.97. All models have RMSDavg less
than 0.16 e and Davg less than 0.12 e, while 16 models have
RMSDavg less than 0.10 e and Davg less than 0.07 e. The values
obtained for the majority of models are comparable to previous
EEM parametrizations published in the literature.
There are diverging trends in literature regarding the level of
detail that should be included in the atom type classiﬁcation used
for EEM model parametrization. One direction supports the
use of general atom types,33
while the other direction supports
the use of very detailed atom types.40,41
Our results in Table 3
(see also Supporting Information Table S2) suggested that the
ﬁner grained atom classiﬁcation EX only modestly improved the
accuracy compared to the classiﬁcation E based on chemical
elements alone, and not for all models. In any case, both atom
classiﬁcations can provide satisfactory results for proteins, but we
rather support the use of general atom types to avoid the extra
step and possible errors associated with assigning hybridizations.
Thus, in further we discuss only the results for the models based
on general atom types E, while the complete results can be found
in Supporting Information Table S2.
Accuracy of the EEM Models. A more detailed view of the
accuracy that can be expected for the EEM models developed in
this study is given in Figure 3. Approximately 50% of the
predicted values are expected to contain an error of less than
0.05 e, while approximately 30% of the predicted values are
expected to contain an error between 0.05 and 0.1 e. Finally,
approximately 5% of the values are expected to contain an error
larger than 0.2 e.
Table 3. Validation of the 24 EEM Models Obtained in This Studya
internal validation (training data set) external validation (insulin) external validation (ubiquitin)
EEM model Ravg RMSDavg [e] Davg [e] Ravg RMSDavg [e] Davg [e] Ravg RMSDavg [e] Davg [e]
E-MPA/6-31G*/gas 0.975 0.079 0.062 0.972 0.080 0.064 0.969 0.083 0.065
E-MPA/6-31G*/PCM 0.976 0.080 0.065 0.973 0.081 0.066 0.972 0.081 0.066
E-MPA/6-31G**/gas 0.977 0.067 0.053 0.976 0.065 0.052 0.973 0.069 0.054
E-MPA/6-31G**/PCM 0.977 0.068 0.053 0.976 0.066 0.052 0.973 0.071 0.054
E-NPA/6-31G*/gas 0.975 0.083 0.064 0.971 0.086 0.066 0.971 0.086 0.066
E-NPA/6-31G*/PCM 0.975 0.092 0.067 0.971 0.091 0.065 0.973 0.087 0.063
E-NPA/6-31G**/gas 0.976 0.084 0.065 0.971 0.086 0.067 0.971 0.086 0.066
E-NPA/6-31G**/PCM 0.975 0.093 0.068 0.971 0.092 0.066 0.973 0.088 0.063
E-HiI/6-31G*/gas 0.965 0.125 0.092 0.965 0.114 0.083 0.969 0.113 0.080
E-HiI/6-31G*/PCM 0.948 0.123 0.087 0.948 0.116 0.081 0.958 0.108 0.075
E-HiI/6-31G**/gas 0.967 0.121 0.088 0.965 0.111 0.080 0.970 0.109 0.077
E-HiI/6-31G**/PCM 0.962 0.128 0.094 0.961 0.119 0.087 0.965 0.116 0.084
EX-MPA/6-31G*/gas 0.976 0.076 0.056 0.970 0.082 0.059 0.974 0.076 0.058
EX-MPA/6-31G*/PCM 0.979 0.073 0.056 0.976 0.075 0.057 0.975 0.076 0.058
EX-MPA/6-31G**/gas 0.975 0.070 0.053 0.969 0.073 0.056 0.971 0.072 0.055
EX-MPA/6-31G**/PCM 0.961 0.090 0.069 0.958 0.087 0.067 0.959 0.088 0.065
EX-NPA/6-31G*/gas 0.979 0.077 0.059 0.974 0.081 0.062 0.975 0.080 0.061
EX-NPA/6-31G*/PCM 0.978 0.079 0.063 0.975 0.080 0.063 0.974 0.081 0.063
EX-NPA/6-31G**/gas 0.979 0.077 0.062 0.975 0.081 0.062 0.975 0.080 0.061
EX-NPA/6-31G**/PCM 0.980 0.076 0.062 0.977 0.078 0.062 0.976 0.079 0.062
EX-HiI/6-31G*/gas 0.919 0.148 0.109 0.913 0.146 0.107 0.934 0.130 0.095
EX-HiI/6-31G*/PCM 0.910 0.166 0.118 0.911 0.156 0.110 0.930 0.142 0.099
EX-HiI/6-31G**/gas 0.910 0.156 0.118 0.903 0.154 0.117 0.927 0.137 0.103
EX-HiI/6-31G**/PCM 0.917 0.161 0.117 0.912 0.156 0.112 0.931 0.141 0.101
a
Internal validation denotes validation for the molecules in the training data set, while external validation denotes validation on the test molecules.
Statistical descriptors comprising the average correlation coeﬃcient (Ravg), the average root mean square deviation (RMSDavg), and the average
absolute diﬀerence (Davg) are given. All quantities are given in elementary charges (1 e ∼ 1.602 × 10−19
coulombs).
Journal of Chemical Information and Modeling Article
dx.doi.org/10.1021/ci400448n | J. Chem. Inf. Model. 2013, 53, 2548−25582553
With respect to the practical implications of employing EEM
models for calculating atomic partial charges, it is worth
discussing the expected accuracy of the EEM models in
reproducing not only QM atomic charges, but also various
quantities derived from these charges. Since it is not possible to
give a general evaluation of the expected accuracy of the EEM
models in all possible practical applications, we focus here on two
common uses of atomic charges, namely electrostatic potential
(ESP) and docking calculations.
Figure 4 (see also Supporting Information Table S3) shows
that the ESP computed from EEM charges deviates from the
ESP computed from QM charges on average by 0.0071 au for
insulin and 0.0058 au for ubiquitin, respectively; whereas, the
average correlation coeﬃcient is 0.9 for insulin and 0.87 for
ubiquitin.
To evaluate the accuracy of EEM charges in a typical docking
calculation, we performed the blind docking of glycerol onto the
ubiquitin fragment previously used in our study as a test molecule
for the validation of EEM models. Glycerol was chosen as a
potential ligand because it has been found to stabilize the native
state of ubiquitin.68
The ubiquitin fragment was used as a
receptor in favor of the native ubiquitin dimer because of the size
restrictions imposed by the reference QM calculations. Figure 5
(see also Supporting Information Table S4) shows that the
docking results obtained using QM charges are well reproduced
using the EEM charges given by the corresponding EEM model.
The EEM binding pose diﬀers by 0.07 kcal/mol and an RMSD of
0.131 Å from the binding pose given using QM charges. By
comparison, using Gasteiger−Marsili or AMBER ﬀ9469
charges
on ubiquitin produces diﬀerent binding poses. Speciﬁcally, the
binding pose given by Gasteiger−Marsili charges diﬀers from
that given by QM charges by 0.99 kcal/mol and an RMSD of
3.244 Å. The binding pose given by AMBER ﬀ94 charges diﬀers
by 1.57 kcal/mol and an RMSD of 3.235 Å.
Sensitivity of the EEM Models. We have evaluated the
performance and predicted the accuracy of the EEM models
developed in this study. It is also necessary to translate the
meaning of this accuracy with respect to the ability of the EEM
models to diﬀerentiate between types of charges, since many
times diﬀerent modeling applications rely on diﬀerent types of
charges. For example, in the particular case of pKa prediction via
Figure 2. Validation of EEM models by comparing the predicted EEM
atomic charges against the reference QM atomic charges. Internal validation
denotes validation for the molecules in the training data set. Statistical
descriptors comprising the average correlation coeﬃcient (Ravg), the
average root-mean-square deviation (RMSDavg), and the average absolute
diﬀerence (Davg) are given. All quantities are given in elementary charges
(1e ∼1.602× 10−19
coulombs).ThenamesoftheEEM modelsencodethe
QM scheme and atom classiﬁcation used in their parametrization. Only the
models based on general atom types (E) are given here, while the complete
results can be found in Table 3 (see also Supporting Information Table S2).
Good agreement between QM and EEM charges was found for all data sets,
as Ravg is close to 1, and RMSDavg and Davg are minimal.
Figure 3. Expected accuracy of the EEM models developed in this study, measured as the percentage of atoms for which the error of the EEM vs QM
prediction lies in a certain interval. Only the models based on general atom types E are included in this analysis. The error is computed as the absolute
diﬀerence between the predicted EEM value and reference QM value of the atomic charge. The gray blocks represent the error distribution averaged
over all 12 EEM models obtained in this study, while the black lines indicate the minimum and maximum values for these distributions. (A) Values
obtained for insulin. (B) Values obtained for ubiquitin.
Journal of Chemical Information and Modeling Article
dx.doi.org/10.1021/ci400448n | J. Chem. Inf. Model. 2013, 53, 2548−25582554
QSPR modeling, it was shown that QSPR models which use QM
MPA charges as descriptors perform better than QSPR models
which use QM charges derived from electrostatic potentials (ESP
charges).72,73
On the other hand, QSPR models which use EEM
ESP charges perform comparably well as the QSPR models
which use EEM MPA charges,50
suggesting that the error of the
EEM vs QM prediction could very well overwhelm the
distinction between diﬀerent atomic charge deﬁnitions.
Therefore, one last aspect to be studied is the sensitivity of the
EEM models produced in this study with respect to population
analysis, basis set, and environment. For this purpose, we
inspected the correlation between the QM charges produced by
each of the 12 QM schemes, and the EEM charges produced by
all 24 EEM models (see Supporting Information Table S2).
Table 4 contains the conclusions for the 12 EEM models based
on general atom types E, for insulin and ubiquitin.
It is clear from Table 4 (see also Supporting Information
Table S2) that the models obtained in this study easily
distinguish between population analyses. In all cases, EEM
models parametrized onto MPA charges provide the best
prediction for QM MPA data. Similarly, EEM models parametrized
onto NPA charges always provide the best prediction
for QM NPA data, and EEM models parametrized onto HiI
charges always provide the best prediction for QM HiI data.
Further, in the case of MPA charges, the models easily distinguish
between basis sets, which is expected, since MPA charges are
known to be basis set dependent. As such, EEM models
parametrized onto MPA/6-31G* charges provide the best
prediction for QM MPA/6-31G* data. The equivalent is true
for 6-31G**. In the case of NPA and HiI charges, the models do
not distinguish between basis sets, which correlates with the fact
that NPA and HiI charges have low basis set dependence.74
As
such, EEM models parametrized onto NPA/6-31G* charges
provide the best prediction for both QM NPA/6-31G* and
NPA/6-31G** data. Similarly, EEM models parametrized onto
HiI/6-31G* charges provide the best prediction for both QM
HiI/6-31G* and HiI/6-31G** data. On the other hand, the
EEM models are not able to distinguish between the gas phase
and implicit solvation conditions. In many cases, EEM models
parametrized onto gas phase data provide the best prediction for
QM PCM data, and vice versa.
Availability of Implementation. The models developed in
the present study are fully compatible with any implementation
of the EEM formalism given by eq 3, allowing the computation
of accurate, conformationally dependent atomic charges in
proteins with hundreds of residues in only a few minutes.
In particular, these models can be used with EEM_SOLVER,
our previously published EEM implementation, which
has already been implemented in the Parallel Virtual Machine
(PVM) environment and scales very favorably for large
systems.55
Figure 4. Comparison between the QM and EEM based ESP for insulin and ubiquitin. Only the models based on general atom types E are included in
this analysis. The gray blocks represent averages over all 12 EEM models, while the black lines indicate the minimum and maximum values. The ESP was
calculated using the biomolecular electrostatics software APBS.67
(A) Deviation between QM and EEM based ESP measured as RMSD. (B) Correlation
between QM and EEM based ESP measured as Pearson’s squared correlation coeﬃcient.
Figure 5. Blind docking of glycerol (ochre, licorice representation) onto
the ubiquitin fragment (surface representation colored according to
atomic charges, where red signiﬁes more negative charge, while blue
signiﬁes more positive charge). The ﬁxed receptor was placed in a 100 ×
90 × 90 sized grid, with 0.35 Å spacing between the grid points. The
ligand’s initial conformation was taken from the coordinates of the ideal
glycerol model available in Ligand Expo70
and contained ﬁve rotatable
bonds. All calculations were set up using Triton56
and performed with
AutoDock4.2.71
Each docking run employed 200 iterations of the
Genetic Algorithm, with up to 1 000 000 energy evaluations for each
iteration (the rest of the parameters were kept in their default values).
The calculations diﬀer in the type of atomic charges used for the
receptor, while the ligand always carried Gasteiger−Marsili charges. In
each case, the binding pose which gives the best binding energy in ﬁve
independent docking runs is chosen for comparison. (A) Using MPA/6-
31G*/gas QM chargesestimated binding energy −9.64 kcal/mol. (B)
Using E-MPA/6-31G*/gas EEM chargesestimated binding energy
−9.71 kcal/mol, RMSD 0.132 Å compared to the QM pose. (C) Using
Gasteiger−Marsili chargesestimated binding energy −8.65 kcal/mol,
RMSD 3.244 Å compared to the QM pose; (D) Using AMBER ﬀ94
chargesestimated binding energy −8.07 kcal/mol, RMSD 3.235 Å
compared to the QM pose.
Journal of Chemical Information and Modeling Article
dx.doi.org/10.1021/ci400448n | J. Chem. Inf. Model. 2013, 53, 2548−25582555
■ CONCLUSION
The goal of the study was to extend the coverage of the
Electronegativity Equalization Method (EEM) for atomic charge
calculation in proteins. For the purpose of EEM model
parametrization, fragments of experimentally determined protein
structures were used as reference systems. Reference QM atomic
charges given by three population analyses were calculated at the
HF level, with two basis sets and in two environments. A total of
24 EEM models were parametrized and evaluated in the present
study.
Upon validation on insulin and ubiquitin, the models exhibited
high correlation and low deviations between the QM reference
charges and EEM predicted charges. Very good accuracy is
expected for 80% of the predictions, while poor accuracy is
expected for 5% of the predictions. Last, the models were found
to be consistent with respect to basis set and population analysis.
Overall, the results of the evaluation suggest that the EEM
models obtained in this study can be used reliably for the rapid
calculation of conformationally dependent atomic charges in
proteins and protein complexes. The models can be used with
our previously published EEM implementation EEM_SOLVER,
which allows for an eﬃcient estimation of atomic charges with
application in biomolecular modeling investigations.
■ ASSOCIATED CONTENT
*S Supporting Information
Structures of all reference molecules (.pdb format), values of all
QM and EEM atomic charges (.csv format), values of parameters
for all EEM models (Table S1, .pdf format), results of the
validation of all EEM models against all QM schemes (Table S2,
.pdf format), reproduction of ESP for insulin and ubiquitin
(Table S3, .pdf format), and comparison of docking runs using
diﬀerent types of charges for the receptor (Table S4, .pdf
format). This material is available free of charge via the Internet
at http://pubs.acs.org.
■ AUTHOR INFORMATION
Corresponding Authors
*E-mail: jkoca@ceitec.muni.cz.
*E-mail: svobodova@chemi.muni.cz.
Author Contributions
The study was conceived by J.K., while the procedure was
designed by C.-M.I. and R.S.V. The calculations were performed
by C.-M.I. and S.G., and the data was analyzed by all authors. The
manuscript was drafted by C.-M.I. and critically revised by all
authors. All authors have given approval to the ﬁnal version of the
manuscript.
Notes
The authors declare no competing ﬁnancial interest.
■ ACKNOWLEDGMENTS
C.-M.I. is very grateful to Tomáš Bouchal for the graphic design
ideas and to Dr. Sushil Kumar Mishra for the useful discussions.
This work was funded by the Ministry of Education, Youth and
Sports of the Czech Republic (contract number LH13055) and
the European Community’s Seventh Framework Programme
(CZ.1.05/1.1.00/02.0068) from the European Regional Development
Fund and from the “Capacities” speciﬁc program
(Contract No. 286154). The access to computing and storage
facilities owned by parties and projects contributing to the
National Grid Infrastructure MetaCentrum, provided under the
program “Projects of Large Infrastructure for Research,
Development, and Innovations” (LM2010005) is highly
appreciated. C.-M.I. would like to thank Brno City Municipality
for the ﬁnancial support provided to her through the program
Brno Ph.D. Talent.
■ ABBREVIATIONS
E, atom type classiﬁcation approach based on chemical elements;
EEM, Electronegativity Equalization Method; ESP, electrostatic
potential; EX, atom type classiﬁcation approach based on
chemical elements and maximum bond multiplicity; HiI, iterative
Hirshfeld population analysis; MPA, Mulliken Population
Analysis; NMR, nuclear magnetic resonance; NPA, natural
Table 4. Veriﬁcation of EEM Model Consistency with QM
Calculation Scheme with Respect to Population Analysis,
Basis Set, and Environmenta
Ravg best E-EEM model
EEM model insulin ubiquitin
MPA/6-31G*/gas MPA/6-31G*/gas MPA/6-31G*/PCM
MPA/6-31G*/PCM MPA/6-31G*/PCM MPA/6-31G*/PCM
MPA/6-31G**/gas MPA/6-31G**/gas MPA/6-31G**/gas
MPA/6-31G**/PCM MPA/6-31G**/gas MPA/6-31G**/gas
NPA/6-31G*/gas NPA/6-31G*/PCM NPA/6-31G*/PCM
NPA/6-31G*/PCM NPA/6-31G*/gas NPA/6-31G*/PCM
NPA/6-31G**/gas NPA/6-31G*/gas NPA/6-31G**/PCM
NPA/6-31G**/PCM NPA/6-31G*/gas NPA/6-31G*/PCM
HiI/6-31G*/gas HiI/6-31G**/gas HiI/6-31G**/gas
HiI/6-31G*/PCM HiI/6-31G**/gas HiI/6-31G**/gas
HiI/6-31G**/gas HiI/6-31G**/gas HiI/6-31G**/gas
HiI/6-31G**/PCM HiI/6-31G**/gas HiI/6-31G**/gas
Davg best E-EEM model
EEM model insulin ubiquitin
MPA/6-31G*/gas MPA/6-31G*/gas MPA/6-31G*/gas
MPA/6-31G*/PCM MPA/6-31G*/gas MPA/6-31G*/gas
MPA/6-31G**/gas MPA/6-31G**/gas MPA/6-31G**/gas
MPA/6-31G**/PCM MPA/6-31G**/gas MPA/6-31G**/gas
NPA/6-31G*/gas NPA/6-31G**/PCM NPA/6-31G**/PCM
NPA/6-31G*/PCM NPA/6-31G*/gas NPA/6-31G**/PCM
NPA/6-31G**/gas NPA/6-31G*/gas NPA/6-31G**/PCM
NPA/6-31G**/PCM NPA/6-31G*/gas NPA/6-31G**/PCM
HiI/6-31G*/gas HiI/6-31G*/gas HiI/6-31G*/PCM
HiI/6-31G*/PCM HiI/6-31G*/PCM HiI/6-31G*/PCM
HiI/6-31G**/gas HiI/6-31G*/PCM HiI/6-31G*/PCM
HiI/6-31G**/PCM HiI/6-31G*/PCM HiI/6-31G*/PCM
RMSDavg best E-EEM model
EEM model insulin ubiquitin
MPA/6-31G*/gas MPA/6-31G*/gas MPA/6-31G*/PCM
MPA/6-31G*/PCM MPA/6-31G*/gas MPA/6-31G*/PCM
MPA/6-31G**/gas MPA/6-31G**/gas MPA/6-31G**/gas
MPA/6-31G**/PCM MPA/6-31G**/gas MPA/6-31G**/gas
NPA/6-31G*/gas NPA/6-31G*/gas NPA/6-31G**/PCM
NPA/6-31G*/PCM NPA/6-31G*/gas NPA/6-31G**/PCM
NPA/6-31G**/gas NPA/6-31G*/gas NPA/6-31G*/gas
NPA/6-31G**/PCM NPA/6-31G*/gas NPA/6-31G*/gas
HiI/6-31G*/gas HiI/6-31G**/gas HiI/6-31G*/PCM
HiI/6-31G*/PCM HiI/6-31G*/PCM HiI/6-31G*/PCM
HiI/6-31G**/gas HiI/6-31G**/gas HiI/6-31G*/PCM
HiI/6-31G**/PCM HiI/6-31G*/PCM HiI/6-31G*/PCM
a
Only the analysis for models based on E atom type classiﬁcation is
given here, while the complete results can be found in Supporting
Information Table S2.
Journal of Chemical Information and Modeling Article
dx.doi.org/10.1021/ci400448n | J. Chem. Inf. Model. 2013, 53, 2548−25582556
population analysis; PA, population analysis; PCM, polarizable
continuum model; PDB, Protein Data Bank; PVM, parallel
virtual machine; QM, quantum mechanics/mechanical; QSPR,
quantitative structure−property relationships; RMSD, rootmean-square
deviation
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Charge proﬁle analysis reveals that activation
of proapoptotic regulators Bax and Bak
relies on charge transfer mediated allosteric
regulation
178
Charge Profile Analysis Reveals That Activation of Proapoptotic
Regulators Bax and Bak Relies on Charge
Transfer Mediated Allosteric Regulation
Crina-Maria Ionescu1,2
, Radka Svobodova´ Varˇekova´1,2
, Jochen H. M. Prehn3,4
, Heinrich J. Huber3,4
,
Jaroslav Kocˇa1,2
*
1 CEITEC - Central European Institute of Technology, Masaryk University, Brno, Czech Republic, 2 National Centre for Biomolecular Research, Masaryk University, Brno,
Czech Republic, 3 Centre for Systems Medicine, Royal College of Surgeons in Ireland, Dublin, Ireland, 4 Department of Physiology and Medical Physics, Royal College of
Surgeons in Ireland, Dublin, Ireland
Abstract
The pro-apoptotic proteins Bax and Bak are essential for executing programmed cell death (apoptosis), yet the mechanism
of their activation is not properly understood at the structural level. For the first time in cell death research, we calculated
intra-protein charge transfer in order to study the structural alterations and their functional consequences during Bax
activation. Using an electronegativity equalization model, we investigated the changes in the Bax charge profile upon
activation by a functional peptide of its natural activator protein, Bim. We found that charge reorganizations upon activator
binding mediate the exposure of the functional sites of Bax, rendering Bax active. The affinity of the Bax C-domain for its
binding groove is decreased due to the Arg94-mediated abrogation of the Ser184-Asp98 interaction. We further identified a
network of charge reorganizations that confirms previous speculations of allosteric sensing, whereby the activation
information is conveyed from the activation site, through the hydrophobic core of Bax, to the well-distanced functional sites
of Bax. The network was mediated by a hub of three residues on helix 5 of the hydrophobic core of Bax. Sequence and
structural alignment revealed that this hub was conserved in the Bak amino acid sequence, and in the 3D structure of folded
Bak. Our results suggest that allostery mediated by charge transfer is responsible for the activation of both Bax and Bak, and
that this might be a prototypical mechanism for a fast activation of proteins during signal transduction. Our method can be
applied to any protein or protein complex in order to map the progress of allosteric changes through the proteins’
structure.
Citation: Ionescu C-M, Svobodova´ Varˇekova´ R, Prehn JHM, Huber HJ, Kocˇa J (2012) Charge Profile Analysis Reveals That Activation of Pro-apoptotic Regulators
Bax and Bak Relies on Charge Transfer Mediated Allosteric Regulation. PLoS Comput Biol 8(6): e1002565. doi:10.1371/journal.pcbi.1002565
Editor: James M. Briggs, University of Houston, United States of America
Received March 8, 2012; Accepted May 4, 2012; Published June 14, 2012
Copyright: ß 2012 Ionescu et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This work was funded by the Czech Science Foundation (GD301/09/H004), and the European Community’s Seventh Framework Programme (CZ.1.05/
1.1.00/02.0068) from the European Regional Development Fund and from the ‘‘Capacities’’ specific programme (Contract No. 286154). The access to the
MetaCentrum computing facilities was provided under the programme ‘‘Projects of Large Infrastructure for Research, Development, and Innovations’’ LM2010005
funded by the Ministry of Education, Youth, and Sports of the Czech Republic. CMI would like to thank Brno City Municipality for the financial support provided to
her through the program Brno Ph.D. Talent. HJH and JHMP wish to acknowledge funding by Science Foundation Ireland grant PI 08/IN.1/B1949. The funders had
no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: jkoca@ceitec.muni.cz
Introduction
Mitochondrial outer membrane permeabilization (MOMP) is a
hallmark of programmed cell death (apoptosis). Following
MOMP, apoptotic proteins from the mitochondrial inter-membrane
space are released, causing the activation of cell death
proteases which cleave the cell’s cytoskeleton and genetic material.
MOMP is executed by the Bcl-2 family proteins Bak and Bax that,
upon activation during apoptosis, oligomerize and form pores in
the mitochondrial membrane [1–4].
Bak and Bax oligomerisation is controlled by the interplay of
further Bcl-2 proteins [5–8]. While pro-survival Bcl-2 proteins bind
to and deactivate Bak and Bax [9], other apoptotic Bcl-2 proteins
de-repress this inhibition, leaving Bak and Bax free to oligomerize
[10]. Nevertheless, a separate step, whereby a subclass of apoptotic
Bcl-2 proteins such as Bim and Bid directly activate Bak and Bax,
was proposed to be required for oligomerization [11–13].
The activation steps required for Bax oligomerization were
extensively investigated [14–18]. These steps were found to
comprise Bax translocation from the cytosol to the mitochondrial
membrane, and changes of Bax conformation. Conformational
changes of Bax include exposure of its C-domain, insertion of this
C-domain into the membrane, and exposure of the Bax BH3
domain, one of four homology domains of Bcl-2 proteins
(Figure 1).
In inactive Bax, the C-domain is tightly bound inside a
hydrophobic pocket which we henceforth denote as the ‘BH
groove’. This tight binding was suggested to increase the solubility
of Bax and to keep Bax in the cytosol in the absence of stress [16].
Gavathiotis et al. [18] synthesized a helix mimicking the BH3
domain of the activator Bim (Bim-stabilized a-helix of Bcl-2
domains, Bim-SAHB). They subsequently performed NMR
spectroscopy to study the interaction of Bax with the Bim-SAHB
activator. They found that, in the absence of Bim-SAHB, the Bax
PLoS Computational Biology | www.ploscompbiol.org 1 June 2012 | Volume 8 | Issue 6 | e1002565
activation site was blocked by a largely unstructured loop (loop 1–
2), which opens upon incubation with Bim-SAHB. Using Bax
mutants with reduced loop 1–2 mobility, Gavathiotis et al. later
demonstrated that the opening of this loop was a prerequisite for
Bax activation [19]. Interestingly, the suggested Bax activation site
and the Bax C-domain are separated by over 25 A˚ . Since the
binding of Bim-SAHB to Bax is weak and transient, and neither
significant disturbances in the helical packing, nor covalent
modifications have been observed in Bax upon activation, the
mechanism of how C-domain exposure occurs following this
activation remains elusive [20,21].
Charge transfer was found to be significant in many biomolecular
interactions [22–24], and functionally linked to protein
structural dynamics [25]. In this paper, we therefore investigate
the role of charge transfer during Bax activation by employing an
electronegativity equalization model for the calculation of atomic
charges. Following our investigation, we propose that a charge
transfer network is intimately connected to the way that the
activation information travels across Bax, and that a similar
network is plausible in Bak.
Results
Calibration of an EEM Model for Calculating Partial
Atomic Charges in Proteins
The Electronegativity Equalization Method (EEM) [26] is a fast
technique for estimating partial atomic charges, and has been
successfully applied to zeolites, small organic molecules and
polypeptides [27–31]. To use EEM for studying charge transfer
during Bax activation, EEM model parameters need to be
calibrated to charges of reference molecules.
For this purpose we followed our previously published EEM
model calibration procedure [32], with a few modifications that
Figure 1. Bax undergoes several conformational changes enabling it to form pores in the mitochondrial outer membrane. (A) Bax
activation leads to mitochondrial outer membrane permeabilization (MOMP). Inactive Bax is a cytosolic monomer. Activator-induced opening of loop
1–2 allows the activator to bind. Subsequently, the C-domain of the now active Bax vacates the BH groove and inserts into the mitochondrial
membrane. Additionally, the Bax BH3 domain gets exposed. Bax oligomerization ensues via the BH groove and the BH3 domain, eventually leading to
the formation of pores which permeabilize the membrane. (B) Location of the BH3 domain (cyan), the C-domain (yellow), loop 1–2 (pink) in inactive
Bax (the rest of the protein in gray). (C) Location of above domains (same color coding) in active Bax (the rest of the protein in orange). The activator
peptide Bim-SAHB is shown in purple.
doi:10.1371/journal.pcbi.1002565.g001
Author Summary
Apoptosis is a physiological form of cell death that is
fundamental for development, growth and homeostasis in
multi-cellular organisms. Deviations in the apoptosis
machinery are known to be involved in cancer, neurodegenerative
disorders, and autoimmune diseases. The
proteins Bax and Bak are essential for executing apoptosis,
yet the mechanism of their activation is not properly
understood at the structural level. To understand this
mechanism, we investigated how the electronic density is
reorganized (i.e., how charge is transferred) inside the Bax
molecule when Bax binds a functional peptide of its
natural activator protein. We identified the specific
interactions responsible for the exposure of the functional
sites of Bax, rendering Bax active. Furthermore, we found a
network of charge transfer that conveys activation
information from the Bax activation site, through the
hydrophobic core of Bax, to the well-distanced functional
sites of Bax. This network consists of three residues inside
the hydrophobic core of Bax, which are present also in the
hydrophobic core of Bak, suggesting that these residues
are functionally important and thus potential drug targets.
We provide a straightforward and accessible methodology
to identify the key residues involved in the fast activation
of proteins during signal transduction.
Charge Transfer Mediates Allostery in Bax and Bak
PLoS Computational Biology | www.ploscompbiol.org 2 June 2012 | Volume 8 | Issue 6 | e1002565
address the complex nature of proteins. The reference data
consisted of atomic charges for molecules of two disjoint reference
sets RS1 and RS2, and these charges were calculated using the
quantum mechanics (QM) scheme detailed in the Methods
section. Since calculation of QM charges for large molecules such
as proteins would require too high computational costs, previous
EEM models available in literature were calibrated to reference
charges from small molecules [32–38]. Moreover, to make EEM
as generally applicable as possible, these calibrations used mostly
inorganic or drug-like compounds, which do not reflect the
complex nature of proteins as long, non-neutral molecular chains
with complex 3D assembly. Therefore, to retain properties that are
characteristic for proteins and allow a fast calculation of reference
QM charges at the same time, large fragments of experimentally
determined protein structures were used as reference sets in the
present study (see the Methods section for details). We next
determined values for the EEM model parameters by fitting them
to the reference QM charges using a least squares algorithm. Prior
to fitting, we classified atoms according to two schemes. One
scheme was based on chemical elements only (denoted ‘E’), and
the other on chemical elements and maximum bond order for
each atom (denoted ‘EX’, so that, for example, ‘O1’ indicates
simple bonded, and ‘O2’ double bonded oxygen). Fitting the
model parameters for each of the two atom classification schemes
and each of the two reference sets of atomic charges, we obtained
four parameter sets, denoted RS1-E, RS1-EX, RS2-E, RS2-EX.
Finally, we validated our EEM model by assessing the accuracy of
the model in reproducing the original QM charges from reference
sets RS1 and RS2, and from five additional test molecules T1-T5.
Results were evaluated by the average correlation coefficient Ravg
(squared Pearson’s correlation coefficient), the root mean square
deviation RMSDavg, and the average absolute difference Davg. An
overview of the EEM model calibration procedure is given in
Figure 2, and the complete details can be found in the Methods
section.
Overall, the results in Figure 3 suggested that the finer grained
atom classification scheme ‘EX’ only modestly improved the
accuracy compared to the scheme ‘E’ based on chemical elements
alone. The good agreement between QM and EEM charges for all
data sets suggested that both atom classification schemes can
provide satisfactory calibration results. Moreover, our model was
able to compute EEM atomic charges in less than 1 second for any
of the reference or test molecules using our previously published
implementation [39].
Bax Is Activated by Arg94-mediated Abrogation of the
Ser184-Asp98 Interaction, Decreasing the Affinity of the
Bax C-domain for Its Binding Groove
Having developed an EEM based method for rapid calculation
of atomic partial charges, we investigated whether atomic charge
distribution prior and subsequent to Bax activation would reveal
any clues about the mechanisms of the activation. To this end, we
obtained the 3D structure of inactive Bax (Figure 1B), and of active
Bax in complex with the activator peptide Bim-SAHB (Figure 1C)
from the Protein Data Bank (PDB IDs 1F16 [16] and 2K7W [18]
respectively). We then computed EEM atomic charges using
parameter set RS2-E (Figure 2B) for both structures, and assessed
the absolute charge transfer per residue (total difference in charge
per amino acid residue, DQres), and the intra-residue charge density
reorganization (root mean square deviation in charge per residue,
RMSDres). The mathematical derivation of these descriptors can be
found in the Methods section, and their values for all Bax residues
are available in Table S1.
Experimental evidence suggests that, in inactive Bax, the Cterminal
helix is bound tightly to its hydrophobic pocket (‘BHgroove’).
During activation, this binding gets destabilized, causing
the C-domain to subsequently vacate the BH-groove and insert
into the mitochondrial outer membrane. Early mutagenesis studies
revealed a critical interaction between residues Ser184 and Asp98
at the C-domain-BH-groove interface, whose abrogation is
sufficient to immediately activate Bax [16,40]. We therefore
focused on the changes in charge density distribution in the
vicinity of this interaction. While our calculations did not show any
change in the charge profile of Ser184, they indicated that any
interaction that might have taken place between Asp98 and
Ser184 in the inactive structure has been replaced by an Asp98Arg94
salt bridge in the active structure (Figure 4). Upon
activation, Arg94 becomes more positive (see also Table S1),
which is suggested to lead to the recruitment of Asp98, the
abrogation of the Asp98-Ser184 interaction, and ultimately the
destabilization of the C-domain. This demonstrates that the
binding of Bim-SAHB to Bax can activate Bax by destabilizing the
interaction between the Bax C-domain and its binding groove.
A Network of Charge Transfer Extends from the Bax
Activation Site, through Its Hydrophobic Core, to the Cdomain
Binding Groove
It remains puzzling how the BH groove is influenced by the
binding of Bim-SAHB to Bax, given that this interaction occurs on
the opposite side of the Bax molecule, at a distance of 25 A˚ from
the BH groove.
Interestingly, the residues which showed a transfer of charge
one standard deviation higher than average (Table S1) provided a
clue as to how the activation information proceeds through the
protein. Foremost, significant changes in the net residue charges
were found at the Bax activation site, the BH3-domain (required
for oligomerization) and the C-domain (required for membrane
insertion). Since these are all functional sites of Bax, these changes
were not unexpected. For example, George et al [41] found that a
triple alanine mutant at residues 63–65 (on the BH3 domain of
Bax) ablated Bax oligomerisation and apoptotic activity, which
correlates perfectly with the high charge transfer we found on
residues 64 and 65 upon Bax activation (Table S1).
However, in addition to the expected changes, our method
surprisingly identified significant charge transfer also on the
central helix, inside the hydrophobic core of Bax (residues Trp107,
Arg109 and Lys119 on helix 5). The presence of significant
charges and charge transfer in a predominantly hydrophobic
environment suggests that helix 5 acts as a hub which collects and
distributes charge density (Figure 5). We further calculated the
intra-residue redistributions of charge density upon activator (BimSAHB)
binding. Significant such redistributions were observed at
the Bax activation site, BH groove and loop 1–2. Since these are
the functional regions of Bax, these calculations provide further
support for the notion of a charge transfer network that conveys
information across the entire Bax molecule (Figure S1, Table S1).
Hints of such an interaction transfer phenomenon were found
by Gavathiotis et al. [19]. They titrated Bax with increasing
amounts of Bim-SAHB and observed small, but reproducible doseresponsive
changes in NMR resonance behavior for the backbone
N atoms of residues on the Bax C-domain, as well as on helix 5
inside the hydrophobic core of Bax. They concluded that the
binding of the activator induces reverberations in the core of the
Bax protein, which serve to mobilize the C-domain (allosteric
sensing). Our charge analysis explains these reverberations by a
network of charge transfer through the entire Bax molecule.
Charge Transfer Mediates Allostery in Bax and Bak
PLoS Computational Biology | www.ploscompbiol.org 3 June 2012 | Volume 8 | Issue 6 | e1002565
The Residues Essential for the Charge Transfer Network
in Bax Are Conserved in Bak
Unlike Bax, Bak is present at the outer mitochondrial
membrane in absence of apoptotic stimuli. Evidence suggests that
the inactive form of Bak gets recruited to the mitochondrial outer
membrane and forms complexes with the membrane protein
VDAC2. Upon apoptotic stimuli, pro-apoptotic Bcl-2 proteins
such as Bid transiently bind to Bak. This binding breaks down the
VDAC2/Bak complex and exposes the BH3 domain of Bak,
which is essential for Bak oligomerization [42–46]. As the
activation information may be conveyed by a similar charge
transfer network to induce abrogation of VDAC2/Bak binding,
we wondered whether a comparable transfer hub may exist also in
Bak. Since residues that are essential for functionality are most
often conserved in proteins with similar functions, we therefore
first performed the sequence alignment of Bax and Bak. While the
sequence identity between the two proteins was rather low
(ClustalW2 score 19%, see Figure S2), we found that the residues
Figure 2. Flowchart of calibration of an EEM model for calculating partial atomic charges in proteins. (A) The reference data used in this
study consisted of QM atomic charges for protein fragments in two reference sets (RS1, RS2) and one test set (T1–T5). (B) Two atom type definitions
were used. The atomic electronegativity equations were grouped together based on the atom type. The EEM model parameters for each atom type
were then obtained by least squares fitting to reference QM charges. (C) Each EEM model was subjected to internal and external validation by
comparing the EEM charges with reference QM charges for all available data sets (RS1, RS2, T1–T5).
doi:10.1371/journal.pcbi.1002565.g002
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involved in the charge transfer network in Bax were conserved in
Bak. These homologous residues were Trp125, Arg127 and
Arg137 (Figure 6A). We subsequently compared the 3D structures
of Bax and Bak (PDB ID 2IMT [47]), and found that above Bak
residues were organized in a very similar manner to their Bax
homologues (Figures 5B and 6B). These findings suggest that the
mechanism of charge transfer via the hydrophobic core of Bax is
also plausible for Bak, and that similar residues may also play an
essential role during Bak activation.
Discussion
Allosteric proteins are characterized by a regulatory site that is
distinct and often well distanced from the protein’s active site.
Regulation of the protein’s activity which occurs via this distinct
site is termed allosteric regulation. Recent reports indicate that
allosteric regulation is particularly important during cell signaling
processes, where it has been shown to stabilize receptor proteins,
or to be responsible for the rapid, stress induced release of
dormant signaling proteins bound to the cytoskeleton [48,49]. An
interesting structure-function analysis of Bax performed by George
et al. [41] concluded that monomeric Bax may be held in an
inactive conformation by multiple helices in the absence of stress,
and that Bax may be activated through perturbation at multiple
sites. Nevertheless, later Gavathiotis et al. identified a unique and
well defined activation site on Bax [18], and subsequently
demonstrated that binding of an activator BH3 peptide induces
reverberations in the core of the Bax protein, a phenomenon they
named allosteric sensing [19]. The present study found that this
allosteric regulation is mediated by a charge transfer network,
which conveys the activation information from the Bax activation
site to the functional regions of Bax without compromising the
structure of the BH groove (essential for pro-apoptotic activity). As
charge transfer is significantly faster than domain rearrangements,
the charge transfer mediated alosteric regulation in Bax also allows
for a swift control of the apoptotic fate [50].
In addition to suggesting that charge transfer mediated allosteric
regulation is responsible for Bax activation by pro-apoptotic Bcl-2
proteins, our charge profile analysis also indicated several residues
that actively mediate this charge interaction, providing an
opportunity for further in-depth mutagenesis studies or even
pharmacological intervention.
We first confirmed that the abrogation of the Asp98-Ser184
interaction, which has been reported to be responsible for the
mobilization of the C-domain from the BH groove [16,40], indeed
occurs during Bax activation. We propose that Arg94 plays an
essential role in this abrogation, as it can sequester Asp98 and
prevents the formation of the stabilizing Asp98-Ser184 interaction
in active Bax. Indeed, previous mutational studies [41] showed
that a triple alanine Bax mutant at residues 92 to 94 is biologically
inactive, supporting our finding that residue Arg94 plays a role in
Bax activation.
Furthermore, we found that helix 5 acts as a central hub for the
charge transfer network in Bax. We identified three residues,
Trp107, Arg109 and Lys119, that may act as the main mediators
of this charge transfer. Helix 5 has been found to react to BimSAHB
binding in NMR experiments [19]. It was then found that
the Bim-SAHB-induced opening of the Bax loop 1–2 is essential
for Bax activity, and that this opening induces reverberations in
the protein’s hydrophobic core. A deeper look at the NMR data
from their supplement (Figure S1D from [19]) reveals that
activator binding induces pronounced chemical shifts in the Bax
backbone N atoms in the area of residue Trp107 even when the
mobility of loop 1–2 is restricted by chemical tethering. In Figure
Figure 3. Validation of EEM models by comparing EEM atomic
charges against QM atomic charges. Statistical descriptors
comprising the average correlation coefficient (Ravg), the average root
mean square deviation (RMSDavg) and the average absolute difference
(Davg) are given. These descriptors quantify the agreement between
EEM model charges and QM charges for molecules belonging to the
reference sets RS1 and RS2, and for five further test molecules T1–T5. All
quantities are given in elementary charges (1 e,1.602610219
coulombs). The names of the parameter sets encode the reference
set and atom classification scheme based on which they were
developed (RS1-E, RS1-EX, RS2-E, RS2-EX). Good agreement between
QM and EEM charges was found for all data sets, as Ravg is close to 1,
and RMSDavg and Davg are minimal. Calibrations that used the coarse
atom type classification ‘E’ gave a similarly good agreement as those
where the more detailed classification scheme ‘EX’ was used.
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S1B from the same publication [19], we observe that opening this
loop similarly affects the backbone N atoms in the vicinity of
Lys119. While the authors [19] did not explicitly focus on these
residues, our charge calculations make it reasonable to assume that
they are indeed important for allosteric Bax activation. Moreover,
another study [41] found that triple alanine Bax mutants at
residues 109–111 or 118–120 showed decreased biological activity
in the presence of the activator tBid. Therefore, influencing the
activity of Trp107, Arg109 or Lys119 may readily influence the
biological activity of Bax. Because of their positioning, residues
Trp107 and Arg109 are easily accessible and therefore excellent
drug targets.
The results of our investigation agree well with the mutational
study of George et al [41], in that helix 5 is a central mediator of
Bax activity. Both studies further agree that Arg94 is essential for
Bax oligomerisation, and that residues Arg109 or Lys119 may
influence the biological activity of Bax. In addition, George et al.
suggested that the block of four central residues (113–116) is
mandatory for Bax activity. Comparatively, the amount of charge
transferred by these 4 residues upon Bax activation was only
Figure 4. In active Bax, Arg94 recruits Asp98, destabilizing the C-domain inside the BH groove. Upon activation, Arg94 becomes more
positive, leading to the recruitment of Asp98, abrogation of the Asp98-Ser184 interaction, and ultimately destabilization of the C-domain inside the
BH groove [16,40]. The color coding from Figure 1 is maintained. Additionally, the atoms in residues Arg94, Asp98 and Ser184 are displayed explicitly.
Colors are coded according to their EEM charges, where the color scale ranges from red, through green, to blue, as values of atomic charges go from
negative to positive. The EEM charges were computed using parameter set RS2-E (see Figures 2 and 3). (A) In inactive Bax, Asp98 is engaged in an
interaction with Ser184, which keeps the C-domain in its binding pocket. (B) In active Bax, the now more positively charged Arg94 (see also Table S1)
has sequestered Asp98, which no longer contributes to the stabilization of the Bax C-domain in its BH groove.
doi:10.1371/journal.pcbi.1002565.g004
Figure 5. Proposed charge transfer network in Bax, indicated by net changes in residue charges. The information of the Bim-SAHB
induced activation of Bax is transmitted from the Bax activation site via a charge transfer network through the core of the Bax protein, up to the Bax
C- and BH3-domains. Inside the hydrophobic core of Bax, the central helix, helix 5, acts as a hub which collects and distributes charge density, mainly
through residues Trp107, Arg109 and Lys119. The color coding from Figure 1 is maintained. Additionally, helix 5 is highlighted in green. The Bax
residues which transfer an amount of charge of one standard deviation higher than average (Table S1) are explicitly displayed and color coded
according to whether they become more positive (blue) or negative (red) upon activation. (A) The residues which transfer a significant amount of
charge were found at the Bax activation site, on the loop 1–2, inside the BH groove holding the Bax C-domain, and at one end of the C-domain (see
also Figure S1). Additionally, several such residues were found on helix 5, the central helix in Bax, and on the Bax BH3 domain, suggesting that the
interaction at the Bax activation site is transmitted via a network of charges from the activation site, through the protein core, to the C- and BH3domains.
(B) Top view of helix 5 is given. The organization of residues Trp107, Arg109 and Lys119 inside the hydrophobic core of Bax suggests that
helix 5 acts as a charge transfer hub, which integrates and distributes charge density.
doi:10.1371/journal.pcbi.1002565.g005
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slightly above average (Table S1). Nevertheless, we note that this
block of residues resides at the centre of the Bax molecule and is
very bulky, and therefore these residues are very likely essential for
maintaining the helical fold of Bax. Therefore, the observation of
George et al. that a quadruple mutation in the centre of the Bax
molecule impairs biological activity can be easily explained by
change of stability of the helical fold, rather than by a disruption of
the Bax activation mechanism.
Finally, by performing sequence and structural alignment of
Bax and Bak, we identified that Bak residues Trp125, Arg127, and
Arg137 potentially constitute a similar hub of charge transfer
inside the Bak protein. The membrane protein VDAC2 was
reported to recruit Bak to the mitochondrial membrane in the
absence of apoptotic stimuli. Upon apoptotic stimuli, this
VDAC2/Bak binding can be abrogated by Bcl-2 proteins that
transiently bind to Bak [42–46]. Cheng et al. [42] showed that Bak
mutations at residues Leu78 (within Bak’s BH3 domain), Trp125,
Gly126 and Arg127 (on Bak’s central helix) impair complex
formation with VDAC2, and thus concluded that VDAC2 binding
to Bak must occur in the proximity of the above mentioned
residues. Having identified those residues that may constitute a
transfer charge hub during Bak activation, we propose a charge
transfer mediated allosteric activation mechanism of Bak that is
similar to that of Bax. We propose that transient activator binding
in the vicinity of Arg137 is transmitted through allosteric sensing
to the VDAC2 binding site, which is in the neighborhood of
Trp125 and Arg127. Subsequently, Bak disengages VDAC2,
exposes its BH3 domain and oligomerizes. Since the relevance of
residue Arg137 has not been assessed to date, its investigation may
further our understanding of the details of Bak activation and its
de-repression of VDAC2.
Understanding the structural changes of Bax and Bak during
apoptosis provides important insights into the mechanisms of Bax
and Bak activation, which steps and key players are involved, how
aberrant protein folding or mutations may influence the protein’s
function, and how their activation may be influenced by inhibitors
or synthetic drugs. While X-ray crystallography and NMR
spectroscopy provide excellent experimental techniques to obtain
3D-structures, further theoretical data analysis tools are needed to
obtain better mechanistic and functional insights into the
structural aspects of protein activation. We report here the first
successful application of the Electronegativity Equalization Method
to study protein activation during programmed cell death,
which enabled us to detect and track the allosteric effects
responsible for Bax activation by BH3-only proteins. We have
thus shown how knowledge of atomic charges can yield insight into
biological phenomena even without further simulations or intricate
computations. Moreover, the methodology we developed is
directly applicable to other molecular systems, and thus of interest
in biomedical and pharmacological research.
Methods
EEM Formalism
The Electronegativity Equalization Method (EEM) [26] was
employed here to estimate the charge transfer upon Bax activation
using structural data obtained from the Protein Data Bank (PDB).
EEM enables the determination of connectivity- and geometrydependent
atomic charges. Various formalisms are available in
literature [32–38,51–53]. In the present implementation, we
focused on the original work by Mortier et al. [26] with a minor
modification as suggested by Yang and Wang [54] and described
below. Besides enabling a fast and versatile calibration, this
formalism estimates atomic charges via a set of coupled linear
equations which can be efficiently solved by a Gaussian
elimination procedure (see below).
EEM is based on the Electronegativity Equalization Principle
[55], which was proven within the Density Functional Theory [56]
and which states that electronegativity xx is equalized throughout a
molecule (xx~xi). The electronegativity xi of each atom i in this
molecule can be approximated as a linear function of several
terms:
xi~ x0
i zDxi
À Á
z2 g0
i zDgi
À Á
qizk
X
i=j
qj
rij
:
The first term is the effective electronegativity (i.e., the
electronegativity x0
i of the neutral atom, corrected for the presence
of the molecular environment Dxi). The second term is the charge
of the atom qi multiplied by its effective hardness (i.e., the hardness
g0
i of the neutral atom corrected for the presence of the molecular
environment Dgi). Hardness was defined by Parr and Pearson [57]
as the second derivative of the energy with respect to the charge,
and can be thought of as the resistance to change in charge. The
last term k
P
i=j
qj
rij
accounts for the electrostatic interaction with
Figure 6. Proposed Charge Transfer Network in Bak. (A)
Sequence alignment of central helices of Bak and Bax. An asterisk
indicates a single, fully conserved residue. A colon indicates conservation
between groups of strongly similar biochemical properties. A
period indicates conservation between groups of weakly similar
biochemical properties. The residues involved in the charge transfer
network in Bax are conserved in Bak as Trp125, Arg127 and Arg137. (B)
Bak structure (ochre) is displayed according to Figure 5B, with the same
top view of the central helix, and the same color coding for C-domain
(yellow), BH3-domain (cyan), central helix (green) and hub residues (red
and blue). Residues Trp125, Arg127 and Arg137 are organized in a
similar manner to their Bax homologues, suggesting that they may also
play an essential role during Bak activation.
doi:10.1371/journal.pcbi.1002565.g006
Charge Transfer Mediates Allostery in Bax and Bak
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every other charged atom j in the molecule. k is an adjusting factor
first introduced by Yang and Wang [54].
Setting Ai~x0
i zDxi and Bi~2 g0
i zDgi
À Á
, the molecular
electronegativity can be written as:
x~AizBiqizk
X
i=j
qj
rij
:
Considering the total molecular charge Q to be the sum of all
partial atomic charges qi (Q~
P
qi), a system of equations results,
from which the partial atomic charges qi and the molecular
electronegativity x can be calculated:
B1
k
R1,2
Á Á Á
k
R1,N
{1
k
R2,3
B2 Á Á Á
k
R2,N
{1
..
. ..
.
P ..
. ..
.
k
RN,1
k
RN,2
Á Á Á BN {1
1 1 Á Á Á 1 0
0
B
B
B
B
B
B
B
B
B
B
B
B
@
1
C
C
C
C
C
C
C
C
C
C
C
C
A
:
q1
q2
..
.
qN
x
0
B
B
B
B
B
B
B
@
1
C
C
C
C
C
C
C
A
~
{A1
{A2
..
.
{AN
Q
0
B
B
B
B
B
B
B
@
1
C
C
C
C
C
C
C
A
:
Calibration of the EEM Model
The corrections for electronegativity Dxi and hardness Dgi
cannot be measured [26]. Therefore, the effective electronegativity
and hardness contributions given by Ai~x0
i zDxi and
Bi~2 g0
i zDgi
À Á
respectively were calibrated in this study. The
additional parameter k was also determined, as it allows for a
computationally cheap and straightforward sampling of the (A,B)
parameter space, as previously demonstrated by Svobodova´
Varˇekova´ et al. [32].
The EEM equation of the molecular electronegativity can be
rearranged as a linear equation in A and B for each atom in the
system:
AizBiqi~x{k
X
i=j
qj
rij
:
The above linear equations can be grouped together according
to the type of atom they refer to, as each parameter will be valid
only for a particular type of atom. The classification of atoms into
types can be done according to various criteria. As schemes in
literature use different levels of granularity [e.g., 32,33,35], two
schemes of atom classification were tested in the present study (see
also the Results section).
For each atom type, the parameters A and B can be determined
by least squares minimization, provided that the values of all the
other variables in the equation are known. Here the interatomic
distances were calculated from the 3D atomic coordinates. The
reference atomic charges were calculated by the QM scheme
described below. For each molecule, the value of the global
electronegativity was approximated as the harmonic average of the
electronegativities of its constituent atoms [58]:
x~n
Xn
i~1
1
x0
i
!{1
,
where n is the number of atoms in the molecule, and the values of
x0
i correspond to Pauling electronegativities [59,60]. The extra
parameter k present in this particular formalism was sampled on
several intervals. For each discrete value of k, the least squares
minimization was performed in order to obtain the (A,B)x
parameters, where x goes over all atom types considered. Upon
internal validation, the result was the set of parameters [k,(A,B)x]
which gives the best Ravg (see below) between the reference QM
values and the predicted EEM values for atomic charges. A
scheme of the calibration step is given in Figure 2B, while a
detailed description of this procedure can be found in the work of
Svobodova´ Varˇekova´ et al. [32].
Reference Data Used for EEM Model Calibration
Obtaining appropriate reference data is essential for the
accuracy and applicability of a predictive model. The reference
data used in this study consisted of atomic charges for molecules of
two disjoint reference sets RS1 and RS2, and these charges were
calculated using quantum mechanics (QM) (see below). These
reference molecules were fragments extracted from calcium
containing proteins which were obtained from PDB and whose
structures had been determined by X-ray crystallography or
solution state NMR experiments. Each of the fragments consisted
of amino acid chains, calcium ions and water molecules, and was
obtained from the 3D structure of its parent protein using the
program Triton [61]. The fragments were curated manually to
ensure that, while they are sufficiently small for QM calculations,
they remained biochemically meaningful. For each fragment,
reference QM atomic charges were obtained from a Mulliken
population analysis performed at the HF/6-31G* theory level
using the program Gaussian 03 [62].
An overview of the composition of all fragments used for EEM
model calibration is given in Table 1, while the 3D structures of
these fragments are available online in PDB format at www.ncbr.
muni.cz/,ionescu/Supporting_Data_Sets.zip. Reference sets
RS1 and RS2 were used for model calibration, and internal and
external validation (see below). Five additional test molecules T1T5
were used for external validation. A brief summary regarding
the reference data is given in Figure 2A.
Validation of the EEM Model
The accuracy of the EEM models in reproducing the original
QM charges from reference sets RS1 and RS2, and from five
Table 1. Summary of the atomic composition of all the
protein fragments used for EEM model calibration.
System RS1 RS2 T1 T2 T3 T4 T5
Atoms 23259 42295 1167 1125 1065 1040 1075
Fragments 57 43 1 1 1 1 1
C 6649 12522 350 342 305 298 260
H 10434 20995 562 505 498 503 558
N 2730 3339 117 129 123 104 75
O 3332 5225 136 144 136 133 176
S 30 149 0 3 2 0 6
Ca 84 65 2 2 1 2 0
Reference sets RS1 and RS2 were used for model calibration, and internal and
external validation. Five additional test molecules T1–T5 were used for external
validation.
doi:10.1371/journal.pcbi.1002565.t001
Charge Transfer Mediates Allostery in Bax and Bak
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additional test molecules T1–T5 was evaluated by internal and
external validation. In the internal validation step, the charges
predicted by the EEM model with parameter sets RS1-E and RS1EX
(RS2-E and RS2-EX respectively) were compared against QM
charges from the associated reference set RS1 (RS2 respectively).
In the external validation step, EEM and QM charges were
compared for five test molecules T1–T5 which were not contained
in the original reference sets RS1 and RS2, but were obtained in a
similar manner. Since the reference sets RS1 and RS2 were
disjoint, two further external validations were performed. Therefore,
EEM charges obtained by using parameter sets RS1-E and
RS1-EX (RS2-E and RS2-EX respectively) were compared
against QM charges from the non associated reference set RS2
(RS1 respectively). A schematic representation of the EEM model
validation step is given in Figure 2C.
The correlation between the sets of QM and EEM charges was
assessed by three indicators. The first indicator was the average
correlation coefficient (squared Pearson’s correlation coefficient),
computed for each molecule, and averaged over all molecules in a
set:
Ravg~
PN
I~1
PnI
i~1
q
QM
i
{q
QM
I
 
