Review
You are lost without a map: Navigating the sea of protein structures
Audrey L. Lamb a,
⁎, T. Joseph Kappock b
, Nicholas R. Silvaggi c,
⁎⁎
a
Department of Molecular Biosciences, University of Kansas, Lawrence, KS 66045, United States
b
Department of Biochemistry, Purdue University, West Lafayette, IN 47907, United States
c
Department of Chemistry and Biochemistry, University of Wisconsin—Milwaukee, Milwaukee, WI 53211, United States
a b s t r a c ta r t i c l e i n f o
Article history:
Received 8 December 2014
Accepted 22 December 2014
Available online 29 December 2014
Keywords:
Protein structure
X-ray crystallography
Molecular models
Electron density maps
Atomic coordinate ﬁles
Atomic displacement parameters
X-ray crystal structures propel biochemistry research like no other experimental method, since they answer
many questions directly and inspire new hypotheses. Unfortunately, many users of crystallographic models mistake
them for actual experimental data. Crystallographic models are interpretations, several steps removed from
the experimental measurements, making it difﬁcult for nonspecialists to assess the quality of the underlying data.
Crystallographers mainly rely on “global” measures of data and model quality to build models. Robust validation
procedures based on global measures now largely ensure that structures in the Protein Data Bank (PDB) are
largely correct. However, global measures do not allow users of crystallographic models to judge the reliability
of “local” features in a region of interest. Reﬁnement of a model to ﬁt into an electron density map requires interpretation
of the data to produce a single “best” overall model. This process requires inclusion of most probable
conformations in areas of poor density. Users who misunderstand this can be misled, especially in regions of
the structure that are mobile, including active sites, surface residues, and especially ligands. This article aims to
equip users of macromolecular models with tools to critically assess local model quality. Structure users should
always check the agreement of the electron density map and the derived model in all areas of interest, even if
the global statistics are good. We provide illustrated examples of interpreted electron density as a guide for
those unaccustomed to viewing electron density.
© 2014 Elsevier B.V. All rights reserved.
1. Introduction
Advances in crystallization, data collection, and computers have
made macromolecular crystal structures commonplace. Biochemists,
medicinal chemists, chemical biologists and many others have come
to rely on macromolecular structural data as never before, and it has
become routine to read, write, and review manuscripts that contain
crystal structures. Furthermore, advances in the ﬁeld have made it
possible for scientists with limited training in crystallography to determine
protein structures. Thus, even scientists with no formal background
in crystallography need to know how to critically evaluate
these complex experiments. While it has been noted recently that
poorly determined structures have a negative impact on the drug design
community [2], the focus here is on how to avoid the improper use of
well-determined structural models. The ﬁrst step is to understand
how crystallographic models are made.
Every atom in the repeating unit of a crystal (the unit cell) contributes
to the intensity of every reﬂection in the diffraction pattern. The
measured intensity for each diffraction spot is the result of scattering
from the entire model. Particular data points cannot be associated with
speciﬁc parts of a model. For example, there is no “metal spot” in data
collected from a metalloprotein crystal; the metal contributes to the
intensity of every reﬂection (see Box A for a description of the crystallographic
experiment). While crystallographic statistics reported in structure
papers provide numerical indications of the overall quality of the
diffraction data (for an excellent review, see [3]), these do not report
on how well-determined individual parts of a model are. The Protein
Data Bank (PDB)1
has recently adopted a new structure report format
that gives a graphical representation of how a given model compares
with others in the PDB in terms of ﬁve statistical measures of model
quality [4–7]. These reports are based on the excellent work of numerous
leaders in the ﬁeld of X-ray structure determination [6]. As good
as these reports are, they are focused on the global quality of the
structure.
Even in the best cases, there are areas of the electron density map
that are poorly deﬁned (Fig. 1). Thus, even a crystal structure that
is based on high quality diffraction data and was carefully and competently
built and reﬁned will have local areas of the model that are
less reliable than the rest. Very often, these regions are on the surface
of a protein, and for most users, will not be important in drawing
conclusions about molecular structure and function. Of course, if one
Biochimica et Biophysica Acta 1854 (2015) 258–268
⁎ Corresponding author. Tel.: +1 785 864 5075.
⁎⁎ Corresponding author. Tel.: +1 414 229 2647.
E-mail addresses: lamb@ku.edu (A.L. Lamb), silvaggi@uwm.edu (N.R. Silvaggi).
1
The current Protein Data Bank is a cooperation of three different organizations, RCSB
PDB, PDBe, and PDBj which all contribute entries to the wwPDB (wwpdb.org) [1].
http://dx.doi.org/10.1016/j.bbapap.2014.12.021
1570-9639/© 2014 Elsevier B.V. All rights reserved.