qEEM
i
{qEEM
I
 
nI {1ð Þs
QM
I
sEEM
I
0
B
B
@
1
C
C
A
2
N
,
where the index i = 1 …N described all atoms in molecule I, qQM
I
and qEEM
I represented average atomic charges in molecule I, sQM
I
and sEEM
I were standard deviations of the atomic charges in
molecule I, nI was the number of atoms in molecule I, and N was
the number of molecules in a given set.
The second indicator was the root mean square deviation,
computed for each molecule, and averaged over all molecules in a
set:
RMSDavg~
PN
I~1
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
PnI
i~1
q
QM
i
{qEEM
i
 2
nI
v
u
u
t
N
:
The third indicator was the average absolute difference,
computed for each molecule and averaged over all molecules in
a set:
Davg~
PN
I~1
PnI
i~1
Dq
QM
i
{qEEM
i
D
nI
N
:
Evaluating Differences in Charges upon Bax Activation
The EEM charge calculations for both Bax structures were
done using the program EEM_SOLVER [39] which implemented
the above mentioned EEM formalism and employed the
parameter set RS2-E developed in the present study.
Two indicators were employed in order to quantify the changes
in the charge profile of Bax upon activation. The first indicator
was the total difference in charge per amino acid residue:
DQres~
Pnres
i~1
qactive
i {qinactive
i
À Á
nres
,
where qactive
i denoted atomic charges in the active Bax, qinactive
i
denoted atomic charges in the inactive Bax, and nres was the
number of atoms in the residue. DQres assessed the amount of
charge that had been transferred to or from each residue. The
second indicator was the root mean square deviation in atomic
charge per residue:
RMSDres~
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
Pnres
i~1
qactive
i {qinactive
i
À Á2
nres
v
u
u
u
t
:
RMSDres assessed the intra-residue charge density redistributions.
Sequence and Structural Alignment between Bax and
Bak
The Bax/Bak sequence alignment was done for the UniProtKB/Swiss-Prot
entries Q07812 (BAX_HUMAN) and
Q16611 (BAK_HUMAN), and was performed using ClustalW2
with default parameters on the EBI server [63]. The structural
models were visualized using VMD [64].
Supporting Information
Figure S1 Activator binding induces significant reorganization
of intra-residue charge density in the functional
regions of Bax. Upon activator (Bim-SAHB) binding to Bax,
significant reorganization of the intra-residue charge density is
observed in the functional regions of Bax, suggesting that the
activation is conveyed across the entire Bax molecule. The color
coding from Figure 4 is maintained, with the C-domain in yellow,
BH3 domain in cyan, central helix in green, the rest of active Bax
in orange, and Bim-SAHB in purple. Additionally, the amino acid
residues which suffer significant redistributions of their charge
density are displayed explicitly (RMSDres one standard deviation
higher than average; see Table S1). These residues can be found at
the Bax activation site, on loop 1–2, inside the BH groove holding
the Bax C-domain, and at the two ends of the C-domain itself. (A)
Side view is given. (B) Top view of helix 5 is given.
(PDF)
Figure S2 Sequence alignment between Bax and Bak
reveals rather low sequence identity (ClustalW2 Score
19%). An asterisk indicates a single, fully conserved residue. A
colon indicates conservation between groups of strongly similar
biochemical properties. A period indicates conservation between
groups of weakly similar biochemical properties. The sequence
alignment for the central helices and the structural alignment are
given in Figure 6.
(PDF)
Table S1 Changes in the charge profile of all Bax
residues upon Bax activation. Net charge transfer was
computed as the total difference in charge per residue (Qres). The
intra-residue charge density redistributions were evaluated as the
root mean square deviation in charge per residue (RMSDres). Both
descriptors were computed using EEM atomic charges, and their
mathematical derivation can be found in the Methods section. All
quantities are given in elementary charges (1 e has approximately
1.602610219
coulombs). The cell background colors mark the
Charge Transfer Mediates Allostery in Bax and Bak
PLoS Computational Biology | www.ploscompbiol.org 9 June 2012 | Volume 8 | Issue 6 | e1002565
various domains of the Bax molecule in agreement with Figure 1
(BH3-domain in cyan, C-domain in yellow, loop 1–2 in pink, and
helix 5 in green). The residues which exhibited a net charge
transfer of more than one standard deviation over the average are
marked in bold, and the color of the font indicates whether the
respective residues became more positive (red) or more negative
(blue) upon activation. These residues are also displayed explicitly
in Figure 5.
(PDF)
Acknowledgments
The authors would like to thank Ms. Niamh M. Connolly and Mr. Sushil
Kumar Mishra for thorough revision of the original manuscript.
Author Contributions
Conceived and designed the experiments: RSV HJH JK. Performed the
experiments: CMI. Analyzed the data: CMI RSV JHMP HJH JK.
Contributed reagents/materials/analysis tools: RSV HJH. Wrote the
paper: CMI RSV JHMP HJH JK.
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MOLEonline 2.0: interactive web-based
analysis of biomacromolecular channels
190
MOLEonline 2.0: interactive web-based analysis of
biomacromolecular channels
Karel Berka1
, Ondrˇej Hana´ k1
, David Sehnal2,3
, Pavel Bana´ sˇ1
, Veronika Navra´ tilova´ 1
,
Deepti Jaiswal2
, Crina-Maria Ionescu2
, Radka Svobodova´ Varˇekova´ 2
, Jaroslav Kocˇ a2,
*
and Michal Otyepka1,
*
1
Regional Centre of Advanced Technologies and Materials, Department of Physical Chemistry, Faculty of
Science, Palacky University Olomouc, tr. 17. listopadu 12, 771 46 Olomouc, 2
Central European Institute of
Technology and National Centre for Biomolecular Research, Masaryk University Brno, Kamenice 5, 625 00
Brno-Bohunice, Czech Republic and 3
Faculty of Informatics, Masaryk University Brno, Botanicka´ 68a, 602 00
Brno, Czech Republic
Received January 30, 2012; Revised April 6, 2012; Accepted April 10, 2012
ABSTRACT
Biomolecular channels play important roles in many
biological systems, e.g. enzymes, ribosomes and ion
channels. This article introduces a web-based interactive
MOLEonline 2.0 application for the analysis of
access/egress paths to interior molecular voids.
MOLEonline 2.0 enables platform-independent,
easy-to-use and interactive analyses of (bio)macromolecular
channels, tunnels and pores. Results are
presented in a clear manner, making their interpretation
easy. For each channel, MOLEonline displays a
3D graphical representation of the channel, its
profile accompanied by a list of lining residues and
also its basic physicochemical properties. The users
can tune advanced parameters when performing a
channel search to direct the search according to
their needs. The MOLEonline 2.0 application is
freely available via the Internet at http://ncbr.muni.
cz/mole or http://mole.upol.cz.
INTRODUCTION
Tunnels or channels, pores, cavities and voids are structural
features of many biomolecular systems possessing
signiﬁcant biological functions. The following are just a
few of the numerous examples where channels play an
important biological function; highly selective ion
channels (1–6), channels and pathways in photosystem II
(7,8), ribosomal polypeptide exit channel (9), substratedetermining
active site access channels of Cytochrome
P450 (10–15) and haloalkane dehalogenases, where mutagenesis
of substrate access channels alters enzyme activity
(16,17). As an empty interior space is a key feature of this
type of biomolecule, a considerable amount of attention
has been paid to analyzing its properties (18–20). Many
algorithms and software tools have been developed to
identify these structures in (bio)macromolecules, including
grid (16,21–24), space ﬁlling (25) and slice methods
(26,27), and Voronoi diagrams (18,28–30).
CAVER (16), MOLE (28), MolAxis (29,30) and
PROPORES (31) are all dedicated software tools for
analyzing molecular channels. CAVER 1.0 (16) involves
grid nodes evaluated by a cost function based on the
square of reciprocal distance to the closest atom, and
then employs the Dijskstra’s algorithm (32) to select the
shortest and most geometrically convenient pathway from
an internal to external point. In 2005, CAVER 1.0 represented
a considerable advance in the automatic detection
of channels. However, its algorithm suffered from several
limitations, which have since been overcame in the later
issued software named MOLE (28). The core of the
MOLE 1.0 algorithm again utilizes the Dijkstra’s path
search algorithm, which is applied to a Voronoi mesh
(33,34). A later published software, MolAxis (29,30),
uses an algorithm similar to MOLE. Another recent
tool, PROPORES (31), searches for channels in a
similar fashion to CAVER, but it also rotates side
chains along the channel so that they adopt sterically
allowed positions in order to enlarge possible bottlenecks.
This article presents the web-based MOLEonline application
(ver. 2.0), which offers a user-friendly, interactive
and platform-independent environment for the setup,
manipulation, analysis and printing of channel search
results. Besides structural features, MOLEonline also
allows analysis of the basic physicochemical properties
of (bio)macromolecular channels, tunnels and pores.
*To whom correspondence should be addressed. Tel: +420 585634756; Fax: +420 585634761; Email: Michal.Otyepka@upol.cz
Correspondence may also be addressed. to Jaroslav Kocˇ a. Tel: +420 549492685; Fax: +420 549491060; Email: Jaroslav.Koca@ceitec.muni.cz
W222–W227 Nucleic Acids Research, 2012, Vol. 40, Web Server issue Published online 2 May 2012
doi:10.1093/nar/gks363
ß The Author(s) 2012. Published by Oxford University Press.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/
by-nc/3.0), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
byguestonFebruary21,2016http://nar.oxfordjournals.org/Downloadedfrom
DESCRIPTION OF THE TOOL
The procedure in using the MOLEonline 2.0 application
involves three steps: (i) setup; (ii) calculation; and (iii)
results visualization and manipulation.
Setup
The structure to be analyzed can be either taken from the
Protein data bank (PDB) server (35) or uploaded in the
PDB format. Once the structure is uploaded, it is
visualized by the Jmol Java plugin (36). In addition, the
sequence corresponding to the structure can be explored in
an interactive window, enabling selection of the starting
residues (Figure 1). MOLEonline enables the user to deﬁne
the starting point based on the center of mass of selected
residues, either by selection from the sequence or
manually by selection of x, y and z coordinates. In the
case of known and annotated enzyme structures,
MOLEonline allows the use of information on the active
site residues from the catalytic site atlas (CSA) database
(37) and use of biological unit instead of asymmetric one.
The last possibility is to use ‘Automatic starting points’.
These points are the deepest points in the protein’s cavities
and using them can provide primary information on the
layout of channels inside a protein.
Calculation
After setup, the calculation of channels is executed by the
MOLE 2.0 software (D. Sehnal et al., unpublished data)
running on a server. All setup and structure information
are deposited on the server in a unique directory (which is
translated as a unique URL for a web browser). After the
MOLE 2.0 calculation, further analyses of the channel
results are carried out, providing comprehensive and
easily interpretable information about the channels (see
below).
The channel computation in the MOLE 2.0 software is
performed in several steps as follows:
(1) the Voronoi diagram is computed;
(2) the Voronoi diagram is reﬁned and split into several
smaller parts called cavity diagrams, representing all
the empty space in the molecule;
(3) starting and ending points are identiﬁed in each of
the cavity diagrams; and
(4) Dijkstra’s shortest path algorithm is used to ﬁnd the
channels between the pairs of starting and ending points.
Figure 1. MOLEonline 2.0 setup webpage for channel calculation. Each job is assigned a job ID to allow easy access to the results. Setup starts with
the selection of a PDB ﬁle (here 1TQN) either from the PDB database or uploaded as a user ﬁle. The tunnel starting point can be selected
automatically (inside cavities detected by MOLE 2.0 algorithm) or manually, by using CSA (37), via selection through the interactive sequence
applet on the bottom of the page or by specifying of x, y, z coordinates in advanced settings. Advanced settings also enable the adjustment of
parameters determining the tunnel searching algorithm. All parameters are set in A˚ ngstro¨ ms (for details see the text).
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The Voronoi diagram divides a metric space according to the
distances between discrete sets of speciﬁed objects. In our
case, the objects are atomic centers with van der Waals
(vdW) radii assigned according to the parm99 force ﬁeld
(38). Molecular surface is calculated as a probe accessible
surface with a deﬁned probe radius (default 3 A˚ ). A vertex of
the Voronoi diagram is removed if a sphere with interior
threshold (default 1.25A˚ ) radius cannot pass through any
of the tetrahedron sides. The Voronoi diagram is split into
several smaller cavity diagrams that are analyzed for suitable
channel start and end points between vertices of the cavity.
Starting points are initially estimated by considering a
centroid from all the corresponding atomic centers of the
residues selected by the user. Starting points are then
selected within a speciﬁed origin radius (default 3 A˚ ) as the
closest vertex for each cavity. End points are selected for
each cavity diagram as the tetrahedra on the boundary
vertices. Channel exits can only be assigned to those
tetrahedra that are separated by a distance equivalent to
the surface cover radius (default 10 A˚ ). Finally, when the
set of start and end points has been identiﬁed for each
cavity, the Dijkstra’s shortest path algorithm is used to
ﬁnd the channels between all pairs of start and end points.
The edge weight function used in the algorithm takes into
account the distance to the surface of the closest vdW sphere
and the edge length. The channel centerline is represented as
a 3D natural spline. Depending on the density of computed
exits, the algorithm may ﬁnd duplicate channels. Therefore,
in the ﬁnal post-processing step, if two channels are nearly
identical, the longer one is removed. A detailed explanation
of the algorithm (also as a scheme) and parameters of the
calculation can be found on the MOLEonline webpage
(e.g. http://mole.upol.cz/documentation/). MOLE 2.0
outperforms the original MOLE (28) algorithm in many
aspects. For instance, it is quicker due to the division of
the internal space within the macromolecule to separate
subcavities. There is no need to determine the number of
channels prior calculation. MOLE 2.0 enables automatic
selection of the starting points and calculation of some
basic physicochemical properties of the channel-lining
residues.
Results visualization and analysis
Proﬁles of the channels found are presented in three ways:
(i) plots of channel radii against length (visualized using
gnuplot—http://www.gnuplot.info—as PNG images); (ii)
an interactive table summarizing the set of lining residues
and physicochemical properties; and (iii) the channel
isosurface along its centerline, which is visualized in the
Jmol plugin (36).
MOLEonline 2.0 also allows calculation of basic
physicochemical properties along the unique channellining
amino acids side chains (these properties are not
calculated for nucleobases). Charge, hydropathy and
hydrophobicity indices (39,40), polarity (41) and mutability
(42) can be estimated.
Charge is calculated as the sum of charges on the side
chains (at pH $7) lining the channel.
Hydropathy (39) is calculated as an average of the
hydropathy index of lining side chains, where the most
hydrophilic is Arg (À4.5) and the most hydrophobic is
Ile (+4.5).
Hydrophobicity (40) is calculated as an average of
normalized hydrophobicity scales, where the most hydrophilic
residue is Glu (À1.14) and the most hydrophobic
residue is Ile (1.81).
Polarity (41) is calculated as an average of amino acid
polarity. Polarity values range from zero for non-polar
amino acids (Ala and Gly), through values of around
1.5 for polar residues (e.g. Ser 1.67), and ﬁnally, to two
digits values for charged residues (Glu 49.90, Arg 52.00).
Mutability (42) is calculated as an average of relative
mutability index. Relative mutability is high for mutatable
amino acids, e.g. small polar amino acids (Ser 117, Thr
107, Asn 104) or small aliphatic amino acids (Ala 100, Val
98, Ile 103). On the other hand, the mutability is low for
amino acids that play important structural roles, such as
aromatic amino acids (Trp 25, Phe 51, Tyr 50) or special
amino acids (Cys 44, Pro 58, Gly 50).
Such an approach gives only an approximate value of
mutability, whereas sequence speciﬁc analyses can be performed
using the multiple sequence alignment tools in
other programs, e.g. ConSurf (43) and Hotspot Wizard
(44). It is worth noting that the estimated physicochemical
properties should be interpreted with care, as the calculation
is based on an assumption that the side chains of the
lining amino acids signiﬁcantly determine the environment
within the identiﬁed channel. The calculation might be
sensitive to exact position of the starting and ending
points.
Users of MOLEonline can download all results as a
report. Channel centerline positions with radii of maximally
inscribed balls values can also be downloaded in
two formats for further analysis and storage: (i) as a
generic PDB ﬁle or (ii) as a python script for visualization
in PyMol (http://www.pymol.org).
RESULTS AND DISCUSSION
Examples of usage
Microsomal Cytochrome P450 (CYP) enzymes are important
for the metabolism of many endogenous
compounds and xenobiotics (45,46). CYPs share a
buried active site (47), which is connected to the outside
environment by various access/egress channels. (15) These
channels are responsible for substrate passage to and
product release from the active site, and they are considered
to be involved in substrate preferences of CYP,
which has been shown to vary considerably among CYP
enzymes (12,13). Figure 2 shows all the channels connecting
the active site of a CYP enzyme [calculation started
from Glu 308 and Thr 309 according to the CSA (37)] of
CYP3A4 (PDB: 1TQN) with the exterior. The top ranked
channel found by MOLEonline (white in Figure 2) is the
solvent channel (15). The solvent channel is 17 A˚ long and
its bottle-neck is 1.41 A˚ wide. The solvent channel is also
rather hydrophilic as its hydropathy equals À1.9. By comparison,
the hydropathy values of channels 2e, 2a and 2f
are À0.2, À0.3 and 0.4, respectively, which suggests that
these channels are less hydrophilic. The same trend can be
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seen in the hydrophobicity index, which again suggests
that the solvent channel is also more hydrophilic (À0.68)
than channels 2e, 2a and 2f, with values of 0.1, 0.08 and
0.1, respectively. These ﬁndings are consistent with
previous data, which have identiﬁed the solvent channel
as the main channel responsible for active site solvation
(48) and hydrophilic product release (13,49), while
channels of 2x family are considered to be involved in
hydrophobic substrate binding (13,50).
The ribosomal exit tunnel (RET) allows nascent peptide
chains synthesized at a peptidyl transferase center to exit
the ribosome (9). Analysis of ribosomal channels represents
a challenge for software tools like MOLEonline,
due to the considerable size and complexity of ribosomes
[approximately 100 000 heavy atoms (28)]. Figure 3 shows
the RET of a large ribosomal unit from Haloarcula
marismortui (PDB: 1JJ2 containing 90 650 atoms). In
order to achieve optimal results, the channel search parameters
had to be adjusted. Since the RET is large enough
for passage of nascent peptide with a channel bottleneck
radius of $3 A˚ , the probe radius has to be greater (6 A˚ ) to
capture the channel. The interior threshold also has to be
increased to avoid additional small channels in the
structure (2.4 A˚ ). In addition, the surface cover radius
should be enlarged to avoid redundant channels appearing
(20 A˚ ). Two residues of the peptidyl transferase center
were chosen as the start of the RET (Chain 0: U 2620,
A 2486). The calculation takes $35 s on the server (CPU
Intel i5 760 2.8 GHz, 4 GB RAM), while the total time,
including transfer of data onto client web pages, takes $1–
2 min. The length of the ribosomal exit channel is $100 A˚
with three bottlenecks of minimum radii $4.5 A˚
(Figure 3). The RET is highly hydrophilic, polar and
mostly lined by negatively charged residues (11 nt from
23 S rRNA have their negatively charged main chains
oriented toward the channel and two Glu residues have
side chains facing the channel); the negative charge is to
some extent compensated by six Arg residues. The
distributed charge of the ribosomal polypeptide exit
channel is important to prevent the nascent peptides
from becoming ‘stuck’ inside the ribosome.
Limitations
The presented application has four main limitations. The
ﬁrst limitation stems from the initial concept that the
channels are extrapolated as sets of maximally inscribed
Figure 2. Results of channel analysis of Cytochrome P450 3A4 (CYP3A4) using the setup shown in Figure 1. Four channels found from
user-speciﬁed starting point are shown, whereas the automatic detection also found additional 17 tunnels which are not shown for clarity. The
proﬁle of the tunnel #1 along the centerline and list of lining residues are shown in the external windows (right-hand side). A list of all the unique
lining residues and the corresponding side chains alone is displayed along with physicochemical properties of the respective channel. Lining residues
can also be visualized along the channel centerline, with the channel represented by maximally inscribed spheres in the Jmol window. It is also
possible to show molecular surface and all detected cavities and their volumes. In addition, starting points can be shown as small cubes for original
user-deﬁned starting point (in magenta), for optimized position of such starting point (in green) and for all automatically detected starting points (in
yellow). Information about tunnel proﬁles and lining residues can be further exported in form of report, PDB ﬁle or python ﬁle for visualization in
Pymol.
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balls along the channel centerline. Such an extrapolation
does not allow complex channels with bulges to be
mapped accurately. The second limitation arises because
the channel-ﬁnding algorithm is applied to an
atom-centered Voronoi mesh. In principle, the additively
weighted Voronoi graph or power diagram offers some
beneﬁts in terms of precision, but the gain in precision is
small compare to the uncertainties associated with the
chosen structures (e.g. X-ray structures with ﬁnite resolution,
which is generally higher than 0.8 A˚ ), treatment
of hydrogen atoms and atomic radii set. The analysis of
transmembrane pores is also limited (or not so convenient)
because the transmembrane pores have to merged from
pore segments identiﬁed as tunnels by MOLEonline 2.0.
The ﬁnal limitation relates to the software and data
handling on the server, which limits the maximal size of
the studied system to around 100 000 atoms (8 MB).
CONCLUSIONS
In this article, we described MOLEonline 2.0 (http://ncbr
.muni.cz/mole or http://mole.upol.cz), a new web-based
interactive tool for the analysis of molecular channels
and pores. The MOLEonline interface enables
platform-independent, easy-to-use and interactive
analyses and offers the prospect of high automation, e.g.
by downloading structures from the PDB database and
employing automatic active site identiﬁcation based on
the CSA. The results of the channel search using
MOLEonline are presented in a clear visual or data
form, making their interpretation and further manipulation
easy.
FUNDING
Czech Science foundation [GD301/09/H004, 303/09/1001,
P303/12/P019, P208/12/G016]; Ministry of Education of
the Czech Republic (ME 08008); Palacky University
[Student Project PrF_2012_028]; the European
Community’s Seventh Framework Program from the
Operational Program Research and Development for
Innovations—European Regional Development Fund
[CZ.1.05/2.1.00/03.0058, CZ.1.05/1.1.00/02.0068],
‘Capacities’ speciﬁc program [Contract No. 286154]; and
European Social Fund [CZ.1.07/2.3.00/20.0017]. D.S. and
C.M.I. also acknowledges ﬁnancial funding through a
PhD. Talent program by Brno City Municipality.
Funding for the open access charge: Czech Science foundation
[P208/12/G016].
Conﬂict of interest statement. None declared.
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SiteBinder: an improved approach for
comparing multiple protein structural motifs
197
SiteBinder: An Improved Approach for Comparing Multiple Protein
Structural Motifs
David Sehnal,†
Radka Svobodová Vařeková,†,
* Heinrich J. Huber,‡
Stanislav Geidl,†
Crina-Maria Ionescu,†
Michaela Wimmerová,†
and Jaroslav Koča†,
*
†
National Centre for Biomolecular Research, Faculty of Science and CEITEC - Central European Institute of Technology,
Masaryk University Brno, Kamenice 5, 625 00 Brno-Bohunice, Czech Republic
‡
Centre of Systems Medicine, Department of Physiology and Medical Physics, Royal College of Surgeons in Ireland,
123 St Stephens Green, Dublin 2, Ireland
*S Supporting Information
ABSTRACT: There is a paramount need to develop new techniques
and tools that will extract as much information as possible
from the ever growing repository of protein 3D structures. We
report here on the development of a software tool for the multiple
superimposition of large sets of protein structural motifs. Our
superimposition methodology performs a systematic search for
the atom pairing that provides the best fit. During this search, the
RMSD values for all chemically relevant pairings are calculated by
quaternion algebra. The number of evaluated pairings is markedly
decreased by using PDB annotations for atoms. This approach
guarantees that the best fit will be found and can be applied even when sequence similarity is low or does not exist at all. We have
implemented this methodology in the Web application SiteBinder, which is able to process up to thousands of protein structural
motifs in a very short time, and which provides an intuitive and user-friendly interface. Our benchmarking analysis has shown the
robustness, efficiency, and versatility of our methodology and its implementation by the successful superimposition of 1000
experimentally determined structures for each of 32 eukaryotic linear motifs. We also demonstrate the applicability of SiteBinder
using three case studies. We first compared the structures of 61 PA-IIL sugar binding sites containing nine different sugars, and
we found that the sugar binding sites of PA-IIL and its mutants have a conserved structure despite their binding different sugars.
We then superimposed over 300 zinc finger central motifs and revealed that the molecular structure in the vicinity of the Zn
atom is highly conserved. Finally, we superimposed 12 BH3 domains from pro-apoptotic proteins. Our findings come to support
the hypothesis that there is a structural basis for the functional segregation of BH3-only proteins into activators and enablers.
■ INTRODUCTION
Nowadays, a large amount of information about the 3D structure
of proteins is available, and more and more structures are
being solved every year because of advances in experimental
techniques and their increased availability. This amount of data
provides the opportunity to compare large sets of protein structural
motifs like binding sites, secondary structure elements,
cavities, and tunnels. Such analyses can help identify the main
characteristics of important protein motifs. The obtained characteristics
can subsequently be used as patterns in drug dis-
covery,1,2
to understand the relationship between a protein’s
structure and its function and even predict its function,3−5
to
classify proteins,6,7
to identify evolutionary relationships
between proteins,8−10
etc. Collecting large sets of protein structural
motifs is a fairly simple task. This task can be accomplished
by employing available software tools or in-house
scripts that retrieve data from structural databases on the basis
of primary or secondary protein structure queries. The more
sophisticated challenge is to perform the comparison of these
large sets of protein structural motifs, as this requires specifically
adapted algorithms and software tools. Such a comparison
is a particular topic because, on the one hand, these motifs are
small compounds, but on the other hand, the motifs are parts of
proteins. To our knowledge, no software tool available to date
can process hundreds of protein structural motifs at one time
and allow for a straightforward comparison within these large
sets of structures. Therefore, our goal was to develop and implement
a new methodology for comparing large sets of protein
structural motifs in an efficient, flexible, and intuitive manner.
The comparison of 3D structures is a complex topic that
can be divided into several subtopics. We distinguish between
methods that compare compounds with identical (or very
similar) 2D structure, as opposed to methods dealing with compounds
for which the 2D structure differs significantly. The
term “2D structure”, as it is introduced in chemoinformatics,11
refers to the topology of the molecule, meaning the nature and
connectivity of the atoms contained in the molecule. We also
Special Issue: 2011 Noordwijkerhout Cheminformatics
Received: September 19, 2011
Published: February 1, 2012
Article
pubs.acs.org/jcim
© 2012 American Chemical Society 343 dx.doi.org/10.1021/ci200444d | J. Chem. Inf. Model. 2012, 52, 343−359
differentiate between the methods on the basis of the type of
molecules they processorganic molecules, proteins, or protein
motifs.
Organic molecules with different 2D structures can be compared
by two principal methods, namely, the rigid body approach
and the flexible body approach.12,13
Rigid body methods12,14
keep
the structure of both molecules fixed and try to find an alignment
by maximizing some kind of volume overlap (i.e., van der Waals
overlap, electron density overlap, electrostatic potential overlap,
etc.). The overlap optimization methods range from simplex
optimization, gradient optimization, and Fourier space methods
to Monte Carlo optimization. Flexible (or semiflexible) body
methods13,15
change the structure of one molecule during the
comparison, thus simulating the process of how the molecule
adapts its shape when undergoing a chemical reaction.
The comparison of proteins with different 2D structures can
be classified as global or local.16
The algorithms and available
software for both of these approaches were reviewed by
Gherhardini et al.17
Global comparison approaches use various
algorithms, such as dynamic programming,18
double dynamic
programming,19
branch and bound approach,20,21
subgraph iso-
morphism,22,23
or extension of seed matches.24
Global comparison
is used to classify protein structures and to identify
evolutionary links between distant homologues. Nevertheless,
the function of a protein usually depends more on the identity
and location of a few residues comprising the active site than on
the overall structure. In order to directly analyze and compare
the residues involved in protein function, local (as opposed to
global) structural comparison methods have been developed.
These methods focus on detecting a similar 3D arrangement of
a small set of residues, possibly in the context of completely different
protein structures. Local structure comparison approaches
are mainly based on algorithms that employ geometric
hashing,25,26
subgraph isomorphism,27,28
recursive search connected
with the branch and bound algorithm,29,30
and graphbased
heuristics.31
To identify local similarities within two
entire protein structures such algorithms can be applied without
any a priori assumption or by using a predefined structural template
to screen a structure. The structural templates can be user
defined.32
A special case of local structure comparison is searching
for a structural motif in a protein by comparing the motif
with a relevant part of the protein. These approaches are reviewed
in a recent paper.33
The development of comparison methods for protein
structural motifs with different 2D structures has become an
important topic of research within the past few years.34,35
These
comparisons are, among others, necessary for the functional
annotation of proteins.36,37
General purpose software tools
able to compare all types of molecules with different 2D structure
(i.e., organic molecules, proteins, and protein motifs) are also
available (e.g., Bauer et al.38
).
Superimposition or superposition16
is the comparison of
molecules with identical (or very similar) 2D structures. Superimposition
can be applied to study different conformers of one
molecule, and these conformers can be obtained from experiment,
from molecular dynamics simulations, or from different
databases of 3D structures. Likewise, superimposition is often
useful to study substructures that were obtained by the analysis
and comparison of the 2D structure of molecules or the
primary structure of proteins. Superimposition approaches are
similar for organic molecules, proteins, and protein motifs.
In brief, superimposition consists of several interdependent
stages.39
First, it is necessary to find the correspondence between
the atoms coming from different structures. We will refer to this
first step, as well as to its results, as atom pairing or simply
pairing. Using an atom pairing is necessary so that the structures
can be processed as sequences of points in the 3D space.
In the second step, the sets of paired 3D points are fitted together
as tightly as possible by a geometrical transformation.
We will refer to this step as optimal fitting because its final
result gives the coordinates of the superimposed structures. The
last phase of the superimposition is to evaluate the quality
of the fit. This is done by computing the root-mean-square
deviation (RMSD) between the sets of 3D coordinates
belonging to the structures that have been superimposed. We
further discuss the currently available methodology for performing
the steps of atom pairing and optimal fitting.
From the mathematical point of view, pairings are bijections,
which are functions where every element from the first set is
assigned to exactly one element from the second set. For structures
with n atoms, n! such bijections can be constructed, and
therefore, n! pairings may exist. It is desirable to find the best
pairing, meaning the pairing that will eventually lead to the
lowest RMSD between the superimposed structures. Finding
the best pairing requires testing all constructed pairings and is
therefore very time demanding. Nevertheless, an incorrect atom
pairing can lead to a poor superimposition. There are several
heuristics and algorithms to solve this problem, such as implicit
pairing,40,41
employing sequence alignment,42,43