Contents lists available at ScienceDirect
Biochimica et Biophysica Acta
journal homepage: www.elsevier.com/locate/bbapap
is interested in protein–protein interactions, these regions are relevant.
One's interests determine which parts of the electron density map to
inspect.
Regions of the electron density map that are poorly deﬁned due to
mobile, disordered sections of the polypeptide frequently have important
functions. For example, an enzyme may adopt multiple conformations
Box A
From X-ray dataset to finished model.
The figure below highlights the steps in X-ray data collection and refinement. A single oscillation image (panel A) is obtained by rotating the crystal
through a small rotation angle while it is illuminated by X-rays. Hundreds of these images comprise a data set that completely samples the
entire three-dimensional diffraction pattern. The resolution of the data increases from the center to the edge of the image. The highest resolution
where the diffraction spots still have measurable intensity gives some idea of the resolution of the data set, about 1.7 Å in this example. The
diffuse grey ring near 3.5 Å is background scattering from solvent surrounding the crystal in the sample holder.
In order to calculate an electron density map, a crystallographer requires both the amplitudes of the diffracted X-ray waves and their relative
phase angles. The amplitudes are measured as the intensities of the diffraction spots in the experiment, but the phase information is lost. This
is the crystallographic phase problem. The missing phase information can be obtained from using the structure of a homologous protein
(molecular replacement) or by a number of experimental methods involving incorporation of heavy atoms (e.g. Hg, Se) into the ordered array
of the crystal. There are a number of excellent introductory and advanced texts that provide excellent explanations of phasing methods2
.
However the initial estimates of the phases are obtained, they typically have large errors, and the resulting electron density maps are relatively
noisy and ill-defined (Panel B). Once this imperfect electron density map is calculated, the process of building a crystallographic model begins.
A macromolecular crystallographer working on a new structure begins with either a molecular replacement model that likely contains significant
portions that need to be rebuilt, or an empty map into which they build the polypeptide chain from scratch or using an automated
algorithm [48–50]. In either case, the initial model is never an optimal match to the electron density. The initial model is iteratively altered to
improve its fit to the electron density by refining some or all atomic parameters (Panel C). When adjustments to the model no longer improve
the phase estimates, refinement is stopped and the model is said to be finished.
2
For readers interested in a more comprehensive explanation of diffraction physics and the X-ray crystallographic experiment, the authors
recommend these outstanding texts, ranked in approximate order of difficulty:
1) Rhodes, Gale. Crystallography Made Crystal Clear. Academic Press, New York, 2000.
2) Blow, David. Outline of Crystallography for Biologists. Oxford University Press, New York, 2002.
3) Glusker, Jenny P. with Lewis, Mitchell and Rossi, Miriam. Crystal Structure Analysis for Chemists and Biologists. Wiley-VCH, New York, 1994.
4) Rupp, Bernhard. Biomolecular Crystallography. Garland Science, New York, 2010.
259A.L. Lamb et al. / Biochimica et Biophysica Acta 1854 (2015) 258–268
associated with substrate entry, catalysis, and product egress. In addition,
no protein model is produced entirely objectively, since human judgment
always plays a role. Recognizing where uncertainty and bias may intrude
is an important skill for a structure user who wishes to extract meaningful
biological or chemical conclusions from a structure model. To assess
which parts of a model are strongly supported by the data and which
are less so, one cannot rely on statistical indicators, but should instead examine
the electron density maps in regions of functional interest. Fortunately,
most journals now require authors to deposit structure factors
(the processed experimental data with associated phase estimates)
along with the atomic coordinates in the PDB, making it easy to generate
maps. The only way for users of macromolecular structures to evaluate
the quality of the electron density maps used to build a model is to actually
look at them. To avoid basing important experiments on weak structural
data, users of macromolecular models must judge which parts of a
model are relevant and trustworthy. The information content of the
model might not support every idea the structure user has about the
molecule.
2. Understanding macromolecular models
2.1. The coordinate ﬁle
Scientists who work with protein structures routinely download
PDB coordinate ﬁles from the Protein Data Bank and view models in a
graphics program such as COOT [8,9], PyMOL [10], Chimera [11], or
JMOL [12]. The coordinate ﬁle is actually a simple text ﬁle that can be
inspected with any text editor (Box B). Model users are encouraged to
inspect the ﬁle in this way, because the header of the PDB ﬁle contains
important information regarding the protein sample, the experimental
setup, and ways to assess the ﬁnal model. Every atom listed in a PDB
ﬁle is associated with at least ﬁve parameters: x, y, and z coordinates
and two highly correlated terms, the atomic displacement parameter
(ADP) and occupancy (Q), that modulate the contribution of that
atom to the overall diffraction pattern.
2.1.1. Atomic displacement parameters (B-factors)
ADPs are historically known and most often referred to in the literature
as B-factors or temperature factors. These parameters describe
the vibration of an atom around a mean position speciﬁed by the atomic
coordinates. B-factors are typically low (5–20 Å2
) for the well-ordered
atoms of the backbone in well-deﬁned secondary structures like an αhelix
or a β-sheet. Loops tend to be more mobile than α-helices and
β-sheets and thus have higher B-factors. Likewise, side chains can
have considerably higher B-factors than main chain atoms. Atoms
with high B-factors are found in poorly deﬁned electron density. In
Fig. 2, notice the poorer ﬁt to the electron density of the aliphatic
chain, which has higher B-factors, than the fused ring system where
the B-factors are lower. It is unlikely that this is due to an error in
structure determination or model building. Consistent with chemical
intuition, the aliphatic chain is not interacting with the protein and is
neither rigid nor constrained by the protein, and so is more mobile
than the fused ring system.
In high-resolution structures (better than 1.5 Å), anisotropic Bfactors
are used to describe the non-spherical atomic shapes that result
from partially restricted motion. Lower-resolution datasets do not contain
enough observations to justify the addition of ﬁve extra parameters
per atom: six values deﬁne an ellipsoid versus one for a sphere [13].
Anisotropic B-factor records are interdigitated in the coordinate section
of a PDB ﬁle, and are only obvious by looking at the coordinate ﬁle in a
text editor (see Box B).
An alternative way of describing atomic displacements, Translation,
Libration, Screw (TLS), is based on the assumption that groups of atoms
in a large molecule undergo correlated, rigid-body motions [14]. In
TLS reﬁnement, protein atoms are placed in several groups and the
parameters deﬁning the anisotropic motion of each group are reﬁned.
Since there are signiﬁcantly fewer TLS groups than atoms, fewer
additional parameters are required to ﬁt the data than with full anisotropic
B-factor reﬁnement. Whereas individual TLS motions can
be visualized [15], they may or may not correspond to real macromolecular
dynamics [16].
2.1.2. Occupancy
Occupancies (or Q-values) are comparable to mole fractions for different
molecular conﬁgurations. They indicate if an atom is found in a
single location in the model (occupancy of 1.0) or multiple locations
(fractional occupancies). Occupancies can be reﬁned, to a value that approximates
the proportion of unit cells that contain the molecule in each
conformation. For example, a crystal soaked with ligand at an insufﬁcient
concentration or for too short a time may not contain a ligand in
every binding site and will therefore have a fractional occupancy. As another
example, side chains can be present in two (sometimes three) different
conformations. To be visible in the electron density map, and thus
included in the model, an alternate conformation of a residue must be
Fig. 1. Examples of local disorder in a protein structure. The arginine residue in (A) is exposed on the surface of the protein MppR. The average B-factor for the main chain atoms is 18.0 Å2
,
while the average for the side chain atoms is 41.5 Å2
. The values increase from 22.4 Å2
at the beta carbon to 57.1 Å2
for one of the guanidino nitrogen atoms. Notice how the electron density
for Cβ is comparable to the main chain, while the entire guanidinium group has only a small scrap of electron density centered on Cζ. At the termini of protein chains (B), highly mobile
sections of the polypetide chain often have little or no electron density. Residues with no electron density are omitted from the model, as shown here for residues 1 through 32. If a
terminus is thought to be important for a proteins' function, model users should be careful to conﬁrm that the density for that terminus is solid.
260 A.L. Lamb et al. / Biochimica et Biophysica Acta 1854 (2015) 258–268
present in at least 20% of the molecules in the crystal (fractional occupancy
0.2). Conformations with occupancies that reﬁne to less than
0.2 are generally not included in a model (Fig. 3).
2.2. Electron density maps
Scientists who work with protein structures routinely download
PDB coordinate ﬁles from the Protein Data Bank (http://www.wwpdb.
org) and view models in a graphics program such as COOT [8,9],
PyMOL [10], or Chimera [11]. It is just as easy to download the structure
factors from the same PDB page, or pre-calculated electron density
maps from the Electron Density Server (EDS; http://eds.bmc.uu.se/
eds/) (Box C) [17]. The PDB entry even includes hyperlinks to the EDS
to facilitate use of these electron density maps. The diffraction spots
measured during a crystallographic experiment (see Box A) arise due
to scattering of the X-rays by the electrons associated with the protein
atoms. The electron density map derived from the diffraction data is a
three dimensional plot that shows where in space electrons are concentrated
within the repeating unit of the crystal. The areas of high electron
density mark the positions of the protein atoms.