systematic
approach,44
or subgraph matching.45,46
We briefly describe
these below.
Implicit pairing associates atoms with the same index or
position (i.e., pairing the i-th atom of the first molecule to the
i-th atom of the second molecule). Pairing atoms by this algorithm
is extremely fast. An additional advantage is that the
subsequent fitting will only be performed once because only
one pairing is produced. However, implicit pairing is suitable
only when the atoms in both molecules are indexed or ordered
identically, as in the case of conformers resulted from molecular
dynamics simulations. Many state of the art programs that
offer the superimposition of organic molecules (e.g., Chimera,41
VMD,47
Gromacs,40
gOpenMol,48
Pymol49
) use implicit pairing.
Employing sequence alignment provides an improvement on
the implicit pairing approach. First, the sequence alignment
is performed by a selected algorithm (e.g., Needleman and
Wunsch alignment,50
ICM ZEGA alignment,51
etc.). Afterward,
the atoms from the aligned residues are paired using an implicit
pairing. This approach is applicable only for the superimposition
of proteins or protein sequences with a reasonable
degree of sequence similarity. Several drug design packages
(e.g., MOE,42
Discovery Studio,52
ICM,43
etc.) implement this
approach.
The systematic approach finds all possible pairings and is
therefore very robust. However, because the fitting will have to
be performed for a large number of pairings, this method is
time consuming and therefore useful mainly for small molecules.
It can be sped up by backtracking,53
a procedure that is
able to discard possible solutions as soon as they appear unfeasible.
Further decrease in computational complexity can be
achieved by pairing only atoms that have corresponding chemical
element symbols and/or come from comparable chemical
neighborhoods.
Subgraph matching, which was originally developed for processing
molecules with different 2D structure, can also be used
for finding a relevant pairing (reviewed by Raymond et al.46
).
Journal of Chemical Information and Modeling Article
dx.doi.org/10.1021/ci200444d | J. Chem. Inf. Model. 2012, 52, 343−359344
This approach identifies the largest possible atom sets that can
be superimposed.
When an atom pairing has been found, the sequences of
paired 3D points can be fitted by performing a geometrical
transformation (composition of a translation and a rotation in
the 3D space). Finding the transformation that will lead to the
optimal fit is a fairly cumbersome task. An iterative solution to
this problem was published by McLachlan et al.,54
while a
closed form solution that utilizes rotation matrices was published
by Kabsch et al.55
This rotation matrix approach was
later reformulated using quaternion algebra. Many authors over
the past 20 years have “rediscovered” the application of quaternions
in the superimposition of 3D points (i.e., Horn,56
Diamond,57
and Kearsley58
). However, within the community of computational
chemists and biologists, quaternions were introduced by
Coutsias et al.39
and are still a topic of research.59
All the closed
form solutions have linear space and time complexity in the
number of atoms. These solutions work by translating both
structures to their common origin and then using singular value
decomposition in the case of rotation matrices or eigenvectors
in the case of quaternions.
Superimposition can be performed for two or more structures
at once, depending on the nature of the investigation.
Superimposing two molecules or motifs is a very useful task if
the purpose is the in-depth structural comparison and characterization
of the two compounds under investigation. Many
software tools offering the superimposition of two compounds
are available,40,41,47−49
all using implicit pairing. Nevertheless,
one often needs to compare the structures of tens or hundreds
of compounds at a time in order to find structural trends or
peculiarities. In this case, it is necessary to perform a multiple
superimposition, which is a fairly more complex procedure than
the superimposition of only two structures at a time. The
quality of a multiple superimposition procedure can be measured
using the generalized RMSD,60
which is the average
RMSD between all pairs of structures. Another possibility is to
compute the RMSD between each structure and the calculated
average structure and then average these RMSD values over all
structures.61
A naive approach to this problem is to pick one of
the structures and superimpose all structures to this chosen
one. A quadratic complexity algorithm to this problem was published
by Konagurthu et al.60
and is used, for example, in Pymol.49
A more advanced approach is to superimpose all pairs of
structures, order the pairs by the quality of the superimposition,
and then superimpose the structures to an iteratively computed
average.6
An improved approach to this problem, with nearly
linear complexity (in the number of structures), was published by
Eidhammer et al.16
and later generalized by Wang et al.61
This
method is based on iteratively superimposing each structure onto
the average model of the structures superimposed in the previous
step until a stable configuration is reached.
In this work, we focus on the comparison of large sets of
protein structural motifs. Such large sets are generally collected
in an automated fashion by querying the primary or secondary
structure of proteins and will thus consist mainly of motifs with
similar 2D structure. The possibility to perform the multiple superimposition
of a large number of protein motifs with similar
2D structure would open the door to innovative thinking.
One could find meaningful structural trends or peculiarities that
could identify evolutionarily related proteins or could explain
and even predict function and activity related features of known
or engineered proteins.
To our knowledge, no implementation of such a methodology
is available to date, even though many state of the art
software packages offer the possibility to superimpose protein
structures to various extents. Thus, our goal was to fill in this
gap and to develop and implement a methodology for superimposing
large sets of protein structural motifs in an efficient,
flexible, and intuitive manner, so as to fuel inquisitiveness and
creativity in the investigation of protein structure and function.
A challenging aspect of protein structural motif superimposition
is that the motifs need not refer only to linear protein subsequences
but may also consist of the 3D surroundings of
residues or sequences, binding sites of metals or sugars, or any
other selected parts of protein 3D structure. This means that
some of the superimposed motifs may not have any sequence
similarity. Our methodology guarantees the best superimposition
even in such cases.
■ METHODS
When performing the superimposition of two protein structural
motifs, one faces two challenges. One challenge is to find the
best pairing of chemically corresponding atoms from the first
and second motif. This pairing establishes which atoms from
the first motif should be fitted to which atoms from the second
motif in the optimal fitting phase. The other challenge is to calculate
the geometrical transformation that optimally fits the
structures of the two protein motifs together.
In our methodology, we address the first issue by a systematic
approach employing heuristics tailored to proteins
(described in detail below) and the second by using a state of
the art quaternion algebra approach.39
A detailed description of
how we employ this approach is provided in the Supporting
Information. The main mathematical object employed in our
methodology is a molecular graph,62,63
which was adapted for
protein structural motifs. The formalized mathematical
description of our methodology is available in the Supporting
Information.
Pairing. Using the most appropriate atom pairing is a prerequisite
for a successful superimposition, and failure to identify
the best pairing leads to poor results, as is shown in Figure 1.
For superimposing protein structural motifs, we cannot use
implicit pairing (i.e., the i-th atom from one motif with the i-th
atom from the other motif) because the order of the atoms or
amino acid residues in the PDB file of one motif might differ
from the order in the PDB file of the other motif. Figure 1
demonstrates that even for the superimposition of two PHE
residues there can be a significant difference between the superimposition
calculated using implicit pairing and the superimposition
calculated using the best possible pairing. Employing
sequence alignment is also not applicable because some of
the superimposed motifs may not have any sequence similarity.
Subgraph matching (i.e., searching for the largest identical
subgraph contained in both motifs) is also not suitable because
protein motifs can consist of several identical residues and can
be very symmetrical, and thus, many relevant subgraphs can be
found. We therefore decided to use a systematic approach,
which tests all possible pairings.
The disadvantage of the systematic approach is its complexity.
When superimposing two motifs with n atoms, there are n!
possible pairings (e.g., about 3 × 1040
pairings for 30 atoms). It
is thus desirable to reduce the number of tested pairings as
much as possible. An initial decrease in the number of pairings
can be achieved by looking only at those pairings that are chemically
meaningful, such that two atoms will be paired only if
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they are of the same chemical element. A further decrease in
the number of tested pairings can be achieved by using the
information available in the PDB files. In the PDB file format,
each atom is assigned to a residue. Each residue is given a name
and a residue identifier (number), which specifies the residue’s
location in the amino acid sequence. All this information is useful
in deciding which atom pairings are worth testing. One can
use residue identifiers to make sure that atoms belonging to a
single residue in the first motif will be paired only to atoms
belonging to a single residue in the second motif and not to
atoms belonging to separate residues. Finally, a very effective
reduction in the number of possible atom pairings can be
achieved if one considers residue names, as this ensures that
only atoms belonging to residues with the same names will be
paired.
Grouping. We described the basic ideas how to reduce the
number of tested atom pairings. To implement these ideas, we
need to group the atoms in both motifs into sets and subsets
according to the above-mentioned properties. The set containing
the atoms from a motif divided into these sets and
subsets is denoted as grouping. The groupings help to markedly
reduce the number of tested pairings because only the pairings
which respect the groupings will be considered. This means
that if some atoms from the first grouping are together in a set
or subset they can be paired only with atoms from the second
grouping that are also together in a relevant set or subset.
Conversely, if the respective atoms are not in the same set or
subset, they cannot be paired with atoms that are together in a
set or subset.
We denote two groupings as compatible if there is at least
one pairing (i.e., bijection) that can be created between their
atoms. Only compatible groupings can be used in the process
of superimposition. We introduce three different types of
groupingsresidue name, residue identifier, and element symbol
grouping.
Residue name grouping assigns atoms to sets according to
the name and identifier of the residue they come from. These
sets of atoms are further divided into subsets according to their
chemical element symbols. For the protein motif in Figure 2,
the residue name grouping is {{{1,3}N
, {2,4,5}C
}HIS1
, {{6,8}N
,
{7,9,10}C
}HIS2
, {{11,12}O
, {13}C
}ASP3
, {{14,15}O
, {16}C
}GLU4
,
{{17}Zn
}Zn5
}. For clarity, the sets and subsets are denoted
by the relevant residue name, residue identifier, and element
symbol; a similar denotation will be used in further examples of
grouping.
We use the residue name and identifier jointly for establishing
the sets because of two reasons. First, if one uses just the
residue names, the atoms from identically named residues will
not be separated. For the motif in Figure 2, the grouping would
then be {{{1,3,6,8}N
, {2,4,5,7,9,10}C
}HIS
, {{11,12}O
, {13}C
}ASP
,
{{14,15}O
, {16}C
}GLU
, {{17}Zn
}Zn
}. Second, if one uses only
residue identifiers, the information about the residue name is
lost, and it is hard to distinguish for example between the atoms
from ASP and GLU in the motif from Figure 2.
Two residue name groupings are compatible if for each set in
one grouping there is a set in the other grouping that contains
the same number of atoms with the same chemical element
symbol that originate from residues with the same name. Thus,
using this grouping type is limited (e.g., there are compatible
residue name groupings for the dipeptides ALA-GLY and ALAGLY,
but there are no compatible residue name groupings for
ALA-GLY and ALA-UNK). On the other hand, the residue
name grouping is the most effective grouping type as it reduces
the number of tested pairings to a minimum.
Residue identifier grouping assigns atoms to sets according to
the identifier of the residue from which they originated. These
sets are further divided into subsets according to chemical element
symbols. For the protein motif in Figure 2, the residue
identifier grouping is {{{1,3}N
, {2,4,5}C
}1
, {{6,8}N
, {7,9,10}C
}2
,
{{11,12}O
, {13}C
}3
, {{14,15}O
, {16}C
}4
, {{17}Zn
}5
}. Two residue
identifier groupings are compatible if for each set in one
grouping there is a set in the other grouping that contains the
Figure 2. Example of a protein motif.
Figure 1. (a) Implicit pairing between residues PHE 83 (blue) and PHE 91 (orange) from the PDB entry 2wh6 and the superimposition calculated
by the program VMD, which uses this pairing. (b) The best possible pairing between PHE 83 (blue) and PHE 81 (orange) from 2wh6 and the
superimposition calculated by our program SiteBinder, which is able to find this pairing. The differences compared to the implicit pairing are
depicted by red arrows. In both (a) and (b), atoms are denoted by their number in the residue, while their PDB name is in brackets.
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dx.doi.org/10.1021/ci200444d | J. Chem. Inf. Model. 2012, 52, 343−359346
same number of atoms with the same chemical element symbols.
Using this grouping type is also limited (e.g., there can be compatible
residue identifier groupings for two dipeptides ALAGLY
and ALA-UNK, but there are no compatible residue identifier
groupings for a dipeptide ALA-GLY and a residue UNK).
The residue identifier grouping is slightly less effective than the
residue name grouping in reducing the number of tested pairings.
Element symbol grouping assigns atoms to sets according
to their chemical element symbols. For consistency, we further
divide these sets into subsets, but these are also based on
chemical element symbols. For the protein motif in Figure 2, the
element symbol grouping is {{{1,3,6,9}N
}N
, {{2,4,5,7,8,10,12,14}C
}C
,
{{11,13,14,16}O
}O
, {{17}Zn
}Zn
}. Two element symbol groupings
are compatible if for each set in one grouping there is a set
in the other grouping that contains the same number of atoms
that have the same chemical element symbol. This grouping type
is very general and can be used in all cases where the superimposed
motifs have the same molecular formula. On the other
hand, the element symbol grouping has the lowest effectiveness
in reducing the number of tested pairings.
Generating Atom Pairings. Before generating all relevant
atom pairings that will be tested, it is desirable to find the most
effective grouping type that can be used. We first prepare residue
name groupings for both motifs and test if these groupings
are compatible. If the residue name groupings are compatible,
we can employ them. Otherwise, we prepare residue
identifier groupings for both motifs and test their compatibility.
If the residue identifier groupings are compatible, we can
employ them. Otherwise, we prepare element symbol groupings
for both motifs. If the element symbol groupings are compatible,
we employ these groupings. If no compatible grouping can
be found, the motifs cannot be superimposed, and the user needs
to change the selection of atoms in at least one of the motifs.
Once we have found compatible groupings for our motifs, we
create all possible pairings (i.e., bijections), which respect the
groupings (as described above).
Complete Algorithm for Superimposing Two Protein
Motifs. To summarize the description given above, we provide
a pseudocode of the algorithm for superimposing two motifs.
• Step 1: Prepare the residue name groupings for both motifs.
If they are compatible, go to Step 5.
• Step 2: Prepare the residue identifier groupings for both
motifs. If they are compatible, go to Step 5.
• Step 3: Prepare the element symbol groupings for both
motifs. If they are compatible, go to Step 5.
• Step 4: There is no compatible grouping. Modify the
atom selection in at least one motif and go to Step 1.
• Step 5: Use the groupings resulted in the last performed
step and generate all possible atom pairings, which
respect the groupings.
• Step 6: For each generated pairing do the following: Use
quaternion algebra and calculate the transformation that
optimally fits one motif to the other. Fit the motifs together
using this transformation and calculate the RMSD
value.
• Step 7: Find the pairing (among all the generated pairings)
that leads to the smallest RMSD.
• Step 8: Superimpose the motifs using the pairing found
in Step 7. Return the new coordinates of the motifs (i.e.,
return the superimposed motifs) and the RMSD value.
Multiple Superimposition of Protein Motifs. Our goal is
to provide the most effective solution for this problem that
would fit a whole set of protein motifs together as tightly as
possible. For this purpose, selecting one of the motifs and
superimposing all the others to this one is not a feasible solution
as it would only provide an indication of how the rest of
the motifs differ from the selected one. Therefore, we designed
a multiple superimposition approach that uses the method
published by Wang et al.,61
adapted it to protein motifs and
combined it with our algorithm for the superimposition of two
motifs. This approach minimizes the RMSD of the whole set of
motifs:
∑ ∑=
−
=
−
= +
( )M
m
M MRMSD( )
2
RMSD( , )
i
m
j i
m
i j
1
1
1
1
2
(1)
where M is the set of motifs, and m is the number of motifs in
this set.
The multiple superimposition approach works in two steps.
First, each motif is superimposed to the first one. This simple
superimposition of two motifs is done as described in the pseudocode
above, and its purpose is to establish an initial pairing of the
atoms and calculate an initial RMSD value. We use this atom
pairing and calculate an average motif (Mavg) as the arithmetic
average of the x, y, and z coordinates of the corresponding atoms.
Next, all the motifs in the set are superimposed to the average
motif. The new coordinates of all these superimposed motifs are
stored, together with the new atom pairing. From these new coordinates,
we calculate a new RMSD value (denoted RMSD′).
We then calculate the normalized difference (δ) between the
original and new RMSD
δ =
− ′RMSD RMSD
RMSD (2)
If δ ≤ ε, where ε is a constant set to 0.005, the process is
complete, and the new coordinates are returned. If not, we
replace the original coordinates by the new ones, the original
pairing by the new one, set the value of the RMSD to RMSD′,
and repeat the process. For clarity, we provide also the
pseudocode of this approach:
• Step 1: Perform the superimposition of each motif to the
first one in order to obtain an initial pairing and calculate
an initial value for the RMSD.
• Step 2: Calculate the average motif Mavg using the pairing.
• Step 3: Superimpose all motifs to Mavg and store the new
coordinates and new pairing. Calculate RMSD′ and δ.
• Step 4: If δ ≤ ε, go to Step 6.
• Step 5: Replace the original coordinates of the motifs by
the new ones, the original pairing by the new one, set
RMSD = RMSD′, and go to Step 2.
• Step 6: The process is complete. Return the new coordinates
and RMSD′.
Advantages and Limitations of the Methodology. A
great advantage of our methodology is that the accuracy of the
superimposition does not depend on the sequence similarity of
the superimposed motifs, as all the relevant pairings are tested.
This guarantees that the methodology will find the best superimposition
(i.e., the superimposition providing minimal
RMSD), even when the input motifs do not have any sequence
similarity. An example of employing our methodology for the
superimposition of motifs that have low sequence similarity
(Figure S0 a) and that do not have any sequence similarity
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(Figure S0 b) is given in the Supporting Information. On the
other hand, the degree of sequence similarity may affect the
speed of our approach. Generally, the higher sequence similarity,
the fewer pairings need to be tested, and thus, the faster the
best pairing will be found. Another advantage of our methodology
is that it can very effectively employ information from the
PDB files and use this information to decrease the number of
tested pairings (i.e., by using groupings). A further significant
advantage is that the multiple superimposition does not depend
on the order of superimposed motifs. Last but not least, the
methodology is able to process any residues in the PDB files,
including ligands.
Implementation. We implemented the above-described
methodology and developed the Web application SiteBinder,
which provides an effective, intuitive, and user-friendly IT solution
for the superimposition of multiple protein structural motifs.
SiteBinder is implemented in C# using the Microsoft Silverlight
platform. Currently, the application can be run in any common
Internet browser under Windows and Mac. Full Linux support
will be available as soon as the new version of the Moonlight
framework plugin (Linux adaptation of Microsoft Silverlight)
will be released. The user interface of SiteBinder (depicted
in Figure 3) consists of three basic elements: the rendering view,
the input panel, and the results panel. The input panel includes
the list of motifs and the selection tree.
• The rendering view allows the user to view, rotate, and
zoom the motifs; change the visualization mode (balls and
sticks or sticks); or change the background. Here, the user
can also select individual atoms by clicking on them.
• The list of motifs is part of the input panel and shows the
loaded motifs grouped by the residues they contain. The
user can add or remove motifs from this list and select the
particular motifs that will be superimposed at one time.
• The selection tree is also part of the input panel and allows the
user to select specific atoms or residues for superimposition.
• The results panel shows the RMSD value of the set of RMSD
superimposed motifs. It also provides a list of all superimposed
motifs and for each motif its RMSD compared to
the average motif (RMSDM). This list of superimposed motifs
is sorted according to RMSDM. In addition, the motifs are
grouped on the basis of the difference (DM) between RMSD
and RMSDM. There are four groups: DM < σ, σ ≤ DM < 2σ,
2σ ≤ DM < 3σ, and finally DM ≥ 3σ, where σ is the standard
deviation of the set of DM values. The RMSD data can be
exported into a CSV table and the atomic coordinates into a
PDB file. The exported atomic coordinates reflect the
superimposition. The structure of the average motif structure
can also be written out.
The SiteBinder is a powerful tool but still has some technical
limitations. It can superimpose any motifs as long as the atom
selections are compatible, meaning that the same number of
atoms of the same chemical element need to be selected in each
motif. SiteBinder can process at most 7000 to 10000 motifs at a
time depending on the computer memory available. For optimum
performance, each residue in a superimposed motif
should not contain more than 12 atoms of the same element.
The reason is that we employ a systematic approach to search
for a relevant pairing, which can become significantly slower if
each motif contains more than 12 atoms of the same element.
■ RESULTS AND DISCUSSION
Benchmarking StudyComparison of Eukaryotic
Linear Motifs. Linear motifs (LMs) are short elements embedded
within larger protein sequence segments. They operate as regulatory
sites and can be found in a wide range of proteins.64
ELM, the Eukaryotic Linear Motif database,65,64
is a bioinformatics
resource for investigating candidate linear motifs in eukaryotic
proteins. ELM currently contains 174 motifs, represented by
regular expressions, which describe the occurrence of amino acids
in the motif. For example, the regular expression ″RF[∧
P][IV]″
indicates that the motif should contain arginine followed by
phenylalanine, then any aminoacid except for proline, afterward
isoleucine or valine, and finally another amino acid.
This large and heterogeneous resource provides us with a
rich area for analysis of protein motifs using SiteBinder. In our
investigation, we asked two questions. First, is SiteBinder
robust and fast enough to process large sets of low homology
linear motifs? Second, do some linear motifs retain conservation
at the level of their 3D structure?
In order to address these questions, we first prepared a data
set. For each of the 174 linear motifs in ELM (access date:
1.12.2011), we found all its instances in the Protein Data Bank
(access date: 1.12.2011). These instances correspond to the
ELM regular expressions and may or may not perform the
biological function assigned to them in the ELM database.
Figure 3. User interface of SiteBinder.
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The files containing the instances of motifs were named
pdbid_index.pdb, where pdbid is the PDB ID of the parent protein,
and index is the PDB file atom index of the first atom in the motif.
Information about the number of instances of each motif and the
number of proteins containing at least one instance of each motif
is provided in the Supporting Information (Table S1). The
program we used for identifying and retrieving ELMs from PDB is
also provided in the Supporting Information (program_1). From
these 174 linear motifs, we selected 32 as a relevant sample for our
benchmarking study. The following criteria were used for this
selection. The motif should be frequent enough but not too
general (number of instances between 1000 and 30000). The
motif should contain at least two identical amino acid residues,
and one amino acid residue position defined by a selection of at
most four possibilities. In this way, we ensure that it is
meaningful to evaluate the structural conservation of the motif.
After applying these criteria, we selected the minimum number
of motifs so that each of the 20 amino acid residues appears as
a firm part of some motif at least once. This procedure provided
us with a strong data set for our benchmarking study.
The names, regular expressions, and number of residues for the
ELMs used in this study are summarized in Table 1.
We then focused on the first question and tested the performance
of SiteBinder. For each linear motif in our data set,
we selected 1000 instances. Specifically, we went through all P
instances of the motif in PDB (sorted alphabetically according
to their file names) and took each (P/1000)th
instance (e.g., each
second instance if the motif appeared 2000 times in PDB). Subsequently,
in order to simplify the process of superimposition in
SiteBinder, we used a unifying renaming convention for each
motif. For instance, the residues in motif ″RF[∧
P][IV]″ were
renamed as ″ARG-PHE-RE1-IL_-RE2″. The renaming program
(program_2), the unifying residue names for each motif (Table S2),
as well as the 1000 renamed instances of each motif are given in
the Supporting Information. For each motif, we loaded the
1000 renamed instances into SiteBinder, selected all compatible
atoms, and performed the superimposition. By “compatible
atoms”, we denote all heavy atoms shared by all instances of a
particular motif. Table 1 shows the number of atoms used, the
duration, and RMSD for each motif. The SiteBinder
Table 1. Summary Information about ELM Data Set and Results of Performance and Conservation Study Performed with
SiteBindera
information about the motif performance study conservation study
1000 motifs
1000
motifs motifs with RMSD < σ
name regular expression no. of res.
no. of compatible atoms in a
motif
time
(s)
RMSD
(Å)
RMSDB
(Å)
no. of
motifs
RMSDσ
(Å)
LIG_AP2alpha_2 DP[FW] 3 24 10 1.936 0.833 820 0.657
LIG_RGD RGD 3 23 59 2.603 1.077 883 0.998
LIG_MAPK_2 F.FP 4 33 60 2.693 1.443 833 1.063
LIG_HCF-1_HBM_1 [DE]H.Y 4 32 84 3.238 1.584 816 1.448
LIG_WW_1 PP.Y 4 30 31 2.987 1.601 859 1.519
LIG_EH_1 .NPF. 5 34 50 2.689 1.705 767 1.259
TRG_Cilium_RVxP_2 RV.P. 5 33 80 2.801 1.777 801 1.363
LIG_SPAK-OSR1_1 RF[∧
P][IV]. 5 37 77 3.108 1.962 802 1.428
LIG_TRFH_1 [FY].L.P 5 34 55 3.029 1.869 839 1.525
LIG_APCC_KENbox_2 .KEN. 5 34 79 3.044 1.83 849 1.535
LIG_AP2alpha_1 F.D.F 5 38 79 3.245 1.995 807 1.657
LIG_BIR_III_2 DA.P. 5 28 51 2.641 1.865 853 1.68
LIG_WW_3 .PPR. 5 33 101 2.901 1.962 887 1.714
LIG_BIR_III_4 DA.G. 5 42 30 2.615 1.961 882 1.744
CLV_PCSK_FUR_1 R.[RK]R. 5 37 103 3.65 2.021 819 1.774
LIG_SH3_5 P..DY 5 35 20 3.188 1.963 844 1.856
LIG_EVH1_2 PP..F 5 33 41 3.027 2.096 835 1.944
LIG_PTAP_UEV_1 .P[TS]AP. 6 32 51 2.684 2.121 788 1.895
CLV_PCSK_PC7_1 [R]...[KR]R. 6 41 91 3.884 2.392 791 1.986
LIG_SH3_2 P..P.[KR] 6 33 39 3.033 2.267 883 2.113
LIG_14−3−3_1 R.[∧
P]([ST])[∧
P]P 6 35 77 3.257 2.311 861 2.131
LIG_TRAF2_2 P.Q..D 6 36 51 3.337 2.44 854 2.317
LIG_NRBOX [∧
P]L[∧
P][∧
P]LL[∧
P] 7 40 73 2.069 1.678 884 0.657
LIG_PP2B_1 .P[∧
P]I[∧
P][IV][∧
P] 7 38 82 2.937 2.45 842 1.924
LIG_SH3_1 [RKY]..P..P 7 36 100 3.079 2.586 870 2.384
LIG_USP7_2 P.E[∧
P].S[∧
P] 7 38 42 3.3 2.847 828 2.592
LIG_BRCT_BRCA1_2 .(S)..F.K 7 42 71 3.803 2.928 811 2.607
LIG_RRM_PRI_1 .[ILVM]LG..P. 8 40 110 3.555 3.011 818 2.75
LIG_SH3_4 KP..[QK]... 8 43 92 4.015 3.159 866 2.935
LIG_MDM2 F...W..[LIV] 8 50 211 4.262 3.177 853 2.949
MOD_TYR_ITSM ..T.(Y)..[IV] 8 46 70 3.976 3.31 885 3.134
MOD_PKB_1 R.R..([ST])[∧
P].. 9 51 181 4.615 3.573 858 3.26
a
Motifs are sorted first according to their number of residues and then according to RMSDσ. Motifs with conserved 3D structure are marked in bold.
A brief explanation of the special characters used in the regular expressions can be found on the ELM Help Page.66
Journal of Chemical Information and Modeling Article
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successfully performed the superimposition in all cases,
regardless of the number (3 to 9), size (23 to 51 compatible
atoms), nature (all 20 amino acids), or degree of conservation
of the residues. These results demonstrate the robustness of
SiteBinder. The performance test also highlights an exclusive
feature of our multiple superimposition methodology, which is
that optimal atom pairing can be achieved, and the superimposition
can be performed regardless of the degree of amino
acid sequence similarity.
We then addressed the second question and investigated
whether some linear motifs have a particularly conserved 3D
structure. For this stage of the benchmarking, which we denote
the “conservation study”, we used the same 32 motifs, each with
1000 (renamed) instances, but this time we used only the backbone
atoms for the superimposition and obtained RMSDB. To
further refine our findings, we performed an additional superimposition
for each motif, using only those instances with
RMSDB < σ and thereby obtained RMSDσ. The results of the conservation
study are also given in Table 1.
The RMSDσ values provide the most relevant information
for evaluating the 3D structure conservation of each motif. The
RMSDσ grows with the growing number of residues in the
motif (Figure 4a), and the dependency is mainly linear.
However, seven motifs do not respect this linear trend (marked
in red in Figure 4 and in bold in Table 1) and therefore seem
much more structurally conserved than the other linear motifs.
To clearly identify these motifs, we computed the normalized
RMSDσ value by dividing RMSDσ by the number of residues in
each motif. We can now clearly visualize the degree of structural
conservation. The same seven motifs easily stand out in
this analysis, as they have the lowest values of normalized
RMSDσ (Figure 4b). The motif LIG_NRBOX seems to be the
most structurally conserved by far (Figure 5). Several studies
(e.g., Leers et al.,67
Johansson et al.,68
Phillips et al.69
) come to
substantiate our finding that LIG_NRBOX is highly conserved.
Thus, our analysis was able to easily point out several eukaryotic
linear motifs that are conserved at the structural level
regardless of the degree of sequence similarity between their
Figure 4. (a) Dependency of RMSDσ on the number of residues in the motif. (b) Dependency of normalized RMSDσ (RMSDσ/number of residues)
on the number of residues. Motifs with conserved 3D structure are marked red.
Figure 5. Superimposition of LIG_NRBOX motif instances for which RMSD < σ (only the first 80 instances are shown).
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parent proteins, and the results of this study are in agreement
with published experimental results.
Case Study IComparison of Sugar Binding Sites in
Pseudomonas aeruginosa Lectin II. Pseudomonas aeruginosa
(PA) is an opportunistic pathogen that can infect almost every
human tissue when immunity barriers are lowered.70
Chronic
lung colonization by the bacterium is the major cause of morbidity
and mortality in cystic fibrosis patients.71
P. aeruginosa produces
the lectin PA-IIL (Pseudomonas lectin II, LecB), which is
one of the virulent factors of the pathogen. Each monomer of
this lectin contains a sugar binding site that aids the pathogen
in host recognition. Knowledge of its structure can lead to
better design of new antibacterial−adhesion drugs that minimize
the risk of infection. The binding site contains two close
calcium cations that mediate the binding of the sugar. These
cations are coordinated by seven amino acids, namely, three
aspartic acids, two asparagines, one glutamic acid, and one glycine
from the adjacent monomer (Figure 6). The sugar is
further stabilized by hydrogen bonds with other neighboring
amino acids as shown by Mitchell et al.70
PA-IIL strongly prefers fucose, but it can also bind other
saccharides, albeit with lower affinity. An interesting question
that helps to understand the behavior and activity of PA-IIL is
whether the structure of this binding site changes when different
sugars are bound. We employed SiteBinder to address
this question. First, we identified all samples of PA-IIL and its
mutants present in the Protein Data Bank (access date:
3.8.2011). We then processed these samples by a program
(Supporting Information, program_3) to find and extract the
sugar residue, the pair of calcium atoms, and the surrounding
seven amino acid residues, as described above and depicted in