There are a number of ways to calculate electron density maps, and
the map types most frequently mentioned in the literature are: Fo −
Fc, 2Fo − Fc, the maximum likelihood-weighted versions of these
(mFo − DFc and 2mFo − DFc), and various ﬂavors of “omit” maps. The
maximum likelihood weights, ‘m’ and ‘D’, effectively reduce the contributions
of poorly estimated structure factors to the electron density calculation.
This has the effect of making the maps more interpretable by
reducing model bias (see [18,19] for more detailed discussion). The
EDS allows one to choose both the format (CCP4 [20] format is the
most widely accepted by crystallographic software) and type of map
(either 2mFo − DFc or mFo − DFc). Since the structure factor ﬁle that
can be downloaded from the PDB cannot be directly displayed in molecular
visualization software, we strongly suggest that users download the
pre-calculated maps from the EDS. It is also worth noting that the EDS
provides per-residue plots of the real space correlation coefﬁcient
(RSCC) [21], which provides a statistical measure of how well each residue
ﬁts within the electron density. The RSCC values can thus be used to
guide visual inspection of the model.
2.2.1. Fo − Fc or mFo − DFc maps
To calculate an electron density map, the structure factor amplitudes
are combined with corresponding phase estimates (see Box A) in a Fourier
series. The direct experimental map calculated from the observed
structure factor amplitudes (Fo) is relatively difﬁcult to interpret,
Box B
A PDB coordinate file as seen in an editor.
The first amino acid of a protein refined with isotropic B-factors:
The first amino acid of a protein refined with anisotropic B-factors (note that the hydrogens were refined with isotropic B-factors):
It is sobering to think that months, even years, of work can be distilled into something as humble as a simple text file, but that is precisely what
a PDB-formatted structure file is. It can be viewed in any program capable of opening ASCII text files (such as your favorite word processing
program), and it is good practice to scan the header, since this normally contains a wealth of information about the experiment and the model
itself. The ATOM records below the header section are, collectively, the model (only one residue is shown for brevity). The atomic coordinates
(green) give the position of the atom. The occupancy (blue) should be 1.0 for most of the atoms. The B-factors (red and orange) can be modeled
in one of several ways, depending on the resolution of the data and the preference of the crystallographer. Without looking directly at the PDB
file it is often impossible to know which type of B-factors were used in the refinement. In the simpler case of a model with isotropic B-factors,
there are no ANISO lines, only the single B-factor parameter (red). If full anisotropic treatment was used to refine B-factors, there would be
ANISOU lines (orange). If TLS parameters were refined, ANISOU lines are also added (though their meaning is different) and a TLS record would
appear in the header.
261A.L. Lamb et al. / Biochimica et Biophysica Acta 1854 (2015) 258–268
especially for incomplete models. This is why crystallographers calculate
difference maps. An Fo − Fc or mFo − DFc map is calculated by
subtracting the observed structure factor amplitudes from those calculated
from the current model (Fc). In areas where there is good agreement
between the experimental data and the model, there is no
density. In areas where the model is missing atoms, there will be a
peak in the Fo − Fc map. Where the model contains atoms that should
not be there, the Fo − Fc map will have a hole (i.e. a negative “peak”).
Thus, the Fo − Fc map shows where the model and experimental data
differ. It can aid interpretation of the 2Fo − Fc map (see below). Fo − Fc
maps are contoured at (+) and (−) 3.0 σ to show areas for which the
model does not adequately account for the electron density (positive)
or where atoms are partially disordered or have been incorrectly
placed (negative). Typically the peaks in the Fo − Fc map are colored
green and the minima are colored red. The sigma level is an estimate
of the noise in the map, and is analogous to setting a minimum elevation
on a topographical map, such that only peaks above a certain
threshold are drawn. Some graphics programs set the map contour in
units of electrons per Å3
, but the idea is the same: only regions with
electron density above the threshold value are drawn.
2.2.2. 2Fo − Fc or 2mFo − DFc maps
The 2Fc − Fc or 2mFo − DFc map, where the model-derived structure
factor amplitudes are subtracted from twice the observed structure factor
amplitudes, can be thought of as a combination of the direct Fo map
and the Fo − Fc difference map. The observed structure factor amplitudes
are weighted more heavily, so that even areas where the model
and data agree will be covered by the electron density. Atoms that
should not be at their current positions in the model will have little to
no electron density, while empty peaks mark positions where atoms
must be added to the model to agree with the data. To inspect a completed
structure, set the 2mFo − DFc map contour level between 1.0
and 1.5 σ. The 2mFo − DFc map should be fairly continuous (occasional
breaks are normal, especially at lower resolutions) and should cover
most of the atoms in the model. One expects less well-deﬁned maps
at low resolution, and thus more discontinuities in the main chain electron
density and “naked” atoms than would be tolerated at higher resolution
(see below).