Figure 6. By this procedure, we obtained 18 structures of PA-IIL
and its mutants, which gave us a total of 67 sugar binding sites.
Most of these complexes are unique combinations of sugars and
the PA-IIL protein or its mutants. There are just three exceptions,
i.e., three PDB structures (1gzt, 1oxc, and 1uzv)
containing wild-type PA-IIL complexed with α-L-fucose
ligands. From these three closely related structures, we kept
only the structure with the best resolution (i.e., 1uzv with a resolution
of 1 Å) and removed the other two structures.
However, we provide a comparison of these three structures in
the Supporting Information (Figure S1). It documents the
influence of the source organism (1gzt was purified from
P. aeruginosa, 1ixc and 1uzv were purified from E. coli) and the
resolution.
We thus obtained a set of 16 PA-IIL structures containing 61
sugar binding sites. These protein structures appear as protein−
sugar complexes with nine different sugars. The sugar varies
from monosaccharides (i.e., α-L-fucose, α-D-mannose, or αL-galactose),
via their simple derivatives (i.e., methyl-β-D-arabinoside,
methyl-α-D-mannoside), to complex synthetic ligands
(i.e., 2G0 or LZ0). Basic information about the PA-IIL PDB
entries used in this case study can be found in the Supporting
Information (Table S3).
In the next step, we used SiteBinder to superimpose the
binding sites that bind the same saccharide. The most representative
results of this comparison are shown in Figure 7,
while the complete set of results can be found in the
Supporting Information (Figure S2). These results demonstrate
that the binding sites for the same sugar have a very similar
structure in different PDB entries (RMSD <0.14 Å), and this
feature does not depend on the size of the ligand Figure 7a
compared to Figure 7b). The only exception is the binding site
of α-methyl-fucoside (RMSD ≤ 0.478 Å).
For obtaining a broader overview and in the search for an
explanation for the higher RMSD in the case of MFU binding
sites, we again employed SiteBinder and superimposed all 61
sugar binding sites. The results of the superimposition are
depicted in Figure 8a), and the RMSDM values are summarized
in the Supporting Information (Table S4). This comparison
shows that, despite the binding sites originating from different
PA-IIL samples (wild types or mutants) and binding different
sugars, their structure is very similar (RMSD 0.214 Å). This
general comparison also explains the higher RMSD for the
binding site of α-methyl-fucoside. The reason is that two of the
four binding sites in a mutant of PA-IIL (PDB ID 2jdp) differ
from the remaining 59 binding sites (i.e., they have the RMSDM
> 0.7 Å, while the other motifs have the RMSDM < 0.2 Å). The
main difference in these binding sites is that glycine is oriented
outward and does not support the binding of the calcium ion
(Figure 8b). Nevertheless, this exception does not change the
main conclusion, which is that the sugar binding site in PA-IIL
is highly conserved.
Our findings that the structure of the sugar binding site in
PA-IIL is very similar for nine different sugars could be in direct
correlation with the fact that PA is able to infect so many kinds
of tissues. In addition, the high level of conservation of this
binding site raises the question whether this motif can be used
also by other organisms, and because the motif has such a welldefined
3D structure, it can be easily identified. Thus, we used
our program_3 to search the complete Protein Data Bank for
this motif (access date: 3.8.2011). We searched for two close
calcium atoms surrounded by exactly five oxygens from ASP,
two oxygens from ASN, two oxygens from GLU, and one oxygen
from GLY. From each of the structures found, we obtained
the binding site by extracting the sugar residue, the calcium
atoms, and the seven surrounding amino acids, as depicted in
Figure 6. This way, we collected the 11 sugar binding sites
described in Table 2.
These binding sites originate from the proteins Chromobacterium
violaceum lectin II (CV-IIL) and Burkholderia
cenocepacia lectin A (BclA). Table 2 shows that the sugar binding
sites in these bacteria are very similar as in PA-IIL (RMSD
< 0.65 Å). This is in agreement with the fact that the biological
activity of BclA71,72
and CV-IIL73
is very similar to that of PAIIL.
Moreover, the characteristic propeller assembly of their
Figure 6. Amino acids coordinating calcium ions in the PA-IIL binding
site with α-L-fucose. The depicted binding site originates from the
monomer A of the structure with PDB ID 1uzv.
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beta strands classifies these proteins as one family. Our superimposition
analysis was able to immediately direct us to identify
related family members without any prior knowledge of this
fact (i.e., only a calculated model of the sugar binding site in
PA-IIL and its mutants was used). One could envision that such
analyses could be used to identify related proteins that have
been misplaced in different families based on their dominant
fold.
Case Study IIComparison of Zn Binding Sites in
Cys2His2 Zinc Fingers. Cys2His2 zinc fingers are one of the
most common structural motifs in eukaryotes.74,75
Each finger
recognizes three to four base pairs of DNA, and several fingers
can be linked in tandem to recognize a broad spectrum of DNA
sequences with high specificity.76
There is evidence that some
Cys2His2 zinc fingers bind RNA and that others may participate
in protein−protein interactions, but it appears that their predominant
role is in protein−DNA recognition.74
Individual
fingers contain approximately 30 amino acids, and the hallmark
of the motif is the presence of two cysteines and two histidines
that serve as zinc ligands. The simplest definition of such zinc
finger motifs is based on the spacing of the zinc ligands in the
amino acid residue sequence. This spacing has the pattern X2−
CYS−X2−4−CYS−X12−HIS−X3−5−HIS,77
where X represents
any amino acid residue. The abundance of this motif, its biological
importance, and its simple but apposite description make
it an attractive target for research.
We used SiteBinder to determine whether the center of the
zinc finger motif (i.e., two CYS, two HIS, and a Zn atom) has a
conserved geometry. In order to do this, we went through a few
different stages. First, we used a simple program (Supporting
Figure 7. Representative results of the superimposition of PA-IIL binding sites that bind the same sugar-based ligand. Only the atoms in red were
used for the superimposition.
Figure 8. (a) Superimposition of all 61 sugar binding sites, RMSD 0.222 Å, duration 16 s. (b) Comparison of the sugar binding site in the wild type
of PA-IIL (PDB ID 2jdm, monomer D, in blue) and in its mutant (PDB ID 2jdp, monomer D, in orange), RMSD 0.754 Å. Part of the calcium
binding site in detail.
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Information, program_4) and collected all motifs from the
Protein Data Bank (access date: 3.8.2011) that fulfill the description
of zinc fingers (i.e., Zn coordinated by two CYS and
two HIS that are part of a pattern of the type X2−CYS−X2−4−
CYS−X12−HIS−X3−5−HIS). If a protein structure was
obtained by NMR, only the motifs from the first model contained
in the PDB file were used in our study. We found 329
zinc fingers from 205 different Protein Data Bank entries. For
each hit, we extracted the zinc atom and the two HIS and two
CYS surrounding this atom. By this procedure, we obtained the
zinc finger central motifs and subsequently used these motifs as
inputs for SiteBinder. We performed four superimpositions for
our set of zinc finger central motifs. These procedures differed
in the number of atoms selected for superimposition (displayed
in red in Figure 9).
The first superimposition was done using only nine atoms
from each motif (zinc, the nitrogens from the imidazole cycle of
each HIS, and the sulfur and beta carbon of each CYS), the
second superimposition with 15 atoms from each motif (to the
previous selection, we added the rest of the imidazole ring
atoms of each HIS and the alpha carbon of each CYS), the third
with 19 atoms (to the previous selection, we added the beta
carbon of each HIS and the carboxylic carbon of each CYS),
and the fourth superimposition used all atoms. The superimposed
motifs are depicted in Figure 9, which contains also the
RMSD values and durations of the superimposition. The values
of RMSDM for each individual motif in all four superimpositions
are given in the Supporting Information (Table S5). The RMSD
values for the first three superimpositions are similar (between
0.5 and 0.6 Å), which demonstrates that the part of the motif
which closely surrounds Zn has a stable structure. Figure 9
demonstrates that the conformation of more distant parts of CYS
and HIS may differ.
We further note that, despite the fact that we compared 329
motifs with 9−33 atoms, the superimposition took about 2 min
even for the most complex case.
Then we focused on a special group of zinc finger Cys2His2
motifs, namely, those known to bind RNA. Superimposing
them reveals a very interesting feature. The motifs coming from
the PDB entry 1zu1 are markedly different than those in the
other RNA binding proteins we investigated (Table 3). This is
likely explained by the fact that one of the two HIS residues is
facing the binding site with the opposite face of the imidazole
ring (Figure 10). What is even more interesting is the biological
consequence of this change. Unlike the other zinc finger motifs
we discuss here, the motifs contained in 1zu1 have evolved to
bind double stranded RNA.78
The structural peculiarity that
we identified by our superimposition analysis without any prior
knowledge of RNA binding preference was confirmed by
Moller et al.78
The fact that this structural peculiarity is immediately
connected to a functional peculiarity reinforces the
structure−function paradigm. This reasoning could be generally
applied in order to identify other proteins containing the same
functional motif but with slightly different functionality and
possibly different behavior toward the same drug molecules.
Case Study IIIComparison of BH3 Domains in
Apoptotic Proteins. Apoptosis is a form of cell death that
helps to maintain tissue homeostasis and removes malignant
cells upon internal and external cellular stress in a biochemically
controlled fashion. Apoptosis is downregulated (decreased) in
cancer and excessive in neurodegenerative diseases or stroke.
The decision whether an initial cellular signal, like a receptor
induced stimulus, is tolerated or leads to cell death is controlled
by a carefully balanced biochemical cascade of pro-survival or
pro-apoptotic proteins of the BCL-2 family.79,80
The proteins
from a pro-apoptotic subgroup of the BCL-2 family, the BH3only
proteins, integrate specific stress signals such as genotoxic
stress,81
serum-deprivation stress,82
or stress due to the accumulation
of unfolded proteins83
into downstream apoptotic
signals. These proteins are called “BH3-only” because they
share only the third (of a total of four) BCL-2 homology (BH)
domains with the rest of the BCL-2 family. The proteins Bax
and Bak, from another pro-apoptotic subgroup, induce the
formation of pores into the mitochondrial outer membrane.
This phenomenon is a decisive step in apoptosis execution. On
the other hand, pro-survival BCL-2 family proteins bind to Bak
and Bax, as well as to BH3-only proteins, to prevent unwanted
apoptosis. The interaction between pro-survival and pro-apoptotic
BCL-2 proteins is mediated by the BH3 domain.84
The
BH3 domains of BH3-only proteins consist of an amphipathic
α helix and contain 9−16 amino acids.85
A controversy has arisen regarding the role of BH3-only
proteins. Originally, it was thought that stress-induced upregulation
(increase) of BH3-only proteins is sufficient to release
Bax and Bak from their complexes with pro-survival
proteins and thus lead to pore formation. Nonetheless, increasing
evidence indicates that an additional step is necessary, namely,
the direct activation of Bax and Bak.86
If such a step is required,
two distinct groups of BH3-only proteins are predicted. One
group is denoted as “enablers” and comprises the proteins Noxa,
Bad, Bmf, Hrk, and Bik. These proteins presumably only bind to
pro-survival proteins and thereby release Bax and Bak. The
second group of BH3-only proteins, denoted as “activators” are
believed to activate Bax and Bak in an explicit activation step.
The proteins Bid, Bim, and Puma are examples of activators.87
Table 2. Sugar Binding Sites with a Very Similar Structure as
the PA-IIL Sugar Binding Site
protein
name
PDB
ID organism sugar monomer
RMSD to
the average
motifa
(Å)
CV-IIL 2boi Chromobacterium
violaceum
MFU A 0.136
CV-IIL 2boi Chromobacterium
violaceum
MFU B 0.118
CV-IIL 2bv4 Chromobacterium
violaceum
MMA A 0.155
CV-IIL 2bv4 Chromobacterium
violaceum
MMA B 0.189
BclA 2vnv Burkholderia
cenocepacia
MMA A 0.621
BclA 2vnv Burkholderia
cenocepacia
MMA B 0.553
BclA 2vnv Burkholderia
cenocepacia
MMA C 0.633
BclA 2vnv Burkholderia
cenocepacia
MMA D 0.567
BclAb
2wr9 Burkholderia
cenocepacia
MAN A 0.576
BclA 2wr9 Burkholderia
cenocepacia
MAN C 0.543
BclA 2wr9 Burkholderia
cenocepacia
MAN D 0.521
a
The average motif was calculated by SiteBinder from all PA-IIL sugar
binding sites except those from the mutant 2jdp. b
The binding site
from monomer B of BclA was not included in this study because no
sugar was found in the crystal structure at this site.
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We used SiteBinder to compare the 3D structures of the
BH3 domains of different BH3-only proteins with the goal to
investigate whether there is a structural basis of this segregation
in activators and enablers. Specifically, we focused on the proteins
for which the primary structure of the BH3 domain was
described and aligned by Chipuk et al.79
We obtained the structures
of these proteins from the Protein Data Bank, except for
the proteins Hrk and Bik, whose structures are not available in
this database. The Noxa A protein (PDB ID 2rod) was omitted
because its PDB structure was determined by NMR, while the
structures of all other BH3-only proteins considered here were
determined by X-ray crystallography. The protein names, their
PDB identifiers, the BH3-only pro-survival complex from which
the structure was derived, and the amino acid sequences are
given in Table 4.
As shown in Table 4, the structures of the BH3-only proteins
we are using were obtained from larger complexes, in which
they are bound to various pro-survival BCL-2 proteins. This
complex binding may affect the structural features of the BH3only
proteins. To estimate the influence of these other proteins,
we built a reference data set comprising only complexes of the
BH3-only protein Bim with all relevant pro-survival BCL-2
proteins (Table 5).
Figure 9. Superimposition of 329 zinc finger central motifs. From (a) to (d), the number of atoms used in the superimposition procedure (displayed
in red) increases step by step. For ease of visual interpretation, only the first 80 motifs are displayed.
Table 3. Results of the Superimposition of Zinc Finger
Central Motifs of RNA Binding Proteins
protein PDB ID index of Zn atom RMSD from the average model (Å)
1un6 4524 0.814
2hgh 3176 0.829
2j7j 717 0.830
1un6 4530 0.880
2hgh 3166 0.881
1un6 4523 0.898
2j7j 718 0.929
1un6 4534 0.956
2ab7 511 0.981
2ab3 494 0.984
2yu5 640 1.108
1zu1 1951 1.821
1zu1 1952 1.834
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We next extracted the BH3 domains characterized by the
amino acid sequence described in Table 4 from the PDB files
mentioned in Tables 4 and 5. The amino acid residues that had
to be superimposed have different names. In order to simplify
their processing by SiteBinder, we introduced a simple unifying
denotation for amino acid residue names. Specifically, we renamed
the BH3 domain amino acids in the SiteBinder input
files according to their position in the sequence (Table 4).
This solution was implemented with minimal effort and was
feasible because the sequences had already been aligned. The
original and modified SiteBinder input files are available in the
Supporting Information.
For each of our three groups of motifs (activators, enablers,
and Bim samples), we did the following:
• Superimpose the entire motifs (amino acids A01−A13)
• Superimpose the inner parts of the motifs (amino acids
A03−A10)
• Superimpose the conserved parts of the motifs (amino
acids A03, A05, A06, A08−A10)
All motifs in a group were employed in the superimposition.
Only backbone atoms were used (in red in Table 6), and thus,
the RMSD reflects only the backbone geometry conservation.
The results of this superimposition are summarized in Table 6
and in the Supporting Information (Table S6). Each multiple
superimposition procedure took less than 5 s. The results in
Table 6 indicate that activators have a very conserved BH3
domain (RMSD < 0.25 Å, even when considering the entire
motifs). On the contrary, the structure of the BH3 domain in
the enablers group shows significant dissimilarity within the
group, as well as to the activators group (RMSD > 0.5 Å, even
for the inner or most conserved part of the motifs). In addition,
comparing Bim motifs extracted from various pro-survival complexes
showed smaller RMSD differences than for the activators
group in general. This confirms that the pro-survival proteins
did not cause significant structural changes upon complex
formation. Overall, our results support the hypothesis that activators
and enablers may be two functional subgroups of BH3only
proteins. Moreover, they suggest that all activators act in a
similar manner to induce cell death. In contrast, the structural
Figure 10. (a) Example of a common structure of the zinc finger central motif in RNA binding proteins (PDB ID 1un6, zinc ion with index 4524).
(b) Example of a rare structure of the zinc finger central motif (PDB ID 1zu1, zinc ion with index 1951).
Table 4. Names, PDB Identifiers, and BH3 Domain Amino Acid Sequences of the Activators, and Enablers Used for the
Superimposition with SiteBindera
group PDB ID BH3-only protein complexed with amino acid sequence in BH3 domainb
activators 2voi Bid A1 ILE ALA ARG HIS LEU ALA GLN ILE GLY ASP GLU MET ASP
2vm6 Bim A1 ILE ALA GLN GLU LEU ARG ARG ILE GLY ASP GLU PHE ASN
2vof Puma A1 ILE GLY ALA GLN LEU ARG ARG ILE ALA ASP ASP LEU ASN
enablers 2bzw Bad BCL-XL TYR GLY ARG GLU LEU ARG ARG MET SER ASP GLU PHE GLU
2vog Bmf A1 ILE ALA ARG LYS LEU GLN CYS ILE ALA ASP GLN PHE HIS
2nla Noxa B MCL-1 GLU CYS ALA GLN LEU ARG ARG ILE GLY ASP LYS VAL ASN
SiteBinder denotation A01 A02 A03 A04 A05 A06 A07 A08 A09 A10 A11 A12 A13
a
We also mention the pro-survival proteins present in the complexes obtained from PDB. The last row shows our unifying denotation used in the
SiteBinder input files. b
The amino acids that have a degree of conservation higher than 50% for all BH3-only proteins are in bold. Information about
the degree of conservation was obtained from the work of Chipuk et al.79
Table 5. Summary Information about the Bim Molecules Superimposed Using SiteBindera
PDB ID 2vm6 3fdl 2wh6 2nl9 2pqk 3kj0 3kj1
complexed with A1 BCL-XL BHRF1 MCL-1 MCL-1 MCL-1 MCL-1
a
Entries 3kj0 and 3kj1 contain Bim mutants.
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heterogeneity of the BH3 domains of different enablers advocate
for a specific binding to pro-survival proteins. As different
stresses and cells specifically express distinct enablers, this
provides a flexible, cell and stress specific, gate-keeping mechanism
for enabling or preventing the activation step by the
activators.
■ CONCLUSION
In our work, we focused on the superimposition of very large
sets of protein structural motifs. We found the most appropriate
state of the art superimposition algorithms available in
literature, improved and compiled them, and developed a
methodology that is fully tailored to the multiple superimposition
of protein structural motifs. This methodology employs
the systematic approach for finding the equivalence between
atoms and decreases its complexity by using heuristics that consider
several types of atom grouping. Fitting the motifs is solved
by quaternion algebra. The described superimposition methodology
guarantees that the best fit will be found and can be
applied even when sequence similarity is low or does not exist at
all. Multiple motifs are processed by iteratively superimposing all
the structures to an average model until a stable configuration is
reached. We have implemented this methodology and have
created the Web application SiteBinder. This application is able
to process up to thousands of protein structural motifs in a very
short time (from a few seconds to a few minutes). Moreover, it
provides an intuitive and user-friendly graphical interface, which
allows the user to visualize the motifs, select specific atoms or
residues for superimposition, export the coordinates of the superimposed
structures, as well as the RMSD values, etc.
We have performed a benchmarking analysis by superimposing
1000 experimentally determined structures for each of
32 eukaryotic linear motifs. This analysis shows that our methodology
and its implementation are robust, efficient, and
versatile. It also demonstrates that SiteBinder can be used for
studying general trends in large data sets of low homology
protein structural motifs. The applicability of SiteBinder was
demonstrated using three case studies that dealt with the
comparison of large sets of biochemically important motifs. In
the first case study, we compared the structural motifs of 61
PA-IIL sugar binding sites containing nine different sugars. The
comparison showed that, despite the binding sites originating
from different PA-IIL samples (wild types or mutants) and
binding different sugars, their structure is very similar (RMSD
0.222 Å). This finding correlates with the ability of this pathogen
to infect many kinds of host cells. In addition, we were able
to identify the related proteins CV-IIL and BclA simply by
studying the binding site motifs in PA-IIL. This is an example
of how a superimposition analysis done with SiteBinder can
help in identifying functionally related proteins. The second
case study was focused on the analysis of Cys2His2 zinc finger
structures contained in the Protein Data Bank (more than
300 motifs). We performed four different superimpositions of
these motifs, successively increasing the number of superimposed
atoms. The results demonstrated that the part of the
motifs that closely surrounds Zn has a stable structure (RMSD
values are between 0.5 and 0.6 Å). Moreover, we found that a
small difference in the structure of RNA binding motifs could
be responsible for binding double stranded RNA. In the last
case study, we attempted to superimpose 12 BH3 domains
from several pro-apoptotic proteins. The results indicated that
the activators have a very conserved BH3 domain (RMSD <
0.25 Å, even for the entire motifs). On the contrary, the structure
of the BH3 domain in enablers differs across this group of
proteins and also differs significantly from the activator group
(RMSD > 0.5 Å, even for the most conserved part of the
motifs). These results are in agreement with the hypothesis that
two functional subgroups of BH3-only proteins, activators and
enablers, are present during apoptosis. The three case studies
demonstrate the versatility of SiteBinder and show how our
Table 6. Superimposition of the BH3 Domains from Several Data Sets (Activators, Enablers, Bim Samples)a
a
Only the backbone atoms (in red) were used for the superimposition, and thus, the RMSD values reflect the backbone structural conservation.
Journal of Chemical Information and Modeling Article
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software can be used to gain insight into the relationship between
protein structure and function. The software is available to the
community at http://ncbr.muni.cz/SiteBinder.
■ ASSOCIATED CONTENT
*S Supporting Information
Superimposition of motifs having low or no sequence similarity
(Figure S0), detailed description of the quaternion algebra approach,
formalized mathematical description of our superimposition
methodology, program to extract the ELMs from
PDB (program_1), program for renaming the residues in the
ELM PDB files (program_2), summary information about
ELMs and their occurrence in PDB (Table S1), unifying residue
names for each ELM (Table S2), PDB files of the protein motifs
used in benchmarking study, program to extract sugar binding
sites (program_3) and zinc fingers (program_4) from PDB,
PDB files of the protein motifs used in all case studies, results of
the superimposition of PA-IIL sugar binding sites from proteins
1gzt, 1oxc, and 1uzv (Figure S1), results of the superimposition
of PA-IIL binding sites which bind the same sugar based ligand
(Figure S2), basic information about the PA-IIL PDB entries
used in case study I (Table S3), RMSDM values of the superimposed
motifs from case study I (Table S4), case study II
(Table S5), and case study III (Table S6). This material is
available free of charge via the Internet at http://pubs.acs.org/.
■ AUTHOR INFORMATION
Corresponding Author
*E-mail: svobodova@chemi.muni.cz (R.S.V.); jaroslav.koca@
ceitec.muni.cz (J.K.).
Notes
The authors declare no competing financial interest.
■ ACKNOWLEDGMENTS
This work was supported by the Ministry of Education, Youth
and Sports of the Czech Republic (ME08008 to M.W.), the
Czech Science foundation (GD301/09/H004 to C.M.I.), the
Science Foundation Ireland Grant 08/IN.1/B1949 to H.J.H. and
by the European Community’s Seventh Framework Programme
(CZ.1.05/1.1.00/02.0068 to J.K. and R.S.V.) from the European
Regional Development Fund. C.M.I. and D.S. thank Brno City
Municipality for the financial support provided to them through
the program Brno Ph.D. Talent. The access to MetaCentrum
supercomputing facilities provided under the research intent
MSM6383917201 is highly appreciated.
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Predicting pKa Values of substituted phenols
from atomic charges: comparison of diﬀerent
quantum mechanical methods and charge
distribution schemes
215
r XXXX American Chemical Society A dx.doi.org/10.1021/ci200133w |J. Chem. Inf. Model. XXXX, XXX, 000–000
ARTICLE
pubs.acs.org/jcim
Predicting pKa Values of Substituted Phenols from Atomic Charges:
Comparison of Different Quantum Mechanical Methods and Charge
Distribution Schemes
Radka Svobodova Varekova,†
Stanislav Geidl,†
Crina-Maria Ionescu,†
Ondrej Skrehota,†
Michal Kudera,†
David Sehnal,†
Tomas Bouchal,†
Ruben Abagyan,‡
Heinrich J. Huber,§
and Jaroslav Koca*,†
†
National Centre for Biomolecular Research, Faculty of Science and CEITEC À Central European Institute of Technology,
Masaryk University Brno, Kamenice 5, 625 00, Brno-Bohunice, Czech Republic
‡
Skaggs School of Pharmacy and Pharmaceutical Sciences, University of California, 9500 Gilman Drive, MC 0657, San Diego, California,
United States
§
Systems Biology Group, Royal College of Surgeons in Ireland, 123 St Stephens Green, Dublin 2, Ireland
bS Supporting Information
’ INTRODUCTION
The acid dissociation (ionization) constant pKa is one of the
fundamental properties of organic molecules determining the
degree of dissociation at a given pH. Dissociation constants are
of interest in chemical, biological, environmental, and pharmaceutical
research because the important physicochemical
properties, like lipophilicity, solubility, and permeability, are
all pKa dependent. The values of these constants are, e.g.,
essential for absorption, distribution, metabolism, elimination
(ADME) proﬁling.1
Ionization constants also provide an
insight into interactions of drugs containing ionizable groups
with a receptor. In drug formulation, pKa is important for the
choice of an appropriate excipient and counterion. Furthermore,
pKa is often used as a descriptor for quantitative
structureÀactivity relationship (QSAR) models. For these
reasons, there is a strong interest in the development of
reliable methods for pKa prediction.
Numerous pKa prediction methods based on diﬀerent
approaches were developed. The linear free energy relationships
(LFER) method,2,3
applying the Hammett and Taft
equations, is one of the ﬁrst approaches used for pKa prediction.
LFER models are still used and have been implemented
in popular software packages, such as ACD/pKa,4
EPIK,5
and
SPARC.6
Database methods use similarity metrics7
to assign
the pKa value of the molecule of interest to the pKa value
obtained from the most similar molecule found in dedicated
databases. Likewise, the decision tree method uses similarity
metrics and builds a tree which provides a decision path for
processing a compound. Ab initio quantum mechanical (QM)
methods have often been found to be the most accurate,8
such
as the Jaguar pKa prediction module,9
which performs geometry
Received: March 18, 2011
ABSTRACT: The acid dissociation (ionization) constant pKa is
one of the fundamental properties of organic molecules. We
have evaluated diﬀerent computational strategies and models to
predict the pKa values of substituted phenols using partial
atomic charges. Partial atomic charges for 124 phenol molecules
were calculated using 83 approaches containing seven theory
levels (MP2, HF, B3LYP, BLYP, BP86, AM1, and PM3), three
basis sets (6-31G*, 6-311G, STO-3G), and ﬁve population
analyses (MPA, NPA, Hirshfeld, MK, and L€owdin). The
correlations between pKa and various atomic charge descriptors
were examined, and the best descriptors were selected for preparing the quantitative structureÀproperty relationship (QSPR)
models. One QSPR model was created for each of the 83 approaches to charge calculation, and then the accuracy of all these models
was analyzed and compared. The pKas predicted by most of the models correlate strongly with experimental pKa values. For
example, more than 25% of the models have correlation coeﬃcients (R2
) greater than 0.95 and root-mean-square errors smaller than
0.49. All seven examined theory levels are applicable for pKa prediction from charges. The best results were obtained for the MP2
and HF level of theory. The most suitable basis set was found to be 6-31G*. The 6-311G basis set provided slightly weaker
correlations, and unexpectedly also, the STO-3G basis set is applicable for the QSPR modeling of pKa. The Mulliken, natural, and
L€owdin population analyses provide accurate models for all tested theory levels and basis sets. The results provided by the Hirshfeld
population analysis were also acceptable, but the QSPR models based on MK charges show only weak correlations.
B dx.doi.org/10.1021/ci200133w |J. Chem. Inf. Model. XXXX, XXX, 000–000
Journal of Chemical Information and Modeling ARTICLE
optimization at the density functional theory (DFT) B3LYP/
6-31G* level, or the approach of Shields et al.,10
which used
the CPCM11
continuum solvation model in Gaussian 98.12
On
the other hand, the applicability of these approaches is limited
due to their computational complexity. A popular way to
beneﬁt from quantum mechanical calculations while keeping
lower computational costs is to use QM descriptors which
have a strong correlation with pKa. Such descriptors include,
e.g., polarizability,13
free energies [phenoxide highest occupied
molecular orbital (HOMO) energy,14
relative proton transfer
energy,14
minimum surface local ionization energy],15
partial
atomic charges,16,17
group philicity,18
molecular electrostatic
potential,19
etc. Information-based descriptors (i.e., molecular
tree structured ﬁngerprints or 2D substructure ﬂags,20
topological
sphere descriptors,21
steric descriptors,21
etc.) are also
applicable. One of the most common techniques that uses
descriptors in pKa prediction is QSAR or quantitative structure À
property relationships (QSPR) in combination with partial leastsquares
(PLS) or multiple linear regression (MLR), while other
methods include artiﬁcial neural networks (ANN).8
Unfortunately,
pKa values remain one of the most challenging physicochemical
properties to predict.
Using partial atomic charges to estimate the relative acidity or
reactivity of organic compounds has a long history in organic
chemistry. Speciﬁcally, the partial atomic charges concept allows
the prediction of relative acidity or reactivity by estimating the
extent of charge delocalization based on molecular structure
information.
Therefore, the correlation between pKa and relevant atomic
charges calculated by diﬀerent ab initio or semiempirical approaches
has been analyzed. For example, Gross et al.22
studied
which population analyses provide a good correlation at the
B3LYP/6-311G** level of theory for substituted phenols and
anilines, and Kreye et al.23
compared three diﬀerent levels of
theory for substituted phenols (RM1 with and without the SM8
solvent model and B3LYP/6-311G** and B3LYP/6-31+G* with
the SM8 solvent model). Partial atomic charges are also often and
successfully used as part of the descriptors set in QSAR/QSPR
models. Dixon et al. calculated pKa from σ and π partial
charges,17
Citra16
used partial charges and bond order, Xing
et al.24
charges and polarizabilities, Soriano et al.25
charges and
frontier orbital energy, and Yangjeh13
combined charges, polarizability,
molecular weight, hydrogen-bond accepting capability,
and partial-charge weighted topological electronic descriptors.
The above studies demonstrate that charges are very powerful
descriptors for pKa modeling and show linear dependency
between charges and pKa. Charge utilization has been limited
by the high computational cost of their quantum mechanical
calculation.
Nowadays, computers are powerful enough to make QM
charges accessible in a much shorter time. Moreover, empirical
charge calculation approaches, like equalization methods,26
are
able to mimic QM methods with high accuracy, and such
empirical approaches are even markedly faster than QM methods
themselves. These facts create a good reason to develop accurate
pKa prediction models that are based on QM charges, because
they can subsequently be used in techniques like virtual
screening.
In the present study we report on the evaluation of pKa
prediction QSPR models based on 83 diﬀerent charge calculation
approaches. Speciﬁcally, we applied 83 combinations of theory
levels (MP2, HF, B3LYP, BLYP, BP86, AM1, and PM3), basis
sets (6-31G*, 6-311G, STO-3G) and population analyses (MPA,
NPA, Hirshfeld, MK, and L€owdin). Then, we compared the
correlations between experimental pKa values and various atomic
charge descriptors and used the best descriptors for designing the
QSPR models. We created a model for each of the 83 approaches
of charge calculation and subsequently analyzed the ability of
these models to predict pKa. The analysis was performed on
phenol molecules, a class of compounds frequently used for the
evaluation of pKa prediction models.16,22,23
There are basically two possible ways to create a QSPR model
of a feature to be predicted. The ﬁrst is to create as general a
model as possible, with the risk that the accuracy of such a model
may not be high. The second approach is to develop more
models, each of them being dedicated to a certain class of
compounds. In our work, we follow the second approach and
start with phenols.
’ METHODS
Data Sets. Our data set contains the 3D structures of 124
distinct phenol molecules. The list of the molecules, including
their experimental pKa values, can be found in the Supporting
Information. This data set is of high structural diversity, meaning
it contains a wide range of electron-withdrawing and electrondonating
substituents, covering a pKa range of about 10 log units.
The molecules were obtained from the NCI Open Database
Compounds.27
This database consists of organic molecules
tested against cancer, and it includes their two-dimensional
(2D) structures and also their 3D structures predicted by
CORINA 2.6.28
The main reason we used the CORINA
approach is speed and compatibility with some other studies.
The key point is speed. Our final goal with the approach is to use
it when searching large databases for virtual screening purposes.
CORINA provides an approximation of the global minimum
conformation very quickly. Moreover, it is quite a common
software for the preparation of 3D structures used in the
validation of pKa prediction models.20,21,29
pKa Values. The experimental pKa values were taken from the
Physprop database.30
The structures of phenol molecules from
the NCI Open Database and their Physprop pKa values were
paired using the CAS registry numbers, which are unique
identifiers in both databases.
Atomic Charge Calculation. All atomic charge calculations
were carried out using Gaussian03 from Gaussian Inc.31
The
merely inputs for charge calculations were the 3D coordinates
generated by CORINA, i.e., without any further geometry
optimization (in a similar way as Ertl et al.).20
The reason why
QM optimization was skipped is again the speed of the approach.
An optimization procedure even based on a QM method would
bring the problem to a different level of computational complexity
and related cost, which would not allow it to be used for our
intended purposes, i.e., searching large databases.
Five ab initio levels of theory were examined. The ﬁrst two
were the standard HartreeÀFock (HF) method and the secondorder
MøllerÀPlesset (MP2) perturbation theory, which includes
more sophisticated approximations of the Hamiltonian
compared to HF. A computational cost of HF and MP2 is θ(N4
)
and θ(N5
), respectively, where N is the number of basis functions.
The other three were the DFT methods with BLYP, BP86,
and B3LYP functionals. BLYP is a representative of gradient
corrected functionals and is denoted according to its authors
(Becke, Lee, Yang and Parr). BP86 (Becke Perdew 1986) is
C dx.doi.org/10.1021/ci200133w |J. Chem. Inf. Model. XXXX, XXX, 000–000
Journal of Chemical Information and Modeling ARTICLE
similar to BLYP but uses an older correlation functional (Perdew-
86). B3LYP(Becke, three-parameter,LeeÀYangÀParr) is a hybrid
functional constructed as a linear combination of the HF and BLYP
functionals. A computational cost of all these DFT methods is
θ(N3
). The basis sets STO-3G, 6-31G*, and 6-311G were used for
each level of theory, therefore 15 combinations of theory levels and
basis sets were studied (HF/STO-3G, HF/6-31G*, HF/6-311G, ...,
BP86/STO-3G, BP86/6-31G*, and BP86/6-311G). Five types of
charges were calculated for each of these 15 pairs of theory levels
and basis sets—charges derived from: natural population analysis
(NPA), Mulliken charges (MPA), L€owdin charges, Hirshfeld
charges, and MerzÀSinghÀKollman charges ﬁt to the electrostatic
potential (MK). Moreover, the application of two semiempirical
methods Austin model 1 (AM1) and parameterization method 3
(PM3) with four PA (Mulliken, L€owdin, Hirshfeld, and MK) was
analyzed.BothAM1andPM3 exhibit computationalcostofθ(N3
).
Consequently, this publication examines 83 approaches for charge
calculation and analyzes their relevance for pKa calculation.
Descriptors. The selection of appropriate descriptors that are
significantly related to the property of interest is very important
for predictive QSPR models. The descriptors can be chosen
using domain knowledge about the examined property, or the
mathematical methods for the selection of descriptors can be
applied. In our work, we have utilized both approaches. We have
focused on atomic charges and their ability to estimate the pKa of
phenols. Therefore, atomic charges and their sums and differences
have been employed as the descriptors. First, according to
traditional knowledge about atomic charge influence on pKa in
phenols, we selected the atomic charge of the hydrogen atom
from the phenolic OH group (qH) and the atomic charges of the
atoms close to this hydrogen as descriptors. These atoms and
their denotations are shown in Figure 1. We also verified in all our
molecules that this hydrogen is the most positively charged
hydrogen, and therefore this hydrogen will dissociate first.
Further descriptors are therefore the charge on the oxygen atom
(qO), the charge on the C1 carbon atom (qC1), and the charge on
the C4 carbon atom (qC4). Because it is not possible to
distinguish between the charges on C2 and C6, the sum of these
charges was used as a descriptor (qC2+C6) and the same for C3
and C5 (qC3+C5). We further evaluated as descriptors also the
sums and the differences of these atomic charges—the difference
between the O and H charge (qOÀH), the sum of charges on C1,
C2, and C6 (qC1+C2+C6), the sum of charges on C3, C4, and C5
(qC3+C4+C5), and the sum of charges on all carbons in the
phenolic group (qphe). After this we evaluated the correlation
between these 10 descriptors and the experimental pKa values
using the squared Pearson correlation coefficient (R2
) and the
Student’s statistic of the regression (t) in order to find descriptors
significantly correlating with pKa. These descriptors were used to
establish the QSPR models.
QSPR Models: Parametrization and Quality Evaluation.
The general equation for our QSPR models is
pKa ¼ param1 3 descr1 þ param2 3 descr2 þ ... þ paramn 3 descrn
þ paramnþ1 ð1Þ
where descr1, descr2, ..., descrn are the descriptors mentioned
above; param1, param2, ..., paramn+1 are parameters of the QSPR
model (i.e., constants derived by multiple linear regression), and
n is the number of descriptors in the QSPR model. The
parametrization of the QSPR models was done by MLR. We
prepared one model for each procedure of charge calculation;
therefore 83 different QSPR models were generated. The quality
of the QSPR models, i.e., the correlation between experimental
pKa and the pKa calculated by the model, was evaluated using the
squared Pearson correlation coefficient (R2
), root-mean-square
error (RMSE), average absolute pKa error (Δ), standard deviation
of the estimation (s), and Fisher’s statistics of the regression
(F). The robustness of the models was tested by cross-validation.
Details about this procedure and its results are described in the
following text.
’ RESULTS AND DISCUSSION
Evaluation of Descriptors. As the first step of our study, we
investigated the pKa predicting capabilities of all 10 suggested
descriptors: qH, qO, qC1, qC2+C6, qC3+C5, qC4, ..., qphe. Consequently,
we calculated the atomic charges of all 124 phenol
molecules from the data set via 83 combinations of theory levels
(HF, MP2, B3LYP, BLYP, BP86, AM1, and PM3), population
analyses (natural, Mulliken, L€owdin, Hirshfeld, and MK) and
basis sets (STO-3G, 6-311G, and 6-31G*). And afterward we
calculated the squared Pearson coefficients (R2
) and Student’s
t-value (t) for the correlations between each descriptor and
experimental pKa values for all 83 procedures of charge
calculation.
The Hirshfeld PA demonstrates an untypical correlation
between descriptors and pKa for the basis sets STO-3G and
6-311G with all levels of theory, where the set contains eight
strong outliers, all bromophenol molecules in the data set, and
there is no reasonable correlation (Figure 2a). When the outliers
were removed, the correlations became similar to those for
Mulliken, natural, or L€owdin population analyses (Figure 2b).
When the polarization basis set 6-31G* is used or when the
semiempirical methods are applied, the charges obtained via the
Hirshfeld PA do not contain the outliers. Therefore, we removed
the bromophenols from the data set and recalculated the
correlation coeﬃcients and Student’s t-values for the Hirshfeld
PA and the basis sets STO-3G and 6-311G using this reduced set
of 116 molecules.
The values of R2
and t for all charge calculation procedures
and all descriptors are summarized in the Supporting Information
(Table S1), and a set of selected values of R2
are visualized
in Figures 3À5. These results show that qH and qO have a high
correlation with experimental pKa, i.e., R2
> 0.8 for most charge
calculation approaches. Almost all these correlation coeﬃcients
are statistically signiﬁcant at p = 0.05. It is worth
mentioning that, for the sets with 124 or 116 molecules, the
R2
is statistically signiﬁcant (at p = 0.05) when t > 1.66. Also qC1
exhibits a good correlation, i.e., R2
> 0.5 for some approaches
Figure 1. (a) The atom enumeration in phenols. (b) Markush structure
of molecules from the data set, where R1, R2, ... R5 = ÀCH3, ÀCHdO,
ÀC6H5, ÀOÀCH2ÀCH3, ÀCH(CH3)2, ÀOÀCH3, ÀCdOÀCH3,
ÀCdOÀNH2, ÀCH2ÀOH, ... ÀCl, ÀBr, ÀF, and ÀNO2.
D dx.doi.org/10.1021/ci200133w |J. Chem. Inf. Model. XXXX, XXX, 000–000
Journal of Chemical Information and Modeling ARTICLE
and t > 1.66 for most approaches. The qOÀH shows a good
correlation (R2
> 0.5 and t > 1.66 for many approaches) too,
but this descriptor is only a combination of qO and qH, and both
qO and qH are better descriptors than qOÀH. Therefore, it
Figure 2. Correlations between qH and pKa for HF, STO-3G, and Hirshfeld PA. Graph (a) with and (b) without outliers.
Figure 3. Correlations between descriptors and experimental pKa.
E dx.doi.org/10.1021/ci200133w |J. Chem. Inf. Model. XXXX, XXX, 000–000
Journal of Chemical Information and Modeling ARTICLE
makes no sense to introduce qOÀH into the models. Further
descriptors show only a weak correlation (<0.5). For these
reasons, the descriptors qH, qO, and qC1 were selected to create
the QSPR models.
Figures 3À5 and Supporting Information (Table S1) also help
us to recognize basic trends in the relevance of the charge
calculation approaches for pKa prediction. All seven theory levels
seem applicable for pKa prediction. Speciﬁcally, most of the
charge calculation approaches utilizing these theory levels provide
qH or qO correlating with pKa with R2
> 0.8 and statistically
signiﬁcant (at p = 0.05). In addition, all three basis sets and four
out of ﬁve examined population analyses seem applicable for the
same considerations. However, the MK PA demonstrates only
weak correlation with pKa and most approaches using MK
provide qH or qO correlating with pKa with R2
< 0.5. Examples
of correlation graphs for the Mulliken and MK population
analyses are shown in Figures 4 and 5.
The trends for Mulliken, natural, L€owdin, and MK PA are in
agreement with the study of Gross et al.,22
who examined the
correlation between qO, qH, and pKa for diﬀerent population
analyses on the B3LYP/6-311G level of theory on a set of 19
substituted phenols. An interesting discovery of these analyses
was also the fact that the correlation between pKa and the atomic
charge descriptors decreases linearly with the distance from the
hydrogen atom of the phenolic OH group.
Parameterization and Validation of QSPR Models. The
descriptors qH, qO, and qC1 were selected as inputs for the QSPR
models, therefore the models have used the following equation
for pKa calculation:
pKa ¼ paramH 3 qH þ paramO 3 qO þ paramC1 3 qC1 þ constant
ð2Þ
where paramH, paramO, paramC1, and constant are the parameters
of the model. The parametrization of the QSPR models
Figure 4. Correlations between qH, qO, and experimental pKa for Mulliken PA and some selected basis sets and theory levels.
Figure 5. Correlations between qH, qO, and experimental pKa for MK PA and some selected basis sets and theory levels.
F dx.doi.org/10.1021/ci200133w |J. Chem. Inf. Model. XXXX, XXX, 000–000
Journal of Chemical Information and Modeling ARTICLE
Table 1. Quality Criteria and Statistical Criteria for All the QSPR Modelsa
model number theory level population analysis basis set R2
RMSE Δ s F number of molecules
1 MP2 Mulliken 6-31G* 0.966 0.403 0.315 0.410 1136 124
2 HF Mulliken 6-31G* 0.966 0.403 0.315 0.410 1136 124
3 MP2 L€owdin 6-31G* 0.966 0.405 0.315 0.412 1136 124
4 HF L€owdin 6-31G* 0.966 0.406 0.315 0.413 1136 124
5 MP2 NPA 6-31G* 0.964 0.419 0.325 0.426 1071 124
6 B3LYP L€owdin 6-31G* 0.963 0.421 0.325 0.428 1041 124
7 HF NPA 6-31G* 0.963 0.421 0.329 0.428 1041 124
8 B3LYP NPA 6-311G 0.962 0.428 0.336 0.435 1013 124
9 MP2 NPA 6-311G 0.961 0.432 0.344 0.439 986 124
10 B3LYP NPA 6-31G* 0.961 0.433 0.332 0.440 986 124
11 HF NPA 6-311G 0.961 0.434 0.346 0.441 986 124
12 BLYP NPA 6-311G 0.96 0.437 0.341 0.444 960 124
13 BP86 NPA 6-311G 0.959 0.443 0.342 0.450 936 124
14 B3LYP Mulliken 6-31G* 0.959 0.443 0.355 0.450 936 124
15 BLYP NPA 6-31G* 0.959 0.444 0.34 0.451 936 124
16 BLYP L€owdin 6-31G* 0.959 0.444 0.34 0.451 936 124
17 BP86 L€owdin 6-31G* 0.959 0.445 0.341 0.452 936 124
18 BP86 NPA 6-31G* 0.959 0.447 0.342 0.454 936 124
19 BP86 Mulliken 6-31G* 0.954 0.471 0.374 0.479 830 124
20 BLYP Mulliken 6-31G* 0.953 0.477 0.377 0.485 811 124
21 MP2 L€owdin 6-311G 0.951 0.486 0.375 0.494 776 124
22 HF L€owdin 6-311G 0.95 0.491 0.38 0.499 760 124
23 HF Mulliken 6-311G 0.945 0.513 0.399 0.521 687 124
24 MP2 Mulliken 6-311G 0.945 0.514 0.401 0.522 687 124
25 BP86 Mulliken 6-311G 0.939 0.541 0.429 0.550 616 124
26 B3LYP Mulliken 6-311G 0.938 0.547 0.433 0.556 605 124
27 B3LYP L€owdin 6-311G 0.937 0.551 0.417 0.560 595 124
28 BLYP Mulliken 6-311G 0.932 0.573 0.452 0.582 548 124
29 BP86 L€owdin 6-311G 0.931 0.577 0.443 0.587 540 124
30 MP2 Hirshfeld STO-3G 0.929 0.594 0.467 0.605 488 116
31 HF Hirshfeld STO-3G 0.928 0.597 0.47 0.608 481 116
32 BLYP L€owdin 6-311G 0.926 0.596 0.451 0.606 501 124
33 AM1 Mulliken À 0.924 0.605 0.452 0.615 486 124
34 AM1 L€owdin À 0.924 0.605 0.452 0.615 486 124
35 MP2 Mulliken STO-3G 0.922 0.615 0.502 0.625 473 124
36 MP2 L€owdin STO-3G 0.921 0.617 0.505 0.627 466 124
37 MP2 NPA STO-3G 0.921 0.618 0.501 0.628 466 124
38 HF Mulliken STO-3G 0.92 0.619 0.508 0.629 460 124
39 HF L€owdin STO-3G 0.92 0.621 0.51 0.631 460 124
40 HF NPA STO-3G 0.92 0.622 0.506 0.632 460 124
41 AM1 Hirshfeld À 0.917 0.631 0.499 0.641 442 124
42 MP2 Hirshfeld 6-31G* 0.912 0.652 0.529 0.663 415 124
43 MP2 Hirshfeld 6-311G 0.91 0.667 0.534 0.679 377 116
44 HF Hirshfeld 6-31G* 0.908 0.665 0.538 0.676 395 124
45 HF Hirshfeld 6-311G 0.907 0.678 0.541 0.690 364 116
46 B3LYP Mulliken STO-3G 0.904 0.68 0.558 0.691 377 124
47 B3LYP Hirshfeld STO-3G 0.902 0.698 0.536 0.710 344 116
48 B3LYP Hirshfeld 6-31G* 0.897 0.705 0.546 0.717 348 124
49 BP86 Mulliken STO-3G 0.896 0.707 0.575 0.719 345 124
50 BLYP Mulliken STO-3G 0.896 0.709 0.581 0.721 345 124
51 B3LYP L€owdin STO-3G 0.895 0.71 0.565 0.722 341 124
52 PM3 Hirshfeld À 0.895 0.711 0.561 0.723 341 124
53 B3LYP NPA STO-3G 0.894 0.715 0.567 0.727 337 124
54 BP86 Hirshfeld 6-31G* 0.89 0.729 0.553 0.741 324 124
G dx.doi.org/10.1021/ci200133w |J. Chem. Inf. Model. XXXX, XXX, 000–000
Journal of Chemical Information and Modeling ARTICLE
was performed for all 83 charge calculation approaches via
MLR. The complete data set of 124 phenol molecules was used
for the parametrization, and the obtained models were validated
for all molecules in the data set. The only exceptions were the
charge calculation procedures containing the Hirshfeld PA and
basis sets 6-311G and STO-3G. In these cases, only 116 phenols
were used for the parametrization and evaluation of the models,
because 8 molecules from the original set were strong outliers.
Table 1 contains the quality criteria (R2
, RMSE, and Δ) and the
statistical criteria (s and F) for all the models. The models are
sorted according to their quality. The parameters of the models
are summarized in the Supporting Information (Table S2). The
most relevant graphs of correlation between experimental and
calculated pKa are visualized in Figure 6. Tables 2À4 provide a
clue for the comparison of QSPR models. Table 2 summarizes
the R2
of all models, Table 3 contains the average values of R2
for all QSPR models which use a specific theory level, basis set,
or PA, and Table 4 summarizes the quality of the charge
calculation approaches which use a specific theory level, basis
set or PA, and whose R2
are in a certain interval.
The results provided in Tables 1À4 and Figure 6 lead us to the
following conclusions regarding the relevance of the charge
calculation method to the ability of the QSPR model to predict
pKa for phenolic compounds.
Comparison of All Models. All the presented models are
statistically significant at p = 0.01. For the sets of 124 or 116
molecules, the models with three descriptors are statistically
significant (at p = 0.01) when F > 3.949. The best models are
MP2/6-31G*/Mulliken and HF/6-31G*/Mulliken (R2
= 0.966,
RMSE = 0.403, Δ = 0.315, s = 0.410, and F = 1136). More than
25% of the analyzed models (22 out of 83) have excellent quality
and statistical criteria (R2
g 0.95, RMSE e 0.491, Δ e 0.38, s e
0.5, and F g 760), and more than 50% (47 out of 83) have very
good statistical criteria (R2
> 0.9, RMSE e 0.698, Δ e 0.54, s e
0.71, and F g 344). About 80% of the models are able to predict
pKa with acceptable quality (R2
> 0.85, RMSE e 0.8, Δ e 0.641, s
e 0.813, and F g 261). Only less than 20% of the models show a
week correlation.
Influence of Theory Level. Ab initio theory levels: All five
examined ab initio theory levels (MP2, HF, B3LYP, BLYP, and
BP86) are applicable to pKa prediction using charges. The best
QSPR models are provided by MP2 and HF (models 1 and 2).
Surprisingly, the differences between MP2 and HF were very
small (illustrated by Tables 2À4). The pKa values calculated
from DFT charges have a slightly weaker correlation with
experimental pKa compared to MP2 and HF. The best performing
DFT functional has been B3LYP, the models created by
BLYP and BP86 have been less accurate.
Table 1. Continued
model number theory level population analysis basis set R2
RMSE Δ s F number of molecules
55 BLYP Hirshfeld 6-31G* 0.886 0.741 0.567 0.753 311 124
56 BLYP Hirshfeld STO-3G 0.886 0.75 0.571 0.763 290 116
57 BP86 Hirshfeld STO-3G 0.882 0.763 0.578 0.777 279 116
58 B3LYP Hirshfeld 6-311G 0.882 0.764 0.599 0.778 279 116
59 PM3 Mulliken À 0.88 0.76 0.581 0.773 293 124
60 PM3 L€owdin À 0.88 0.76 0.581 0.773 293 124
61 BLYP L€owdin STO-3G 0.879 0.764 0.599 0.777 291 124
62 BP86 L€owdin STO-3G 0.878 0.766 0.597 0.779 288 124
63 BLYP NPA STO-3G 0.877 0.769 0.604 0.782 285 124
64 BP86 NPA STO-3G 0.876 0.772 0.601 0.785 283 124
65 BP86 Hirshfeld 6-311G 0.874 0.789 0.613 0.803 259 116
66 MP2 MK STO-3G 0.869 0.795 0.634 0.808 265 124
67 BLYP Hirshfeld 6-311G 0.868 0.807 0.627 0.821 245 116
68 HF MK STO-3G 0.867 0.8 0.641 0.813 261 124
69 BLYP MK 6-311G 0.826 0.917 0.714 0.932 190 124
70 BP86 MK 6-311G 0.825 0.919 0.714 0.934 189 124
71 B3LYP MK 6-311G 0.822 0.926 0.721 0.941 185 124
72 B3LYP MK STO-3G 0.817 0.939 0.749 0.955 179 124
73 BP86 MK 6-31G* 0.813 0.949 0.716 0.965 174 124
74 BLYP MK 6-31G* 0.813 0.95 0.72 0.966 174 124
75 MP2 MK 6-311G 0.812 0.951 0.746 0.967 173 124
76 HF MK 6-311G 0.811 0.954 0.747 0.970 172 124
77 B3LYP MK 6-31G* 0.808 0.962 0.728 0.978 168 124
78 MP2 MK 6-31G* 0.788 1.011 0.773 1.028 149 124
79 HF MK 6-31G* 0.788 1.012 0.773 1.029 149 124
80 BP86 MK STO-3G 0.787 1.014 0.8 1.031 148 124
81 BLYP MK STO-3G 0.786 1.016 0.799 1.033 147 124
82 AM1 MK À 0.447 1.633 1.247 1.660 32 124
83 PM3 MK À 0.445 1.636 1.249 1.663 32 124
a
The models are sorted according their R2
(descending) and afterwards according their RMSE (ascending) and Δ (ascending).
H dx.doi.org/10.1021/ci200133w |J. Chem. Inf. Model. XXXX, XXX, 000–000
Journal of Chemical Information and Modeling ARTICLE
Figure 6. Graphs showing the correlation between experimental and calculated pKa for some selected charge calculation procedures.
I dx.doi.org/10.1021/ci200133w |J. Chem. Inf. Model. XXXX, XXX, 000–000
Journal of Chemical Information and Modeling ARTICLE
Semiempirical theory levels: The semiempirical approaches
tested here provide weaker correlation than ab initio methods but
are still applicable for pKa prediction. The models with AM1 and
Mulliken, Hirshfeld, or L€owdin PA show good correlation (R2
g
0.917). The models using PM3 and Mulliken, Hirshfeld, or
L€owdin PA also demonstrate acceptable correlation (R2
g
0.88). The combination of semiempirical approaches with MK
PA gives the worst models in this study (models 82 and 83).
Influence of Basis Set. The charges most appropriate for
QSPR modeling of pKa are provided by the 6-31G* basis set, and
the accuracy of these models is very high. For example, the model
with HF/6-31G*/Mulliken charges shows R2
= 0.966. The
results for the 6-311G basis set are slightly weaker. Unexpectedly,
also the charges obtained using the STO-3G basis set are suitable
for QSPR modeling, and the quality of these models is acceptable.
For example, the model employing MP2/STO-3G/Hirshfeld
charges exhibits R2
= 0.929.
Influence of Population Analysis. Mulliken, natural, and
L€owdin PAs with all levels of theory and basis sets provide the
charges that are appropriate for pKa prediction. The Hirshfeld
PA with the STO-3G basis set provides results similar to the
Mulliken, natural, or L€owdin PA with the same basis set.
Nevertheless, the Hirshfeld PA with the 6-31G* or 6-311G
basis sets lead to less accurate models than the above-mentioned
population analyses employing these basis sets. Moreover,
the occurrence of strong outliers complicates the
application of the Hirshfeld PA. The charges calculated by
the MK PA show only weak correlation with pKa, and the QSPR
models based on these charges have low accuracy, i.e., the best
of such QSPR models employs HF/STO-3G/MK charges and
shows R2
= 0.867.
Table 2. Squared Pearson Coeﬃcients between Calculated and Experimental pKa
Table 3. Average Squared Pearson Coeﬃcients for All
Charge Calculation Approaches Which Use a Speciﬁc Theory
Level, PA, or Basis Set
theory level BLYP BP86 B3LYP HF MP2 AM1 PM3
average R2
0.894 0.895 0.903 0.915 0.916 0.803 0.775
population analysis MK Hirshfeld L€owdin Mulliken NPA
average R2
0.772 0.898 0.930 0.932 0.940
basis set 6-31G* 6-311G STO-3G
average R2
0.917 0.909 0.887
Table 4. Percentage of Charge Calculation Approaches
Which Use a Speciﬁc Theory Level, PA, or Basis Set and
Whose Squared Pearson Coeﬃcients Are in a Certain
Intervala
theory level interval BLYP BP86 B3LYP HF MP2 AM1 PM3
R2
g 0.95 27 27 29 33 33 0 0
0.95 > R2
g 0.9 13 13 29 47 47 75 0
0.9 > R2
g 0.85 40 40 21 7 7 0 75
R2
< 0.85 20 20 21 13 13 25 25
population analysis interval MK Hirshfeld L€owdin Mulliken NPA
R2
g 0.95 0 0 41 29 67
0.95 > R2
g 0.9 0 47 35 53 13
0.9 > R2
g 0.85 12 53 24 18 20
R2
< 0.85 88 0 0 0 0
basis set interval 6-31G* 6-311G STO-3G
R2
g 0.95 60 28 0
0.95 > R2
g 0.9 12 40 40
0.9 > R2
g 0.85 8 12 48
R2
< 0.85 20 20 12
a
The percentages are calculated from total number of approaches with
the deﬁned theory level, basis set, or PA.
J dx.doi.org/10.1021/ci200133w |J. Chem. Inf. Model. XXXX, XXX, 000–000
Journal of Chemical Information and Modeling ARTICLE
Table 5. Comparison of the Presented QSPR Models with Previous Work
theory level PA basis set descriptors R2
s F number of molecules source
B3LYP NPA 6-311G** qOÀH 0.789 1.300 48 15 Kreye and Seybold,23, a
B3LYP NPA 6-311G** qO 0.731 1.500 38 15 Kreye and Seybold,23, a
B3LYP NPA 6-31+G* qOÀH 0.880 0.970 95 15 Kreye and Seybold,23, b
B3LYP NPA 6-31+G* qO 0.865 1.000 38 15 Kreye and Seybold,23, b
B3LYP NPA 6-311G(d,p) qOÀ 0.911 0.252 173 19 Gross and Seybold14
B3LYP NPA 6-311G(d,p) qH 0.887 0.283 134 19 Gross and Seybold14
B3LYP NPA 6-31G* qH, qO, qC1 0.961 0.440 986 124 this work, model 10
B3LYP NPA 6-311G qH, qO, qC1 0.962 0.435 1013 124 this work, model 8
B3LYP MPA 6-311G(d,p) qH 0.913 0.248 179 19 Gross and Seybold14
B3LYP MPA 6-311G(d,p) qOÀ 0.894 0.274 144 19 Gross and Seybold14
B3LYP MPA 6-311G qH, qO, qC1 0.938 0.556 605 124 this work, model 26
B3LYP MPA 6-31G* qH, qO, qC1 0.959 0.450 936 124 this work, model 14
B3LYP MK 6-311G(d,p) qH 0.344 0.682 9 19 Gross and Seybold14
B3LYP MK 6-311G(d,p) qOÀ 0.692 0.467 38 19 Gross and Seybold14
B3LYP MK 6-311G qH, qO, qC1 0.822 0.941 185 124 this work, model 71
B3LYP MK 6-31G* qH, qO, qC1 0.808 0.978 168 124 this work, model 77
a
With solvent model SM5.4. b
With solvent model SM8.
Table 6. Comparison of R2
and RMSE for Test, Training, and Complete Sets for Model 2 (employing HF, Mulliken, 6-31G*)
Charge Calculation Approaches
complete set
R2
RMSE s F number of molecules
0.966 0.403 0.410 1136 124
cross validation
training set test set
cross-validation step R2
RMSE s F number of molecules R2
RMSE s F number of molecules
1 0.965 0.405 0.413 873 99 0.973 0.405 0.442 252 25
2 0.970 0.382 0.390 1024 99 0.930 0.489 0.534 93 25
3 0.964 0.415 0.424 848 99 0.977 0.357 0.390 297 25
4 0.967 0.394 0.402 928 99 0.966 0.444 0.484 199 25
5 0.968 0.403 0.411 968 100 0.957 0.442 0.484 148 24
Table 7. Comparison of R2
and RMSE for Test, Training, and Complete Sets for Model 14 (employing B3LYP, Mulliken, 6-31G*)
Charge Calculation Approaches
complete set
R2
RMSE s F number of molecules
0.959 0.443 0.450 936 124
cross validation
training set test set
cross-validation step R2
RMSE s F number of molecules R2
RMSE s F number of molecules
1 0.958 0.441 0.450 722 99 0.963 0.452 0.493 182 25
2 0.962 0.434 0.443 802 99 0.925 0.509 0.555 86 25
3 0.955 0.462 0.472 672 99 0.975 0.358 0.391 273 25
4 0.961 0.425 0.434 780 99 0.956 0.516 0.563 152 25
5 0.962 0.435 0.444 810 100 0.950 0.506 0.554 127 24
K dx.doi.org/10.1021/ci200133w |J. Chem. Inf. Model. XXXX, XXX, 000–000
Journal of Chemical Information and Modeling ARTICLE
Comparison with Previous Work. QSPR models similar to
those presented in this paper were previously published by Gross
and Seybold14
and also by Kreye and Seybold.23
Table 5 shows a
comparison of these models with our models. It is seen therein
that our models show markedly higher R2
and F values, even for
simpler basis sets. The reason may be that they employ more
descriptors and were parametrized within a larger training set.
Cross-Validation. The robustness of the models was tested by
cross-validation. The set of phenol molecules was divided into
five parts (each contained 20% of the molecules). Afterward, five
cross-validation steps were performed. In the first step, the first
part was selected as a test set, and the remaining four parts were
taken together as the training set. The test and training sets for
the other steps were prepared in a similar manner by subsequently
considering one part as a test set and the remaining parts
served as a training set. For each step, the QSPR model was
parametrized on the training set. Afterward, the pKa values of the
respective test molecules were calculated via this model and
compared with experimental pKa values. The cross-validation
was performed for all 83 analyzed charge calculation approaches.
The results are summarized in the Supporting Information
(Table S3), and a part of these results is shown in Tables 6
and 7. The cross-validation showed that the models are stable,
and the values of R2
and RMSE are similar for the test, training,
and complete sets.
’ CONCLUSION
The quantum chemical partial atomic charges have been
shown to provide very good QSPR models for the estimation
of pKa. More than 25% of the analyzed models (22 out of 83)
have excellent quality and statistical criteria (e.g., R2
g 0.95), and
more than 50% (47 out of 83) have very good statistical criteria
(e.g., R2
> 0.9). The descriptors used in the models we developed
are the atomic charges of the hydrogen and oxygen from the
phenolic OH group and the charge of the carbon binding to the
OH group. Other atomic charges show only a weak correlation
with pKa. All seven examined theory levels (MP2, HF, B3LYP,
BLYP, BP86, AM1, and PM3) are applicable to predicting pKa
from charges. The best results have been obtained for MP2 and
HF. Utilizing DFT also provides good correlation. Semiempirical
methods have generated weaker but acceptable models. The
most suitable basis set was 6-31G*, while 6-311G provided
slightly weaker correlations, and unexpectedly also the STO-
3G basis set proved applicable to the QSPR modeling of pKa. The
Mulliken, natural, and L€owdin population analyses provided
accurate models for all tested theory levels and basis sets. The
Hirshfeld PA has been also useful, but the QSPR models based
on MK charges showed only weak correlations. It is thus clear
from our study that it is possible to predict pKa values with very
good accuracy using only partial atomic charges, and even
unsophisticated theory levels and basis sets can provide good
descriptors.
’ ASSOCIATED CONTENT
bS Supporting Information. List of phenol molecules employed
in this study, including their experimental pKa, the table
of R2
values for all charge calculation procedures and all
descriptors (Table S1), the table with parameters of all QSPR
models (Table S2) and the table of cross-validation results
(Table S3). This material is available free of charge via the
Internet at http://pubs.acs.org/.
’ AUTHOR INFORMATION
Corresponding Author
*E-mail: jkoca@chemi.muni.cz.
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Electronegativity Equalization Method:
parameterization and validation for large sets
of organic, organohalogene and organometal
molecule
228
Int. J. Mol. Sci. 2007, 8, 572-582
International Journal of
Molecular Sciences
ISSN 1422-0067
© 2007 by MDPI
www.mdpi.org/ijms/
Full Research Paper
Electronegativity Equalization Method: Parameterization and
Validation for Large Sets of Organic, Organohalogene and
Organometal Molecule
Radka Svobodová Vařeková 1
, Zuzana Jiroušková 1
, Jakub Vaněk 1
, Šimon Suchomel 1
and
Jaroslav Koča 1,
*
1 National Centre for Biomolecular Research, Faculty of Science, Masaryk University, Kotlářská 2,
611 37 Brno, Czech Republic; Tel.: +420 549 494 947, Fax: +420 549 492 556,
E-mail: jkoca@chemi.muni.cz
* Author to whom correspondence should be addressed; E-mail: jkoca@chemi.muni.cz
Received: 10 May 2007; in Revised Form: 6 June 2007 / Accepted: 14 June 2007 /
Published: 3 July 2007
Abstract: The Electronegativity Equalization Method (EEM) is a fast approach for charge
calculation. A challenging part of the EEM is the parameterization, which is performed
using ab initio charges obtained for a set of molecules. The goal of our work was to perform
the EEM parameterization for selected sets of organic, organohalogen and organometal
molecules. We have performed the most robust parameterization published so far. The EEM
parameterization was based on 12 training sets selected from a database of predicted 3D
structures (NCI DIS) and from a database of crystallographic structures (CSD). Each set
contained from 2000 to 6000 molecules. We have shown that the number of molecules in
the training set is very important for quality of the parameters. We have improved EEM
parameters (STO-3G MPA charges) for elements that were already parameterized,
specifically: C, O, N, H, S, F and Cl. The new parameters provide more accurate charges
than those published previously. We have also developed new parameters for elements that
were not parameterized yet, specifically for Br, I, Fe and Zn. We have also performed
crossover validation of all obtained parameters using all training sets that included relevant
elements and confirmed that calculated parameters provide accurate charges.
Keywords: Charge distribution, Electronegativity Equalization Method, Parameterization,
Organohalogenes, Organometals.
Int. J. Mol. Sci. 2007, 8 573
1. Introduction
Electronegativity Equalization Method (EEM) [1,2,3] is a fast approach for charge calculation. The
basic idea is based on the density functional theory (DFT) [4,5]. First, Parr et al. applied the DFT and
formulated a new definition and explanation of electronegativity [6,7]. Later on, Mortier et al. applied
Parr's definition of electronegativity and Sanderson's Electronegativity Equalization Principle (EEP)
[8,9,10] and created the EEM.
This method is able to calculate atomic charges markedly faster than common ab initio approaches.
The ab initio charge calculations exhibit time complexity of O(B4
), where B is greater or equal to the
number of valence electrons. The EEM approach shows a time complexity of θ(N3
), where N is the
number of atoms. Nevertheless, accuracy of the EEM corresponds to the ab initio methods.
A challenging part of the EEM is the parameterization that is performed using ab initio charges
obtained for a set of molecules. The parameterization is very time-consuming with time complexity of
O(S.B4
), where S is a number of molecules in the set. The most common parameterization of the EEM
is a parameterization for the HF method with the STO-3G basis set, where the charges are calculated
by Mulliken population analysis (MPA) [11,12]. Principally, it is also possible to parameterize the
EEM for other basis sets (i.e., 6-31G*) and methods for charge calculation (i.e., CHELPG, MK, NPA,
ESP, Hirshfeld method) [13,14]. First attempts to calculate EEM parameters were published in eighties
[1,2]. These publications contained only parameters for C, H, N and O, which were developed using
training sets of about one hundred molecules. Further parameterizations were performed during the
nineties and contained parameters for new elements (S, Si, P, F, Cl) and more complex bases
[15,16,17]. The EEM parameterization still remains attractive to chemists' attention [18,19,20].
The goal of this work is to perform the EEM parameterization based on large sets of organic,
organohalogen and organometal molecules (containing Zn and Fe) selected from databases NCI DIS
[21] and CSD [22], and to validate the quality of calculated parameters on reference sets of molecules
selected from these databases. The parameterization was performed for STO-3G MPA charges.
2. Theoretical basis
2.1. EEM
Using DFT, the effective (charge-dependent) electronegativity of the atom i in a molecule can be
calculated by eq. (1) [1,2 3]:
∑≠=
++=
N
ijj ji
j
iiii
R
q
qBA
)(1 ,
.. κχ (1)
where N is the number of atoms in the molecule, qi and qj are the charges distributed on the atoms i
and j, respectively, Ri,j is the distance between atoms i and j, and κ is the adjusting factor. The
coefficients Ai and Bi are defined by eqs. (2):
( )iiii
iiii
B
A
ηηη
χχχ
∆+==
∆+==
0*
0*
22 (2)
Int. J. Mol. Sci. 2007, 8 574
where χi
0
is the electronegativity of an isolated neutral atom i, ηi
0
is the hardness, and ∆χi
0
and ∆ηi
describe the molecular environment. The coefficients Ai, Bi and κ are empirical parameters, which must
be obtained via EEM parameterization. Such a parameterization is a topic of this work.
According to Sanderson's Electronegativity Equalization Principle [8, 9, 10], the effective
electronegativity of each atom in the molecule is equal to the molecular electronegativity χ :
χχχχ ==== N...21 (3)
The total charge Q of the molecule is equal to the sum of all the atomic charges:
∑=
=
N
i
i Qq
1
(4)
The atomic charges are described using the equation system (5), which contains N+1 equations with
N+1 unknowns: q1, q2, … , qN and χ . This system was derived from equations (1), (3) and (4) [1]:
