2.2.3. Omit maps
Model bias is the result of how maps are calculated: because the
phase estimates for the calculation come from the model, maps will
tend to show electron density for an atom in the model whether it is
truly there or not. A simple omit map is normally a difference (Fo −
Fc) map calculated after omitting speciﬁc atoms from a model, like a ligand
or a functionally important loop. While simple to do, the drawback
to this approach is that leaving out a small percentage of the model does
little to remove model bias. A more rigorous (and computation/timeintensive)
approach is the composite omit map, where sections of a
model (5–10%) are omitted in a series of map calculations, and the
Fig. 2. Correlation of map quality and B-factors in a protein-bound ligand. Cholesterol contains a rigid tetracyclic ring system and a more mobile alkyl side chain (top). Yeast Osh4p (PDB ID:
1ZHY) binds cholesterol in a nearly ﬂat conformation. The magenta mesh is the 2mFo − DFc electron density map from the EDS contoured at 1.0 σ with a 2 Å carve radius (middle). Notice
that the qualitative ﬁt to the electron density is excellent for the fused ring system, but is ambiguous for the more mobile alkyl chain. The relationship between map-model agreement and
B-factor is seen in the view with atoms colored and sized according to B-factor (bottom; ramp from blue [15 Å2
] to red [35 Å2
]). The atoms with weaker electron density have higher B-
factors.
262 A.L. Lamb et al. / Biochimica et Biophysica Acta 1854 (2015) 258–268
relevant regions of each calculation are stitched together to give an electron
density map with much less bias, since the entire model has been
omitted. For further bias removal, a round of simulated annealing reﬁnement
is done at each omit step during the composite omit calculation
to give the simulated annealing composite omit map. This type of
omit map has minimal model bias and is the gold standard for ﬁgures designed
to conﬁrm the electron density of protein·ligand complex structures,
especially if the 2mFo − DFc density is not solid for every atom of
the ligand. If the published electron density images or 2Fo − Fc map
from the EDS lead one to question the validity of a region in the model,
calculating the simulated annealing composite omit map may be
worth the small additional effort. Simulated annealing composite
omit maps are not available directly for download from EDS, but
can be calculated without too much effort by a friendly crystallographer
from the deposited structure factor and coordinate ﬁles using
PHENIX [22] or other software.
2.3. Resolution
High-resolution data add detail to electron density maps (Fig. 4). A 4
Å-resolution map shows the location of secondary structure elements,
but not necessarily their orientation—helices can go in either direction
and the directionality of β-sheets is similarly hard to determine.
A 3 Å-resolution map clearly shows secondary structure
and some side chains. A 2 Å-resolution map will show most side
chains. At resolutions of 1 Å and better, the map shows individual
atoms. At the highest resolutions (0.7 Å and better), it becomes
possible to see electron density between covalently bonded atoms
in stable regions of the molecule. Diffraction data at almost any
resolution can provide valuable information. After all, Rosalind
Franklin's ﬁber diffraction images contained enough information
to construct a hugely inﬂuential model of DNA that was in no
way a “solved” structure [23–25]. Likewise, Roderick MacKinnon's
4 Å-resolution Rb+
or Cs+
soaked potassium channel crystals provided
evidence for the selectivity ﬁlter [26]. The resolution of the
data—the detail available in the electron density map—dictates
the conclusions that can be drawn from a crystallographic model.
Higher resolution data provide more observations against which the
parameters of the model (the x,y,z of atomic locations and B-factors and
occupancies) can be reﬁned. Model reﬁnement is conceptually similar
to non-linear least squares ﬁtting, where the ﬁt can be improved simply
by increasing the complexity of the equation used to ﬁt the data. When
the number of parameters grows too large, a least-squares ﬁt may look
perfect but the model it represents has no basis in reality. While crystallographic
models are more complex, reﬁnement is similarly vulnerable
to overﬁtting and over-parameterization. Parameters are added to a
macromolecular model in the form of additional atoms (e.g. water molecules,
ligands, residues in mobile loops), or by using more realistic
Fig. 3. Alternate conformations of amino acid side chains. Two methionine side chains from MppR. One (A) shows evidence of multiple conformations in the Fo − Fc map (green mesh at +3.0 σ
and red at −3.0 σ), but only the slimmest hint in the 2Fo − Fc map (purple mesh at 1.5 σ) near the green Fo − Fc peak. It may be that in some portion of molecules in the crystal the terminal
methyl group is rotated ~90°, but that population is too small to justify including that conformation in the model. In (B) the occupancies of the two conformations have been reﬁned to 0.35 (left)
and 0.65 (right).