−
−
−
=
































−
−
−
Q
A
A
A
q
q
q
B
B
B
NNNRR
RR
RR
NN
N
N
MM
L
L
MMOMM
L
L
2
1
2
1
2
1
.
0111
1
1
1
2,1,
,21,2
,12,1
χ
κκ
κκ
κκ (5)
The matrix of the equation system (5) is called EEM matrix.
2.2. EEM Parameterization
Empirical parameters Ai, Bi and κ (described by eqs. (1) and (2)) can be calculated in the following
way [17]:
From eq. (1) and (3), eq. (6) can be derived:
∑≠=
++=
N
ijj ji
j
iii
R
q
qBA
)(1 ,
κχ
(6)
Eq. (6) can be rewritten as:
∑≠=
−=+
N
ijj ji
j
iii
R
q
qBA
)(1 ,
κχ
(7)
Meaning that eq. (7) is in the form:
iiii yxBA =+ (8)
where:
,ii qx = ∑≠=
−=
N
ijj ji
j
i
R
q
y
)(1 ,
κχ
Then, empirical parameters can be obtained using eq. (8) in the following way:
1. Selection of a set of molecules used for the EEM parameterization.
2. Ab initio calculation of atomic charges qi for all atoms within all selected molecules.
3. Calculation of the molecular electronegativity χ as a harmonic average of atomic
electronegativities χi
0
(for isolated atoms i):
1
1
0
1
−
=






= ∑
N
i i
N
χ
χ
(9)
4. Selection of κ values for which the parameterization will be performed.
Int. J. Mol. Sci. 2007, 8 575
5. For each of the above selected κ:
• Calculation of xi and yi values for all atoms in all molecules using eq. (8).
• Separation of xi and yi couples into subsets according to the chemical symbol and
hybridization of the atom i (for example C in sp3
, C in sp2
etc.).
• Calculation of parameters Ai and Bi for each of these subsets using the least square
minimization.
6. Finding the optimal κ value.
3. Methods
In this work, two databases were used. The first one was the NCI DIS 3D database [21], created as a
part of DTP NCI (Developmental Therapeutics Program of National Cancer Institute). This database
contains organic molecules tested against cancer, specifically their topologies and also geometries,
predicted by the program CHEM-X [23] and stored in SDF format [24]. The second database used was
CSD (Cambridge Structural Database) [22], administered by CCDC (Cambridge Crystallographic Data
Centre). Geometries of molecules are stored also in SDF format. However, in this case information is
obtained experimentally using the X-ray and/or neutron diffraction. Both these databases are
sufficiently large, containing more than two hundred thousand molecules.
Table 1: Sets of molecules that were used as training and testing sets for the EEM parameterization.
Database Denotation
of the set
Number of
molecules
Atoms
included
Position of the set
in the database
NCI DIS
(predicted
data)
nbeg 2000 C, O, N, H, S beginning (ID between 1 and 3162)
nmid 2000 C, O, N, H, S middle (ID between 300 000 and 314 026)
nend 2000 C, O, N, H, S end (ID between 705 000 and 712 703)
nall 6000 C, O, N, H, S nbeg, nmid and nend
nhal 4000 C, O, N, H, S,
Br, Cl, F, I
beginning (ID between
106498 and 114688)
CSD
(crystallo-
graphic
data)
cbeg 2000 C, O, N, H, S beginning (ID starting by A and B)
cmid 2000 C, O, N, H, S middle (ID starting by J, K and L)
cend 2000 C, O, N, H, S end (ID starting by W and Y)
call 6000 C, O, N, H, S cbeg, cmid and cend
chal 4000 C, O, N, H, S,
F, Cl, Br, I
beginning (ID starting by A, B and C)
cmet 2000 C, O, N, H, S,
Fe, Zn
beginning (ID starting by A and B)
ch,m 6000 C, O, N, H, S,
F, Cl, Br, I, Fe,
Zn
chal and cmet
ID is a unique identification of a molecule in a database. In the NSC DIS database, ID is a number between 1 and about
720 000. Database CSD uses alphabetically sorted string IDs that contains six upper case characters.
Int. J. Mol. Sci. 2007, 8 576
From these two databases, several training sets of molecules were selected (see Table 1). Our goal
was to generate training sets, which cover most of bonding situations and also conformational
variability in real molecules. For that reason, we have chosen large sets containing randomly selected
molecules. As molecules are unsorted in NCI DIS and CSD databases, the simplest random selection is
to take a continuous part of the database. We selected three training sets, containing elements C, H, O,
N and S from each database. To obtain the most versatile training sets, we selected first training set
from the beginning, second from the middle and the third from the end of the databases. We have also
used unions of these sets. For organohalogenes and organometals, we did not need so many training
sets as the process of parameterization was already debugged on above mentioned six training sets and
their unions. Therefore we used only one training set of organohalogenes from each database. Just one
training set (from CSD database) was used for organometals, because the NCI DIS database does not
contain enough organometal molecules. These organometal and organohalogene molecules were
selected from the beginning of the databases.
For the parameterization, ab initio charges were calculated using the HF method with the STO-3G
basis set for all molecules in all sets. The charge calculation was performed by Gaussian 98
program [25]. After that, the EEM parameterization was performed using calculated ab initio charges
for all training sets.
Table 2: Quality of parameters that were obtained by EEM parameterization using all training sets.
Rmol
avg
Training set
Lit. nbeg nmid nend nall nhal cbeg cmid cend call chal cmet ch,m
T
e
s
t
e
d
s
e
t
nbeg 0.966 0.955 0.962 0.930 0.959 0.961 0.950 0.924 0.938 0.945 0.944 0.928 0.938
nmid 0.957 0.939 0.951 0.910 0.947 0.951 0.941 0.902 0.932 0.936 0.930 0.918 0.929
nend 0.960 0.944 0.958 0.922 0.944 0.956 0.956 0.894 0.942 0.945 0.932 0.929 0.942
nall 0.961 0.946 0.957 0.921 0.953 0.956 0.949 0.907 0.937 0.942 0.935 0.925 0.936
nhal - - - - - 0.928 - - - - 0.919 - 0.887
cbeg 0.945 0.918 0.928 0.870 0.928 0.930 0.946 0.917 0.934 0.941 0.936 0.916 0.937
cmid 0.934 0.912 0.922 0.867 0.921 0.920 0.932 0.902 0.921 0.928 0.922 0.898 0.921
cend 0.936 0.913 0.925 0.870 0.922 0.922 0.936 0.902 0.923 0.930 0.927 0.903 0.927
call 0.939 0.914 0.925 0.869 0.924 0.924 0.938 0.907 0.926 0.933 0.928 0.906 0.928
chal - - - - - 0.903 - - - - 0.910 - 0.885
cmet - - - - - - - - - - - 0.887 0.879
ch,m - - - - - - - - - - - - 0.885
Rmol
avg
describes quality of parameters obtained via EEM parameterization using the training set. This value is between 0
and 1. The closer it is to 1, the more accurate charges are provided employing the EEM method using the parameters. The
Rmol
avg
is an average of Rmol values for all molecules in the training set. Rmol is the R-squared value of the linear regression
line, which was inserted into a set of points [qi(ab initio), qi(EEM)], where qi(ab initio) and qi(EEM) are ab initio and EEM
charges (calculated using the parameters) of atom i, respectively. Lit. means parameters obtained from
literature [17]. For our parameters, the best Rmol
avg
for each tested set is bolded.
Int. J. Mol. Sci. 2007, 8 577
Parameters, calculated for all training sets presented in Table 1, and also parameters obtained from
the literature were validated for all training sets that contained suitable atoms. Validation of parameters
for a selected training set was done in such a way that ab initio charges and the EEM charges
calculated for each molecule from the training set using the developed parameters were compared via
the least square method. In other words, the linear regression line was fitted to a set of points [qi(ab
initio), qi(EEM)], where qi(ab initio) and qi(EEM) are ab initio and EEM charges of the atom i,
respectively. Correlation between ab initio and EEM charges was described by the R-squared value
[26] of this line. This R-squared value is between 0 and 1. The closer it is to 1, the better the
correlation is. The R-squared value (Rmol) was calculated for each molecule in the training set. An
average value of (Rmol
avg
) was calculated from all Rmol values in each set to express the quality of
parameters for the set.
Table 3: Information about numbers of molecules and atoms in newly created training sets cbeg2, chal2,
cmet2 and ch,m2. For more details see the text.
Element Bond
order
Number of molecules and atoms in training set
cbeg2 chal2 cmet2 ch,m2
molecules atoms molecules atoms molecules atoms molecules atoms
H 1 530 11187 810 13214 1112 25894 3082 60873
C 1 498 4113 729 5128 1070 10918 2847 24359
N 1 325 605 378 689 641 1353 1598 3195
O 1 400 1162 536 1258 830 2636 2185 6030
S 1 58 116 87 160 168 416 358 756
C 2 518 5871 843 10058 1078 12756 3086 37612
N 2 172 350 289 561 374 825 1062 2163
O 2 401 907 546 991 786 1943 2123 4449
Cl 1 - - 455 1158 - - 929 2319
Br 1 - - 211 324 - - 477 735
F 1 - - 188 805 - - 411 1745
I 1 - - 57 95 - - 134 202
Zn 1 - - - - 103 178 155 268
Fe 1 - - - - 186 317 203 335
Total 544 24311 870 34441 1154 57236 3258 145041
Int. J. Mol. Sci. 2007, 8 578
4. Results
Table 4: EEM parameters A, B and κ (see eqs. (1) and (2)) obtained via parameterization using
training sets cbeg2, chal2, cmet2 and ch,m2.
EEM parameters created using training sets
cbeg2 chal2 cmet2 ch,m2
κ
0.44
κ
0.66
κ
0.42
κ
0.55
Element Bond order A B A B A B A B
H 1 2.396 0.959 2.404 1.461 2.386 0.937 2.394 1.212
C 1 2.459 0.611 2.503 0.899 2.452 0.593 2.476 0.772
N 1 2.597 0.790 2.653 1.017 2.550 0.663 2.597 0.835
O 1 2.625 0.858 2.713 1.211 2.624 0.847 2.676 1.077
S 1 2.407 0.491 2.465 0.705 2.424 0.400 2.440 0.665
C 2 2.464 0.565 2.516 0.850 2.462 0.527 2.495 0.704
N 2 2.554 0.611 2.633 0.869 2.547 0.639 2.600 0.790
O 2 2.580 0.691 2.757 1.348 2.567 0.622 2.622 0.850
Cl 1 - - 2.791 2.365 - - 2.759 2.092
Br 1 - - 2.496 1.345 - - 2.494 1.315
F 1 - - 2.789 1.494 - - 3.032 2.985
I 1 - - 2.421 2.309 - - 2.454 1.387
Zn 1 - - - - 2.378 0.259 2.422 0.301
Fe 1 - - - - 2.557 0.061 2.575 0.087
For each training set of molecules in Table 1, the parameters were found. As it was described in the
Methods section, calculated parameters were validated for all training sets that contained suitable
atoms and also compared with the parameters from literature [17]. As the literature does not show the κ
value (see eq. (1)), we had to find the κ value via our methodology. The best fit for κ was found to
equal 1.25. The results of this parameter quality validation expressed by Rmol
avg
are summarized in
Table 2. This table shows that the quality of parameters varies for different training sets. Moreover, the
quality of parameters from literature is generally slightly better than the quality of our parameters.
Therefore, our effort was to further improve our methodology and parameters. The main idea of this
improvement was based on results, obtained for training sets nall and its subsets nbeg, nmid and nend and
also for training set call with subsets cbeg, cmid and cend. It is seen from Table 2 that Rmol
avg
(nall) is better
than the average value from Rmol
avg
(nbeg), Rmol
avg
(nmid) and Rmol
avg
(nend), but the best results are
obtained for the set nmid. Analogically, in the training set call, the subset cbeg provides the best
parameters. Randomly sorted molecules that create the training sets imply the good accuracy of
parameters from subsets nmid and cbeg. Therefore, the quality of parameters can be increased by
selection of an appropriate subset of the input training set. We have tested two methods of appropriate
subset selection:
1. Select only molecules, which have Rmol greater than a defined limit (for example 0.8).
Int. J. Mol. Sci. 2007, 8 579
2. Sort molecules from the training set T randomly and create a sequence of them (1, 2, ..., |T|),
where |T| is a cardinality of T. Calculate parameters for all subsets STi, where STi is obtained
from T by removing the subset DSTi. The subset DSTi is composed of elements T(i-1).K+1,
T(i-1).K+2, …, Ti.K; where K can be, for example, 100. Now create the selection in the
following way: From the input training set, sorted into the above described sequence, delete
every subset DSTi, for which Rmol
avg
(T) < Rmol
avg
(STi).
By comparison, the second approach was found to be more successful. It is interesting that sets
selected via the first method provide worse quality of parameters than the input training sets
themselves (results not shown here).
Using method 2, we have performed selections based on sets cbeg, chal, cmet and ch,m and created sets
cbeg2, chal2, cmet2 and ch,m2 (see Table 3).
Table 5: Comparison of the quality of parameters obtained using original sets and their selected
subsets.
Rmol
avg
Training set
Lit. cbeg cbeg2 chal chal2 cmet cmet2 ch,m ch,m2
T
e
s
t
e
d
s
e
t
nbeg 0.966 0.950 0.968 0.944 0.958 0.928 0.959 0.938 0.950
nmid 0.957 0.941 0.962 0.930 0.952 0.918 0.951 0.929 0.943
nend 0.960 0.956 0.970 0.932 0.953 0.929 0.956 0.942 0.949
nall 0.961 0.949 0.967 0.935 0.954 0.925 0.955 0.936 0.947
nhal - - - 0.919 0.940 - - 0.887 0.927
cbeg 0.945 0.946 0.960 0.936 0.954 0.916 0.954 0.937 0.947
cmid 0.934 0.932 0.948 0.922 0.943 0.898 0.941 0.921 0.934
cend 0.936 0.936 0.951 0.927 0.945 0.903 0.944 0.927 0.937
call 0.939 0.938 0.953 0.928 0.947 0.906 0.946 0.928 0.939
chal - - - 0.910 0.934 - - 0.885 0.921
cmet - - - - - 0.887 0.927 0.879 0.917
ch,m - - - - - - - 0.885 0.919
For more details about Rmol
avg
see Table 2. Rmol
avg
values of our parameters that are better than the literature parameters
(denoted as Lit., taken from reference [17]) are in italics. The best Rmol
avg
value (our parameters) for each tested set is
bolded.
We have chosen the CSD database as this database contains high quality experimental data. The set
cbeg was selected as it exhibits Rmol
avg
higher than cmid, cend and call. The parameters were calculated for
selected subsets cbeg2, chal2, cmet2 and ch,m2 (see Table 4). Then the parameters were validated for all
training sets containing corresponding atoms (see Table 5 and graphs in supplementary materials).
Int. J. Mol. Sci. 2007, 8 580
It is seen that the selected subsets cbeg2, chal2, cmet2 and ch,m2 provide markedly better parameters than
the input sets cbeg, chal, cmet and ch,m themselves. In all cases we have found parameters that are better
than the literature parameters.
The parameters cbeg2 are of better quality than parameters obtained from literature [17] for both used
databases. The parameters chal2, cmet2 and ch,m2 are of a worse quality than published parameters for the
NCI DIS database, but are better for the experimental database CSD. Moreover, these parameters
contain new data for halogens or Fe and Zn.
Generally, we can conclude, that it is possible to calculate parameters using both the predicted and
experimental databases. However, parameters that are based on experimental structures exhibit better
charge calculation results. It can be caused by the fact that the theoretical structures from NCI DIS
database may include some less realistic geometries compared to the experimental structures from CSD
database. These parameters are more useful as they are portable and can be used for an arbitrary
molecule that contains atoms for which the parameters were developed. Our results also show that it is
useful to work with large training sets and select the best subset that provides the highest quality
parameters. It is also reasonable to test several training sets.
We did a large validation of our parameters. For demonstration, tables with detailed results of EEM
charge calculation method with our parameters for several different organohalogene and organometal
molecules are attached in supplementary material. Also coordinates and charges on single atoms are
available there.
5. Conclusions
In this work, we have improved the published EEM parameters to calculate the STO-3G MPA
charges for C, O, N, H, S, F and Cl. The new parameters provide more accurate charges than those
published previously [17]. We have developed parameters for elements not yet parameterized,
specifically for Br, I, Fe and Zn.
The EEM parameterization we have performed has been based on 12 training sets, which are also
the largest published training sets used for the EEM parameterization ranging from 2000 to 6000
molecules. We have shown that the number of molecules in the training set is very important for the
quality of the parameters.
We have performed crossover validation of all obtained parameters using all training sets that
include relevant elements. To the best of our knowledge, we have performed the most accurate testing
of EEM parameters quality published so far.
This is the first work to compare EEM parameters calculated using two principally different training
sets, one being a database of theoretically predicted 3D structures (NCI DIS) and the second being a
database of crystallographic structures (CSD). Our results show that it is possible to use both
databases, but parameters from the CSD database training sets give more accurate charges. Moreover,
the parameters obtained from the NCI DIS database training sets are not very suitable to calculate
charges for molecules from the CSD database.
These improved and newly developed parameters can be used for charge calculation using the
program EEM SOLVER [27], which we have developed and which is freely available via the internet
on http://ncbr.chemi.muni.cz/~n19n/eem_abeem.
Int. J. Mol. Sci. 2007, 8 581
Acknowledgements
We would like to thank the Supercomputing Centre in Brno for providing us with access to its
computer facilities. This research has been supported in part by Ministry of Education of the Czech
Republic (contracts LC06030 (JK) and MSM0021622413 (RSV)). The financial support is gratefully
acknowledged.
References and Notes
1. Mortier, W.J.; Van Genechten, K.; Gasteiger, J. Electronegativity Equalization: Application and
Parametrization. J. Am. Chem. Soc. 1985, 107, 829-835.
2. Mortier, W.J.; Ghosh, S.K.; Shankar, S. Electronegativity Equalization Method for the Calculation
of Atomic Charges in Molecules. J. Am. Chem. Soc. 1986, 108, 4315-4320.
3. Van Genechten, K.A.; Mortier, W.J.; Greelings, P. Intrinsic Framework Electronegativity: A Novel
Concept in Solid State Chemistry. J. Chem. Phys. 1987, 86, 5063-5071.
4. Parr, R.G.; Yang, W. Density Functional Theory of Atoms and Molecules; Oxford University Press:
New York, 1989.
5. Bartolotti, L.J.; Flurchick, K. An Introduction to Density Functional Theory. Rev. Comp. Chem.
1996, 7, 187-216.
6. Parr, R.G.; Donnelly, R.A.; Levy, R.A.; Palke, W.E.J Electronegativity: The Density Functional
Viewpoint. Chem. Phys. 1978, 68, 3801-3807.
7. Donnelly, R.A.; Parr, R.G. Elementary Properties of an Energy Functional of the First-order
Reduced Density Matrix. J. Chem. Phys. 1978, 69, 4431-4439.
8. Sanderson, R.T. Chemical Bond and Bond Energies; Academic Press: New York, 1976.
9. Sanderson, R.T. Polar Covalence; Academic Press: New York, 1983.
10. Parr, R.G.; Pearson, R.G. Absolute Hardness: Companion Parameter to Absolute Electronegativity.
J. Am. Chem. Soc. 1983, 105, 7512-7522.
11. Grant, G.H.; Richards, W.G. Computational Chemistry; Oxford University Press: USA, 1995.
12. Bachrach, S.M. Population Analysis and Electron Densities from Quantum Mechanics. Rev. Comp.
Chem. 1994, 5, 171-227.
13. Bultinck, P.; Langenaeker, W.; Lahorte, P.; DeProft, F.; Geerlings, P.; Waroquier, M.; Tollenaere,
J.P. The Electronegativity Equalization Method I: Parametrization and Validation for Atomic
Charge Calculations. J. Phys. Chem. A 2002, 106, 7887-7894.
14. Bultinck, P.; Langenaeker, W.; Lahorte, P.; DeProft, F.; Geerlings, P.; Van Alsenoy, C.;
Tollenaere, J.P. The Electronegativity Equalization Method II: Applicability of Different Atomic
Charge Schemes. J. Phys. Chem. A 2002, 106, 7895-7901.
15. Yang, Z.-Z.; Shen, E.-Z.; Wang, L.-H. A scheme for Calculating Atomic Charge Distribution in
Large Molecules Based on Density Functional Theory and Electronegativity Equalization. J. Mol.
Struct. (Theochem) 1994, 312, 167-173.
16. Yang, Z.-Z.; Shen, E.-Z. Molecular Electornegativity in Density Functional Theory (I). Sci. China
B 1995, 38, 521-528.
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17. Yang, Z.-Z.; Shen E.-Z. Molecular Electronegativity in Density Functional Theory (II). Sci. China
B 1996, 39, 20-28.
18. Menegon, G.; Shimizu, K.; Farah, J.P.S.; Dias, L.G.; Chaimovich, H. Parameterization of the
Electronegativity Equalization Method Based on the Charge Model 1. Phys. Chem. Chem. Phys.
2002, 4, 5933-5936.
19. Zhang, Q.; Cagin, T.; van Duin, A.; Goddard III, W.A. Adhesion and Nonwetting-Wetting
Transition in the Al/ α - Al2O3 Interface. Phys. Rev. B 2004, 69, 1-11.
20. Bollmann, L.; Hillhouse, H.W.; Delgass W.N. Calibration of an Electronegativity Equalization
Method Based on Dft Results to Evaluate the Partial Charges, Global Softness, and Local Softness
of Zeolite Structures. Comp. Mol. Sci. Eng. Forum 2005, 21, 597d.
21. Milne, G.W.A.; Nicklaus, M.C.; Driscoll, J.S.; Wang, S.; Zaharevitz. D. National Cancer Institute
Drug Information System 3D Database. J. Chem. Inf. Comput. Sci. 1994, 34, 1219-1224.
22. Allen, F.H.; Kennard, O. Cambridge Structural Database. Chem. Des. Autom. News 1993, 8, 31-37.
23. Eaton, P.E., Millikan, R.; Engel, P. The CHEMX Reference Manual; Chemical Design Ltd: Oxford,
1990.
24. Dalby, A.; Nourse, J.G.; Hounshell, W.D.; Gushurst, A.K.I.; Grier, D.L.; Leland, B.A.; Laufer, J.
Description of Several Chemical Structure File Formats Used by Computer Programs Developed at
Molecular Design Limited. J. Chem. Inf. Comput. Sci. 1992, 32, 244-255.
25. Frisch, M.J.; Trucks, G.W.; Schlegel, H.B.; Scuseria, G.E.; Robb, M.A.; Cheeseman, J.R.;
Zakrzewski, V.G.; Montgomery Jr., J.A.; Stratmann, R.E.; Burant, J.C.; Dapprich, S.; Millam,
J.M.; Daniels, A.D.; Kudin, K.N.; Strain, M.C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.;
Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G.A.;
Ayala, P.Y.; Cui, Q.; Morokuma, K.; Salvador, P.; Dannenberg, J.J.; Malick, D.K.; Rabuck, A.D.;
Raghavachari, K.; Foresman, J.B.; Cioslowski, J.; Ortiz, J.V.; Baboul, A.G.; Stefanov, B.B.; Liu,
G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R.L.; Fox, D.J.; Keith, T.; AlLaham,
M.A.; Peng, C.Y.; Nanayakkara, A.; Challacombe, M.; Gill, P.M.W.; Johnson, B.; Chen,
W.; Wong, M.W.; Andres, J.L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E.S.; Pople, J.A.
Gaussian 98; Gaussian Inc.: Pittsburgh, 2001.
26. Nemhauser, G.L.; Rinnooy, A.H.G. Optimization; North-Holland: Amsterdam, 1989.
27. Svobodová Vařeková, R.; Koča, J. Optimized and Parallelized Implementation of the
Electronegativity Equalization Method and the Atom-Bond Electronegativity Equalization Method.
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© 2007 by MDPI (http://www.mdpi.org). Reproduction is permitted for noncommercial purposes.
Optimized and parallelized implementation
of the Electronegativity Equalization Method
and the Atom-Bond Electronegativity
Equalization Method
240
Software News and Update
Optimized and Parallelized Implementation of the
Electronegativity Equalization Method and the Atom-Bond
Electronegativity Equalization Method
R. SVOBODOVÁ VA ˇREKOVÁ, J. KO ˇCA
National Centre for Biomolecular Research, Faculty of Science, Masaryk University,
Kotláˇrská 2, 611 37 Brno, Czech Republic
Received 15 May 2005; Accepted 19 September 2005
DOI 10.1002/jcc.20344
Published online in Wiley InterScience (www.interscience.wiley.com).
Abstract: The most common way to calculate charge distribution in a molecule is ab initio quantum mechanics (QM).
Some faster alternatives to QM have also been developed, the so-called “equalization methods” EEM and ABEEM,
which are based on DFT. We have implemented and optimized the EEM and ABEEM methods and created the EEM
SOLVER and ABEEM SOLVER programs. It has been found that the most time-consuming part of equalization methods
is the reduction of the matrix belonging to the equation system generated by the method. Therefore, for both
methods this part was replaced by the parallel algorithm WIRS and implemented within the PVM environment. The
parallelized versions of the programs EEM SOLVER and ABEEM SOLVER showed promising results, especially on a
single computer with several processors (compact PVM). The implemented programs are available through the Web page
http://ncbr.chemi.muni.cz/∼n19n/eem_abeem.
© 2005 Wiley Periodicals, Inc. J Comput Chem 27: 396–405, 2006
Key words: charge distribution; electronegativity equalization method; atom-bond electronegativity equalization
method; optimization; parallelization; parallel virtual machine
Introduction
The most common approach for calculation of charge distribution
in a molecule is quantum mechanics (especially ab initio methods).
A disadvantage of quantum mechanics methods is that they are very
time-consuming. Their time complexity is O(B4
), where B is greater
or equal to the number of valence electrons in the molecule.
Therefore,theElectronegativityEqualizationMethod(EEM),1–3
an alternative method of charge calculation, has been developed.
This method is based on density functional theory (DFT).4,5
First,
Parr et al.6,7
applied DFT and formulated a new deﬁnition and
explanation of electronegativity. Later on, Mortier et al.8–10
applied
Parr’s deﬁnition of electronegativity and Sanderson’s Electronegativity
Equalization Principle (EEP) and created the EEM.1–3
This
method is able to calculate atomic charges markedly faster than
ab initio approaches, as the EEM has a time complexity of θ(N3
),
where N is the number of atoms in the molecule.3
The accuracy of
the EEM corresponds to the ab initio method for which the EEM
was parametrized. The most common parametrization of the EEM
is a parametrization for the SCF-HF method with the STO-3G basis
set, where the charges are calculated by Mulliken population anal-
ysis.11,12
Principally, it is also possible to parametrize the EEM for
other basis sets (i.e., 6-31G*) and methods for charge calculation
(i.e., CHELPG, MK, NPA, ESP, Hirshfeld method).13,14
The EEM
was mostly used to calculate charges on relatively small molecules
(composed of less than a hundred atoms),15,16
although applications
on larger systems, for example, biopolymers, are also known.17
This
method was also applied within another context (e.g., calculation of
Fukui function18
and energy,19
reactivity studies,20,21
applications
within molecular simulations,22–26
etc.).
Several improvements of the method have been published
(e.g.,27–30
). The best known extension of the EEM is the Atom-Bond
Electronegativity Equalization Method (ABEEM),19,28,31
which
also considers charges localized on bonds. This method is more
time-consuming than the EEM as it has a time complexity of
θ((N + M)3
), where N is a number of atoms and M a number
of bonds.31
However the ABEEM provides a more exact model of
charge distribution than the EEM, which is the reason why it is more
frequently used for larger molecules.28
Similar to EEM, ABEEM
also has several times been used in molecular simulations.32–36
Correspondence to: J. Koˇca; e-mail: jkoca@chemi.muni.cz
Contract/grant sponsor: Ministry of Education of the Czech Republic;
contract/grant number: MSM0021622413
© 2005 Wiley Periodicals, Inc.
Software News and Update 397
Today, two serial implementations of EEM are publicly available,
GULP37
(free of charge for academic users) and Vcharge38
(commercial software). To the best of our knowledge, there is no
implementation of ABEEM publicly available.
The effectiveness of equalization methods enables their application
to calculations of conformationaly dependent charges in
molecular mechanics or, eventually, even in molecular dynamics
simulations.22–25
This article is focused on an implementation,
optimization, and parallelization of the methods using the Parallel
Virtual Machine (PVM).39,40
Theoretical Basis
EEM
Using DFT, the effective (charge-dependent) electronegativity of
the atom i in a molecule can be calculated by eq. (1):1–3
χi = Ai + Bi · qi + κ
N
j=1( j=i)
qj
Ri, j
(1)
where N is the number of atoms in the molecule, qi and qj are
the charges distributed on the atoms i and j, respectively, Ri, j
is the distance between atoms i and j, and κ is the adjustive factor.
The coefﬁcients Ai and Bi are deﬁned by eq. (2):
Ai = χ∗
i = χ0
i + χi Bi = 2η∗
i = 2 η0
i + ηi (2)
where χ0
i is the electronegativity of an isolated neutral atom i, η0
i is
the hardness, and χi and ηi describe the molecular environment.
The coefﬁcients Ai, Bi and κ [used further in an equation system (5)]
are calculated using a calibration.1,15
According to Sanderson’s Electronegativity Equalization Princi-
ple,8–10
the effective electronegativity of each atom in the molecule
is equal to the molecular electronegativity χ:
χ1 = χ2 = · · · = χN = χ. (3)
The total charge Q of the molecule is equal to the sum of all the
atomic charges:
N
i=1
qi = Q. (4)
The atomic charges are described using the equation system (5),
which contains N+1 equations with N+1 unknowns: q1, q2, . . . , qN
and χ. This system was derived from equations (1), (3), and (4):1