Box C
Downloading and displaying electron density.
The Electron Density Server hosted at Uppsala University (http://
eds.bmc.uu.se/eds) allows users to generate and download the
model and map files for any structure in the Protein Data Bank
for which the structure factor data have been deposited. The
downloaded map files can then be opened in a number of programs,
including COOT [8,9], PyMol [51], Jmol [12], AstexViewer
[52], Chimera [11], and MOE [53]. The authors prefer to examine
electron density in COOT, since it is capable of automatically
downloading and displaying the model, 2Fo − Fc map and
Fo − Fc map with no input beyond the PDB accession code.
Displaying electron density is a simple matter of choosing “Get
PDB & map using EDS…” from the file menu, entering the PDB accession
code for the structure of interest, and pressing the “Get it”
button. That is all there is to it. The contour level of the map can be
changed using the scroll wheel on a PC-style mouse. For more detailed
instructions, see the COOT documentation at http://www2.
mrc-lmb.cam.ac.uk/personal/pemsley/coot. COOT can be
downloaded free of charge for Linux, Windows and Mac and is
straightforward to install.
263A.L. Lamb et al. / Biochimica et Biophysica Acta 1854 (2015) 258–268
models of atomic behavior (B-factors, occupancies). The number of
observations in the diffraction data set must be greater than the
number of reﬁned parameters to support a robust model reﬁnement.
Models can also be overﬁt by violating chemical (e.g. poor stereochemical
restraints) or physical (e.g. steric clashes) principles.
At low resolution, the electron density is simply too ill-deﬁned for
the side chains, especially the longer ones, to be well-modeled, and
the many waters that are part of the hydrogen bond network are not
visible. As a rule of thumb, a model built using 3 Å-resolution diffraction
data is usually sufﬁcient for determining the overall fold of the protein
Fig. 4. The effect of increasing resolution on electron density maps. The panels show the active site of the Clostridium botulinum serotype A neurotoxin with various ligands bound at 4.3 Å
(A), 2.4 Å (B), 1.9 Å (C), 1.4 Å (D), and 1.2 Å (E). The 2mFo − DFc electron density maps are contoured at 1.0 σ (blue) and 3.0 σ (yellow) within a 2.0 Å radius around each atom. The catalytic
Zn(II) ion is shown as a silver sphere. Notice the clear differences in the level of detail in moving from 4.3 to 2.4 Å (A and B), and from 2.4 to 1.9 Å (B and C). Notice also that as the resolution
increases, small differences in resolution give diminishing returns in terms of map detail (e.g. compare 1.4 and 1.2 Å in D and E). The structures shown are PDB ID 3V0C, 2IMB, 2IMA, 3BOO,
and 3BON [54–56].
264 A.L. Lamb et al. / Biochimica et Biophysica Acta 1854 (2015) 258–268
(e.g. for comparison to proteins with similar structure and/or function).
A model determined at 2 Å-resolution can support detailed arguments
about the roles of enzyme active site residues, the binding mode of an
inhibitor, or analysis of the solvent and hydrogen bond network. A
model determined at 1 Å-resolution allows visualization of individual
non-hydrogen atoms and a detailed biophysical analysis.
3. All parts of a model are not of the same quality
3.1. The protein
Structural data consumers should remember that structural models
are not as rigid as they might seem. The ability to “measure” interatomic
distances in hundredths of Ångstroms from a model using a graphics
program does not mean they are actually known to anywhere near
that level of accuracy. A molecular dynamics movie of a protein in solution
shows them to be incredibly dynamic, bouncing and vibrating crazily
(and anisotropically). It is entropically “expensive” to immobilize a
ﬂoppy molecule like a protein in a crystal, and the most ﬂexible regions
are the hardest to constrain.
Crystals are snap-cooled in cryoprotectant agents to minimize the
formation of crystalline ice that can obscure protein diffraction data or
destroy the protein crystal. Snap-cooling does not typically serve as a kinetic
trap, since even at room temperature the crystalline lattice conﬁnes
the protein to a relatively small ensemble of conformations.
(Unstable chemical intermediates can sometimes be trapped by snapcooling
crystals undergoing an enzymatic reaction.) If protein crystal
structures represent a thermodynamic minimum, they should be reproducible.
Independently determined high-resolution models for the
same protein tend to agree [27]. At moderate resolution, different structure
models may be equally plausible since the electron density may
represent an ensemble of conformations [28]. A protein crystallized in
multiple space groups may adopt different conformations [29–31]. In
addition, minor conformational substates with disproportionate functional
signiﬁcance may be thermal “excited states” that are not populated
at cryogenic X-ray data collection temperatures [32,33]. A single
consensus structure is typically reported, not the ensemble it represents
[34]. These motions may be studied using complementary experimental
and computational approaches [35,36].
Low temperatures further limit conformational ensembles in the
crystalline lattice. Proteins undergo a “glass transition” as the temperature
drops below 160–200 K that restricts internal motions [37]. At
cryogenic data collection temperatures (100 K), molecular motions
are almost entirely “frozen out”; even methyl rotation is suppressed
[38]. In relatively unconstrained regions of the crystal, multiple conformations
that have similar energies can be trapped by snap-cooling.
These often correspond to regions that are ﬂexible in solution, like
loops, and they are colloquially referred to as ﬂexible in a crystal, even
though they cannot “move” (interconvert) at cryogenic temperatures.
Disordered regions give weaker electron density maps and higher Bvalues
than other parts of the protein. In many cases, the density is so
weak that there is no justiﬁcation for including part of the protein in
the ﬁnal model (Fig. 1B).
It is often possible to discern mobility in crystal structures, despite
the stabilizing inﬂuences of the crystal lattice and cryogenic temperatures.
As discussed above, the B-factors give an approximation of the degree
of mobility of atoms in the model. In practice, it is difﬁcult to tell if
high B-factors are due to thermal motions, lattice displacements (slight
misalignment of the repeating units of the crystal), or the existence of a
large number of possible conformations. In all three cases, the electron
density blurs and eventually disappears for very mobile parts of the
structure. Mobile side chains can be modeled with alternate conformations
in structures of higher resolution (~2 Å resolution or better), when
there is sufﬁcient crystallographic evidence (density in the map) to warrant
more than one orientation. In favorable cases, only two conformations
of a residue or region contribute to the observed electron density
and both conformations can be built into the model (Fig. 3B). Occupancy
values for each contributor are optimized during reﬁnement. In
unfavorable cases, the ﬂexible bits of the molecule adopt so
many conformations that there is no information on where they
are (no density).
Unfortunately, molecular visualization programs are not designed to
alert the casual user to the use of alternate conformations or high Bfactors.
If a model contains two conformations of a side chain, both
will be displayed by most graphics programs. Most of the time, the
smaller partial occupancy should be at least 20% for inclusion in the
model, since they are distracting and often do not add much to what
can be gleaned from common sense and B-factors. It is usually easy to
color a model by relative B-factor to insure that a region of interest is
not associated with weak electron density. Weak electron density is
often associated with surface-exposed residues since they have no
chemical reason to adopt a particular conformation (Fig. 1A).
Crystallographers disagree about how to handle disordered side
chains. The ﬁrst group omits atoms that have no electron density from
the model. Their rationale is that if there is no evidence to place an
atom at a speciﬁc point, then no atom should be placed there in the
model. This approach, however, leads to confusion about residue identity
(i.e. glutamate winds up looking exactly like alanine). The second
group assumes that the visible portion of a residue constrains where
the invisible (mobile) atoms can be. A somewhat-disordered residue
can be placed intact in the most stereochemically plausible pose and
the B-factors allowed to reﬁne to high values. This avoids confusing residue
truncations, but it obliges structure users to check B-factors and
maps in any interesting region of the model [39]. The third group
models a side chain that has no electron density in the most stable
rotamer and sets the occupancy values to zero for atoms with no electron
density. This obliges structure users to inspect occupancies closely.
Unfortunately, most molecular viewers do not automatically alert the
user to occupancies less than 1. Most of the ambiguity disappears
when one looks at the maps. So, if one is interested in a particular active
site residue or a surface patch that may be involved in a protein-protein
interaction, one must look carefully at the electron density map to decide
if there is sufﬁcient density to support the modeled side chain
orientation.
In addition to making decisions about what to do with surface side
chains, there are several residues (Asn, Gln, and His) with side chain
functional groups that have ﬂat, symmetrical shapes in electron density
maps. In the ﬁnal rounds of reﬁnement, crystallographers decide how to
orient these side chains based on the surrounding hydrogen bonding
network. Sometimes this is straightforward (Fig. 5), and sometimes it
is not. This is a particular concern in enzyme active sites, where a His
side chain, for example, might participate in catalysis. Model users
should always check the surrounding network of hydrogen bonding interactions
to judge if it supports the modeled pose and the proposed
function.