B1
κ
R1,2
· · · κ
R1, N
−1
κ
R2,1
B2 · · · κ
R2, N
−1
...
...
...
...
...
κ
RN,1
κ
RN,2
· · · BN −1
1 1 · · · 1 0









·








q1
q2
...
qN
χ








=








−A1
−A2
...
−AN
Q








. (5)
The matrix of the equation system (5) is called an EEM matrix.
ABEEM
The ABEEM method19,28,31
is similar to the EEM method with
an extension on bonds. In other words, the charges are located not
only on the atoms but also on the bonds. The charge of a bond is
situated in the bond center, which is chosen by a suitable apportionment
of the bond’s length.28
The ABEEM method uses adapted
charges on atoms (Qi) and bonds (QI ), which can be calculated using
eq. (6):
qi = Qi +
M
I=1 (i∈ I)
1
2
· QI (6)
where qi is the charge of the atom i, atoms are denoted by i, j, . . . and
bonds by I, J, . . . . The notation i ∈ I means that the atom i is one
of the bound atoms on the bond I, analogically i ∈ I [see eqs. (7)
and (8)].
As formulated by Yang et al.,28
the effective electronegativities
of the atom i(χi) and the bond I(χI ) can be described by eqs. (7)
and (8):
χi = Ai + Bi · Qi + Ci
M
I=1 (i∈ I)
QI
+ κ


N
j=1 ( j=i)
Qj
Ri, j
+
M
J=1 (i∈ J)
QJ
Ri, J

 (7)
χI = AI + BI · QI +
N
i=1 (i∈ I)
CI,i · Qi
+ κ


M
J=1 (J=I)
QJ
RI, J
+
N
j=1 ( j∈ I)
Qj
Rj, I

 (8)
where N is the number of atoms and M the number of bonds
in the molecule; Qi and Qj are, respectively, charges on atoms
i and j; QI and QJ are, respectively, charges on bonds I and J;
Ri, j, Ri, J , Rj, I , RI, J are distances between appropriate atoms
or bonds; Ai and Bi are the same as in the EEM; AI and
BI are deﬁned by the equations: AI = χ∗
I and BI = 2η∗
I [see
eq. (2)], and Ci, CI,i, and κ are parameters calculated during the
calibration.31
For the ABEEM method, Sanderson’s electronegativity equalization
principle is formulated by eq. (9):
χ1 = χ2 = · · · = χN = χ(1) = χ(2) = · · · = χ(M) = χ (9)
where (1), . . . , (M) are indexes of bonds.
The total charge of a molecule Q is equal to the sum of
the charges on all the atoms and all the bonds in the molecule
[eq. (10)]:
N
i=1
Qi +
M
I=1
QI = Q. (10)
398 Svobodová Vaˇreková and Koˇca • Vol. 27, No. 3 • Journal of Computational Chemistry
Table 1. Molecules Used for EEM SOLVER and ABEEM SOLVER Program Testing.
Number Number Number Number
Molecule of atoms of bonds Molecule of atoms of bonds
Formaldehyde 4 3 Cyclopentane 15 15
Methane 5 4 Cyclohexane 18 18
Ethene 6 5 Alanine dipeptide 23 22
Ethanol 9 8 Gly-Ala-Gly (folded) 27 25
Maleinic anhydrid 9 9 Gly-Ala-Gly (linear) 27 25
cis-2-Butene 12 11 cis-Retinal 49 47
trans-2-Butene 12 11 Tyr-Gly-Phe-Met 68 62
The ABEEM method calculates the charges of atoms and
bonds using the equation system (11), which was derived from
eqs. (7)–(10):
















B1 · · · κ
R1, N
E1,(1) · · · E1,(M) −1
.
.
.
...
.
.
.
.
.
.
...
.
.
.
.
.
.
κ
RN,1
· · · BN EN,(1) · · · EN,(M) −1
E(1),1 · · · E(1),N B(1) · · · κ
R(1),(M)
−1
..
.
...
..
.
..
.
...
..
.
..
.
E(M),1 · · · E(M),N
κ
R(M),(1)
· · · B(M) −1
1 · · · 1 1 · · · 1 0
















·














Q1
..
.
QN
Q(1)
..
.
Q(M)
χ














=














−A1
..
.
−AN
−A(1)
..
.
−A(M)
Q














.
(11)
This equation system contains N + M + 1 unknowns (q1,
q2, . . . , qN ; q(1), q(2), . . . , q(M); χ) and N + M + 1 equations. The
termsEi,I aredeﬁnedasfollows:ifi ∈ I thenEi,I = Ci andEI,i = CI,i,
else EI,i = Ei,I = κ/(Ri,I ). In most cases, Ci−j,i is equal to Ci−j, j
and both are denoted by Ci−j. Only the bonds C—H, N—H, and
O—H are exceptions within all sets of molecules for which the
parametrization was performed,28–31
because CX—H, H are not equal
to CX—H, X . For these bonds, the terms CX—H, H and CX—H, X are
labeled by CX—H and DX—H , respectively.
Implementation
The EEM and ABEEM methods were implemented using the
following algorithm:
1. Calculate distances between atoms and (in ABEEM) between
atoms and bonds and between bonds
2. Create the EEM or ABEEM matrix
3. Solve the equation system described by the EEM or ABEEM
matrix
4. Distribute bond charges to bound atoms using eq. (6) (only for
ABEEM method)
The above algorithms were implemented in C language and
the EEM SOLVER and ABEEM SOLVER programs were written.
Both programs use two input ﬁles: a PDB ﬁle with topology
and coordinates, and a ﬁle with parameters.
Testing the Programs
The parameters used for testing the EEM and ABEEM method
were taken from refs. 2 and 31. Charges were calculated for
14 molecules (see Table 1), each in energy minimum conﬁguration.
The molecules belonged to different classes and were of different
sizes.
The results obtained by EEM SOLVER and ABEEM SOLVER
were compared with atomic charges calculated by the software
package Gaussian41
using the ab initio HF method with a STO-3G
basis set. The comparison is visualized by a linear regression line
and the quality of the correlation between ab initio and EEM or
ABEEM charges is described by the R-squared value42
of this
line. The results are collected in Table 2. They correspond well
with published data conﬁrming that the methods were implemented
correctly.
Figure 1 shows a comparison for an alanine dipeptide. This
molecule was selected because it is often used as a reference system
for the demonstration of equalization methods (e.g., refs. 2
and 17).
Table 2. Comparison of Ab Initio and EEM or ABEEM Charges Using R-Squared Values.
R-squared value R-squared value
Molecule EEM ABEEM Molecule EEM ABEEM
Formaldehyde 0,9932 0,9961 Cyclopentane 0,9913 0,9947
Methane 1,0000 1,0000 Cyclohexane 0,9878 0,9918
Ethene 1,0000 1,0000 Alanine dipeptide 0,9819 0,9840
Ethanol 0,9890 0,9939 Gly-Ala-Gly (folded) 0,9722 0,9804
Maleinic anhydrid 0,9931 0,9946 Gly-Ala-Gly (linear) 0,9779 0,9836
cis-2-Butene 0,9948 0,9972 cis-Retinal 0,9639 0,9736
trans-2-Butene 0,9955 0,9974 Tyr-Gly-Phe-Met 0,9701 0,9753
Software News and Update 399
Figure 1. Comparison of the EEM and ABEEM with ab initio charges for alanine dipeptide. Each point
in the graph represents a single atom.
Using EEM and ABEEM for Charge Calculation on
Several Conformations of the Same Molecule
Before using the EEM or ABEEM methods in molecular mechanics
calculations or molecular dynamics simulations, it is necessary
to verify whether these methods are adequately accurate and can
express differences between the charges of corresponding atoms
in two different conformers of one molecule. Two conformations
of each of three molecules were used to verify whether the EEM
and ABEEM methods are sufﬁciently geometry sensitive: cis-2butene
and trans-2-butene, cis-retinal and trans-retinal, folded and
linear Gly-Ala-Gly (Fig. 2). Ab initio (STO-3G), EEM, and ABEEM
charges were calculated for both conformers of each molecule.
Then, it was determined how large (or better to say, small) the
charge differences are that the EEM and ABEEM methods can
detect.
For illustration, the results for two conformers of Gly-Ala-Gly
are shown (Table 3, Fig. 3). It is seen that both the EEM and ABEEM
methods are sensitive enough to detect even very small charge differences.
It is also seen that charge differences between corresponding
atoms in different conformers are relatively signiﬁcant even if the
tripeptide Gly-Ala-Gly is not a particularly polar molecule.
Figure 2. Atom numbering for Gly-Ala-Gly.
Optimization
The programs EEM SOLVER and ABEEM SOLVER can be divided
into several parts (modules) described in Table 4.
As we expect to use the programs several (many) times on
the same topology ﬁle but with different geometries, it would not
be helpful to repeatedly read the topology of the molecule and the
parameters for the EEM or the ABEEM in each calculation. A more
effective solution is to use a partial evaluation. First, therefore, a
header ﬁle for the input molecule is created. This ﬁle contains the
topology of the molecule and the parameters for the EEM or the
ABEEM. Then, only the coordinates of atoms in the calculated
system are read in from the input. Moreover, we may predeﬁne a
maximum number of atoms (and bonds) during compilation of the
programs. In this way we can replace dynamically allocated ﬁelds
Table 3. STO-3G, EEM, and ABEEM Atom Charges in Folded and Linear
Conformations of Gly-Ala-Gly.
Linear conformer Folded conformer
Atom STO-3G EEM ABEEM STO-3G EEM ABEEM
H13 0.23 0.22 0.22 0.21 0.21 0.20
H18 0.05 0.06 0.06 0.07 0.09 0.08
C21 0.32 0.29 0.33 0.30 0.28 0.30
H7 0.06 0.07 0.07 0.09 0.08 0.09
H23 0.17 0.19 0.15 0.19 0.22 0.19
H8 0.05 0.07 0.05 0.09 0.08 0.08
O12 −0.30 −0.24 −0.29 −0.25 −0.22 −0.25
O4 −0.31 −0.24 −0.28 −0.26 −0.21 −0.24
C11 0.30 0.30 0.30 0.23 0.26 0.21
C3 0.30 0.32 0.30 0.22 0.23 0.24
Only atoms with a charge difference of greater or equal to 0.02 are shown.
400 Svobodová Vaˇreková and Koˇca • Vol. 27, No. 3 • Journal of Computational Chemistry
Figure 3. The absolute values of differences between ab initio (STO-
3G) charges of corresponding atoms in folded and linear Gly-Ala-Gly
peptide.
with static ones. This enables the compiler to perform a markedly
better level of optimization. In both programs, we have also applied
more common optimizations,43
like the moving of redundant variables
and data structures (e.g., ﬁelds of distances) into a proper part
of the code, simpliﬁcation of the code in cycles (i.e., the substitution
of functions by its bodies, the optimization of dependencies between
variables), etc. Some commonly used algorithms were substituted
by more effective methods. For example, Gaussian elimination was
replaced by the Cholesky method in EEM SOLVER (this substitution
was possible only in EEM SOLVER, because the EEM matrix
is symmetrical and the Cholesky method can only be used for this
type of matrix).
The original and optimized versions of the programs EEM
SOLVER and ABEEM SOLVER were executed on ﬁve different
computers (see Table 5) and tested on 10 molecules of sizes of
between 23 and 252 atoms for EEM SOLVER and between 23 and
1608 atoms for ABEEM SOLVER, respectively.
Besides the molecules shown in Table 1, we have also tested the
programs by calculating charges on fragments of cyclin dependent
kinase 2 (CDK2), a protein composed of 283 aminoacids with 4942
atoms, to obtain an idea of how the programs behave when charge
calculations on larger systems are required. The CDK2 fragments
were created in such a way that they always included the N-terminal
part of the protein and were terminally blocked by the OH group
Table 4. Basic Modules of the EEM SOLVER and ABEEM
SOLVER Programs.
Denotation Description Complexitya
Read Reading parameters and information about
a molecule. θ(P2)
Prep Preparation of the EEM or ABEEM matrix. θ(P2)
Calc Solving equation system, described using
the EEM or ABEEM matrix.b θ(P3)
aTime complexity expressed for the worst case (P = N and P = N + M
for EEM and ABEEM method, respectively). Here, N and M stands for the
number of atoms and number of bonds, respectively.
bBond charges are also distributed over bound atoms using eq. (6)-only for
the ABEEM method.
Table 5. Computers Used for EEM SOLVER and ABEEM SOLVER
Optimization.
(a) Computers with a single processor
Operating
Denotation Hardware system
Intel-PIII-700 Dual Pentium III, 700 MHz Linux
Intel-PIII-1000-a Dual Pentium III, 1 GHz Linux
Intel-PIII-1000-b Dual Pentium III, 1 GHz Linux
(b) Multiprocessor computers
Operating Number of
Denotation Hardware system processors
SGI-P12 MIPS R10000, 200 MHz IRIX 6.4 12
SGI-P40 MIPS R10000, 196 MHz IRIX 6.4 40
on the other terminal. The initial geometry was taken as an equilibrated
structure from our MD simulations reported elsewhere.44
The total running time and the periods spent in the Read, Prep, and
Calc modules were measured. The results calculated on SGI-P12
are shown in Table 6. Very similar data was also obtained for other
computers included in the testing.
The data in Table 6(a) clearly shows that the optimized version
of the EEM SOLVER is much more effective compared to the
original one. For small molecules (less than 50 atoms) the optimized
version was about three to ﬁve times faster while for larger
molecules (more than 150 atoms) it was about 20 times faster. The
mostremarkablespeedincreasewasobservedintheCalcpart,where
the Gaussian elimination procedure was replaced by the Cholesky
method. The optimization also brings a reduction of time for the
ABEEM SOLVER (see Table 6), but the increase in speed was not
as remarkable as it was for the EEM SOLVER. The main reason is
that it was not possible to replace the Gaussian elimination method
in this case. For all studied molecules, the optimized version is about
four to eight times faster than the original one.
Parallelization
We have written parallel versions for both EEM SOLVER and
ABEEM SOLVER.
As mentioned above, the most time consuming part of EEM and
ABEEM SOLVER is the Calc module. It is clear that its high time
complexity is caused by the ﬁrst step of the Gaussian elimination,
which is converting the EEM (or ABEEM) matrix to upper triangular
form (reduction of a matrix). The algorithm WIRS (Wrapped
Interleaved Row Storage)45
was used to parallelize this step. WIRS
works with one master process and allows for an arbitrary number
of slave processes. The input of the algorithm is a matrix with K
rows and K columns (K = N + 1 for EEM and K = N + M + 1
for ABEEM, where N is the number of atoms and M the number of
bonds in the molecule). The algorithm works as follows. The master
process executes all slave processes. The lines of the input matrix
are equally distributed between processes. Each process performs
reduction on the lines assigned to it. During this calculation, data
Software News and Update 401
Table 6. Comparison of Running Times for Selected Molecules on Computer SGI-P12.
(a) EEM SOLVER
Not optimized After optimization
Number Read Prep Calc Total Read Prep Calc Total
of atoms (ms) (ms) (ms) (ms) (ms) (ms) (ms) (ms)
23 1.20 0.38 0.74 2.32 0.69 0.06 0.18 0.92
68 3.42 3.62 17.98 25.02 1.88 0.69 1.52 4.09
162 8.10 20.12 215.95 244.17 3.92 2.57 13.82 20.31
252 17.65 54.81 855.61 928.07 7.75 6.72 40.19 54.65
(b) ABEEM SOLVER
Not optimized After optimization
Number Read Prep Calc Total Read Prep Calc Total
of atoms (ms) (ms) (ms) (ms) (ms) (ms) (ms) (ms)
23 1.56 1.03 4.62 7.21 0.74 0.20 0.72 1.65
162 11.14 72.03 1615.53 1692.70 5.12 19.26 179.72 204.10
536 30.08 962.46 73447.47 74440.00 14.30 302.99 19922.71 20240.00
1608 69.25 9092.24 1998878.51 2008040.00 30.53 4060.65 460288.82 464380.00
sent from other processes is also used. A detailed description of the
algorithm is as follows.
The master process:
Executes slave processes on all remaining computers (processors)
in the PVM.
Sends selected lines of the input matrix to a slave process,
which will own them and elaborate them.*
Sends the ﬁrst line of the matrix to all slave processes.
Executes CALCULATION.
Each slave process:
Receives selected lines of the input matrix.
Executes CALCULATION.
CALCULATION:
FOR (i = 1, 2, . . . , K) {
IF (i == 1) {
IF (the process is a slave process) {
The process receives the line i.
}
}
ELSE IF (the process did not send a line in i − 1 step) {
The process receives the line i.
}
FOR (all lines, owned by the process) {
IF (k > i, where k is the index of the line) {
Recalculates line k (using line i) according to
these equations:
l = aki/aii
akj = akj − l.aij ( j = i, i + 1, . . . , K)
where auv is the element on row u and
column v of the matrix
}
}
IF (the process owns line i + 1) {
The process sends this line to other processes
}
}
∗ The process j owns each kth line of the input matrix, for which
(k − 1) mod p = j, where p is the number of processes. The
master process has the number j = 0 and slave processes are
numbered 1, 2, . . . , p.
It is clear from the above description that WIRS is a ﬁnegrained
algorithm. This means that the task (matrix reduction)
is divided into many very simple subtasks (recalculation of single
lines) during parallelization. All effective parallel algorithms
for matrix reduction are ﬁne-grained as the largest part of the
matrix that can be used in a parallel algorithm as an independent
unit is a single line. Fine-grained algorithms are very sensitive
to slow computers in the PVM cluster as they contain a number
of synchronization points where all processes must wait for the
slowest one.
The WIRS algorithm was implemented in PVM39,40
(Parallel
Virtual Machine). We have chosen this platform because of its
robustness, efﬁciency, portability, and ability to connect a heterogeneous
collection of Unix and/or Windows computers.
The parallel version of the program ABEEM SOLVER was
tested on three types of PVM: compact, homogeneous, and heterogeneous.
The parallel version of EEM SOLVER was tested only
on a compact PVM as it requires very high communication speed
to be effective. A compact PVM consists of only one computer,
usually designed as a cluster of processors. A homogeneous PVM
includes several computers with the same architecture and software.
A heterogeneous PVM is composed of computers with different
architecture and software.
402 Svobodová Vaˇreková and Koˇca • Vol. 27, No. 3 • Journal of Computational Chemistry
Table 7. The EEM SOLVER (a) and ABEEM SOLVER (b) Computational Times as Obtained for Different Sizes
of Calculated Molecules and Different Number of Processors (on the SGI-P40 Machine).
(a) EEM SOLVER
Number of atoms in CDK2 fragments
334 433 534 693 1005 1305 1608 1911 2503 3002
Serial t(s) 0.35 0.70 1.25 2.57 8.19 21.30 48.24 84.67 195.88 355.24
Parallel pef 2 2 2 4 4 5 4 7 6 6
t(pef ) (s) 0.47 0.86 1.55 1.99 4.97 10.02 16.69 28.96 53.25 90.74
(b) ABEEM SOLVER
Number of atoms in CDK2 fragments
253 306 334 433 534 601 693 1005 1305 1608
Serial t(s) 1.42 2.57 3.27 7.04 13.50 21.46 37.49 130.48 300.41 580.3
Parallel pid — — — — — 2 4 8 9 12
t(pid) (s) — — — — — 10.53 9.30 16.80 31.61 53.59
pef 4 4 5 6 6 7 8 9 11 12
t(pef ) (s) 0.85 1.23 1.48 2.38 4.10 5.21 6.79 16.22 29.62 53.59
The value of pid is deﬁned as the greatest number of processors for which the scaling is still close to ideal (deviation is
lower than 1%). The pef is deﬁned as a borderline after which adding one more processor increases the absolute time of
calculation.
Compact PVM
For testing, we used fragments of CDK2 with the following numbers
of atoms: 253, 306, 334, 433, 534, 601, 693, 1005, 1305, 1608, 1911,
2503, and 3002. The fragments were created as described above. All
processes were executed subsequently on SGI-P12 and SGI-P40
multiprocessor computers. On each of these two machines, both
programs were executed gradually with each number of processes
until all processors on the computer were used. A relation between
the number of processes, p, which are used by the parallel program,
and the running time of the program, t( p), is in the case of ideal
scaling described by eq. (12).
t( p) = t(1)/p (12)
where t(1) is the running time on a single processor.
The results for the SGI-P40 computer are collected in Table 7
and Figure 4. The results on the SGI-P12 computer exhibit the same
trends.
The distribution of scaling as seen in Table 7 can be explained
in the following way. The serial versions of both programs exhibit
a time complexity of θ(K3
), where K is the size of the matrix,
and it performs only calculations. The parallel programs perform
two types of tasks: calculations and communication. For matrix
reduction, the time complexity of calculation is θ(K3
/p) and the
time complexity of communication is θ(K2
· p), see ref. 45. When
the number of processes is small ( p ≤ pid) and the molecule is
sufﬁciently large, the time spent on communication is negligible
compared to calculation time and the scaling of the parallel version
is close to ideal. An increasing number of processes causes the
calculation time per process to be shorter, but, on the other hand,
the program spends more time in communication. If the number of
processes is greater than pef , the increase in communication time
is larger than the calculation time saving and, therefore, the overall
efﬁciency decreases. It causes a pathological situation when the
absolute time of calculation increases even if more processors are
used. The exact explanation is that even if each process is doing less
calculations (linear descend), it must do too many communication
tasks (quadratic growth), that the total running time is longer than
it was before adding the process.
As we assumed, the scaling of the program EEM SOLVER is
not as good as for ABEEM SOLVER. However, for large systems
also parallel version of EEM SOLVER becomes efﬁcient.
Homogeneous PVM
A homogeneous PVM implementation of the program ABEEM
SOLVER was tested on CDK2 fragments with the following number
of atoms: 334, 433, 534, 601, and 693. Processes were executed
on clusters of computers, as described in Table 8.
The program ABEEM SOLVER was executed gradually with
the following number of processes: 1, 2, 3, . . . , PC; where PC is the
number of computers in the cluster. Each process was executed on a
different computer. The running time was measured for each number
of processes.
The results obtained on the Intel-PIII-700-GE cluster are collected
in Table 9 and Figure 5. It is seen that the parallel version of
the program ABEEM SOLVER is signiﬁcantly less effective for a
homogeneous PVM than for a compact PVM. The reason is that the
speed of communication is substantially higher for a compact PVM
than for a homogeneous PVM. The results also demonstrate similar
trends for the remaining clusters used for testing (not shown here).
It is seen that using the parallel version in a homogeneous PVM
is not effective for small molecules while it is more successful for
larger molecules. But also in this case we need to use a relatively
Software News and Update 403
Figure 4. The EEM SOLVER (a) and ABEEM SOLVER (b) scaling
on the SGI-P40 machine (see Table 5). The relative time was calculated
as ap/a1, where ap and a1 is the absolute time for p processes and for 1
process, respectively. Adding more processes than 25 did not bring any
improvement in scaling.
large number of processes to obtain a considerable decrease in running
time. For example, the running time is only twice as short for
10 processes and a molecule with 601 atoms. Unfortunately, we
were not able to run the parallel version on a substantially larger
system (>1000 atoms) as we did not have a reasonable network
infrastructure available. However, trends for larger molecules are
visible from our tests. We can summarize that using the parallel version
of the program in a homogeneous PVM can only be efﬁcient
for large molecules and with a fast network connection.
Table 9. The ABEEM SOLVER Computational Time as Obtained for
Different Sizes of Calculated Molecules and Different Numbers of
Processes (on the Intel-PIII-700-GE Cluster).
Number of atoms in CDK2 fragments
334 433 534 601 693
Serial t (s) 4.09 8.77 14.71 20.14 30.22
Parallel t(5) (s) 18.98 24.53 30.38 34.20 25.80
t(10) (s) 8.26 10.87 10.74 11.32 21.27
t(15) (s) 14.23 16.89 14.06 14.21 13.67
In the case of homogeneous PVMs the parameters pid and pef (see Table 7)
have no meaning as running time is very distant from the ideal scaling. Also,
the oscillation of curves makes pef deﬁnition impossible.
Heterogeneous PVM
We used the same testing molecules as for the homogeneous PVM,
and the program ABEEM SOLVER was also executed in the same
way. Processes were run on Intel-PIII-700-GE and Intel-PIII-1000b-FE
clusters (see Table 8) and also on the SGI-P12 computer (see
Table 5). We created three heterogeneous PVM’s: Intel-PIII-1000b-FE
and Intel-PIII-700-GE, SGI-P12 and Intel-PIII-700-GE, SGIP12
and Intel-PIII-1000-b-FE. For the ﬁrst one, the running time
Figure 5. The ABEEM SOLVER scaling on a homogeneous PVM (an
Intel-PIII-700-GE cluster, for cluster abbreviation see Table 7).
Table 8. Clusters of Computers, Used to Build Up a Homogeneous PVM.
Network connection
Number of
Denotation Computers Name Transfer speed computers
Intel-PIII-1000-b-FE Intel-PIII-1000-b Fast Ethernet 100 Mb/s 16
Intel-PIII-700-GE Intel-PIII-700 Giga Ethernet 1 Gb/s 16
Intel-PIII-1000-a-FE Intel-PIII-1000-a Fast Ethernet 100 Mb/s 16
Intel-PIII-1000-a-MN Intel-PIII-1000-a Myrinet 1.2 Gb/s 16
All computers in each cluster are identical, details are described in Table 5.
404 Svobodová Vaˇreková and Koˇca • Vol. 27, No. 3 • Journal of Computational Chemistry
Figure 6. The ABEEM SOLVER scaling on a heterogeneous PVM
(Intel-PIII-700-GE and Intel-PIII-1000-b-FE clusters, for cluster abbreviation
see Table 7). The serial version was executed on the Intel-PIII-
1000-b-FE. The calculation was organized in such a way that the ﬁrst
process was executed on the Intel-PIII-1000-b-FE cluster, the second on
the Intel-PIII-700-GE, the third on the Intel-PIII-1000-b-FE, the fourth
on the Intel-PIII-700-GE etc.
is shown in Figure 6 and Table 10. It is seen that the running time
is limited by the slowest connection between two computers in a
heterogeneous PVM.
Other heterogeneous PVM’s tested demonstrate similar trends.
Therefore, it is even more remarkable than in the previous case
that running the parallel version on a heterogeneous PVM only has
meaning for large systems.
Conclusion
The most common method of calculating partial atomic charges
is quantum mechanics, which may, in many cases, be very
time consuming. Electronegativity equalization methods, developed
recently, are alternative approaches. These relatively fast (time complexity
is of class θ(N3
) for molecule with N atoms) methods are
Table 10. Comparison of Running Times for Serial and Parallel Versions of
the Program ABEEM SOLVER in the Intel-PIII-1000-b-FE and
Intel-PIII-700-GE Clusters.
Numbers of atoms in CDK2 fragments
334 433 534 601 693
Serial t (s) 4.04 8.73 16.45 23.41 36.00
Parallel t(8) (s) 25.34 17.50 27.02 31.34 25.71
t(16) (s) 10.38 17.59 20.77 23.17 26.82
t(26) (s) 10.64 15.20 16.85 18.85 22.58
The serial version was executed on the Intel-PIII-1000-b-FE. The calculation
was organized in such a way that the ﬁrst process was executed on the
Intel-PIII-1000-b-FE, the second on the Intel-PIII-700-GE, the third on the
Intel-PIII-1000-b-FE, the fourth on the Intel-PIII-700-GE etc.
based on DFT and their accuracy corresponds to ab initio quantum
mechanical approaches. The goal of this work was to implement
two electronegativity equalization methods, EEM and ABEEM. The
EEM is a simple and very fast method, and it is mostly used for relatively
small molecules. The ABEEM method is more general as it
also includes the inﬂuence of bonds.
The above methods were implemented and the programs EEM
SOLVER and ABEEM SOLVER were written and optimized. The
optimized version of the program EEM SOLVER was found to
be three to ﬁve times faster compared to the original one for
small molecules (less than 50 atoms) and about 20 times faster
for larger molecules (more than 150 atoms). After optimization, the
program EEM SOLVER calculates atomic charges for a molecule
with 23 atoms in 0.92 ms and for a molecule with 252 atoms in
54.65 ms on SGI-P12. The optimized version of ABEEM SOLVER
was about four to eight times faster compared to the original one
and calculates atomic charges for a molecule with 23 atoms in
1.65 ms and for a molecule with 536 atoms in 20.24 s on the same
processor.
We have found out that the programs spent the majority of time
performing reductions of the EEM or ABEEM matrix. This task has
a time complexity of θ(N3
) while the remaining modules of the programs
exhibit a time complexity of no more than θ(N2
). We have,
therefore, implemented the algorithm WIRS (Wrapped Interleaved
Rows Storage), which can sufﬁciently parallelize matrix reduction
and used this algorithm for the reduction of EEM and ABEEM
matrixes. This parallel algorithm was implemented on a PVM (Parallel
Virtual Machine) and tested on a compact PVM, homogenous
PVM and heterogeneous PVM. Parallelization has shown promising
results for the compact PVM. For example, ABEEM charge calculation
for a molecule with 1608 atoms took 53.59 s on 12 processors of
SGI-P40 with a scaling of 11. The scaling of EEM SOLVER was not
as good as for ABEEM SOLVER. However, for large systems also
parallel version of EEM SOLVER becomes efﬁcient. It has also been
shown that the scaling of the parallel program ABEEM SOLVER is
much worse in both homogenous and heterogeneous PVMs. In this
case, it should only be used to calculate charges on large systems
exceeding 1000 atoms. The above observations are not surprising,
because the problem leads to an algorithm that belongs to ﬁne-grain
parallelism, which requires a high level of communication between
processes.
Availability
TheprogramsareavailablethroughtheWebpage:http://ncbr.chemi.
muni.cz/∼n19n/eem_abeem
Acknowledgments
One of the authors (J.K.) would like to thank Prof. Chan-Guo Zhan
(Division of Pharmaceutical Sciences, University of Kentucky, Lexington,
KY) for many fruitful discussions about the role of charges
in molecular mechanics and quantum chemistry. We would like to
thank the Supercomputing Centre in Brno for providing us with
access to its computer facilities. Our thanks are also addressed to
R. Turland (UK) for language corrections.
Software News and Update 405
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