Molecular motions discerned by comparing crystal structures are
only meaningful if the positional uncertainty (coordinate error) of
each structure is known. However, coordinate error is seldom included
in the information contained within the PDB header section. It is not unusual
to see small movements of, for example, a helix or loop when multiple
structures of the same protein in different states (e.g. ligand bound
vs unbound) are compared. Unfortunately, it is difﬁcult to estimate the
precision of atomic positions [40] and thereby to determine if an apparent
motion is signiﬁcant. An apparent movement of 0.4 Å that is based
on a comparison between two structures with coordinate errors of
0.3 Å could be real but it is unlikely to be biochemically relevant. Recall
that most deposited protein structures represent only the most stable
state among the ensemble of states present in the crystal. Claims that
tiny structural shifts have catalytic relevance should be treated with
skepticism except when based on comparison of ultra-high resolution
data sets. Ultimately, any assertion that a minor motion has functional
signiﬁcance requires additional biochemical or biophysical data.
265A.L. Lamb et al. / Biochimica et Biophysica Acta 1854 (2015) 258–268
3.2. Buffer components and solvent
Protein molecules are solvated and contain “ordered” water molecules
that are integral to the structure. These ordered water molecules
are modeled as single oxygens (hydrogens cannot be seen at the resolution
of most structures), found on the exterior of the protein molecule or
in any cavity, but must obey simple rules of hydrogen bonding. The
number of water molecules in a crystallographic model depends on resolution,
with few at 3 Å and as many as two per amino acid at high resolution.
There is some danger in comparing water molecules between
different protein structures unless the structures are determined to sufﬁcient
resolution and the water molecules have appropriate B-factors.
Most protein crystals form in solutions containing organic precipitants
(e.g., polyethylene glycol) and/or Hofmeister “salting-out” ions
(e.g., ammonium sulfate) that stabilize proteins and favor controlled
crystal nucleation and growth. Even though the mother liquor contains
high concentrations of these additives, they appear less often in electron
density maps than might be supposed. Those that do appear often look
very odd, as a consequence of local disorder: for instance, sulfate is a tetrahedral
oxyanion that shows up bound to enzyme active sites where a
phosphate group might normally bind. Sulfate can also appear on the
surface of a protein as a smaller, spherical blob near a positively charged
region, and is identiﬁed primarily on the basis of knowledge of which
chemicals are present and a strong peak of electron density that is inadequately
modeled as water. Alternatively, sulfate may be spotted ﬁrst as
a water molecule with an unrealistically low B-factor.
What about the ammonium ions provided by ammonium sulfate,
which are twice as abundant as the sulfates? About a quarter of deposited
X-ray crystal structures contain sulfate, which is almost two orders
of magnitude more common than structures containing ammonium
(NH4
+
) or ammonia. Many water molecules adjacent to a negative
charge may be ammonium ions. However, neither X-ray crystallography
nor chemical plausibility can support that assignment. One should
nevertheless keep an open mind about whether a solvent molecule
could be something other than water [41].
3.3. The ligands
Ligands, which we deﬁne as interesting buffer components, can be
danger zones. Ligands are noncovalently associated with the protein
(Fig. 6A) so are likely to be present with high B-factors or fractional occupancy.
Flexible parts of the ligand are often incompletely immobilized
in a macromolecular complex, to lessen the entropic cost of binding the
parts of the molecule that make speciﬁc interactions with the protein. In
favorable cases, ﬂexible loops of an enzyme active site become ordered
in the presence of a ligand. It can be difﬁcult to saturate all of the binding
sites in a protein crystal, even when the dissociation constant is small. In
cases of fractional ligand occupancy, only a fraction of the protein molecules
making up the crystal lattice bind to the ligand (simply, only
some active sites have ligand bound) or only a fraction of ligands bind
in the same orientation.
One of the few ways to distinguish fractional occupancies from high
B-factors is to compare B-factors within a ligand. In general, only atoms
that contact the protein directly have B-factors comparable to surrounding
protein atoms. If B-factors range from low to high (partly disordered)
within a ligand molecule, the ligand is probably present at full
occupancy but it is less ordered at one end. If B-factors are consistently
high, the ligand is probably not present at full occupancy; occupancies
may be reﬁned as a group (e.g., all atoms in a ligand). In either case,
we prefer to set all ligand atom occupancies to 1, to force B-factors
higher and thereby to alert the structure user. A good example is
found in the 1.6 Å structure of the yeast oxysterol binding protein
Osh4 bound to cholesterol (PDB ID: 1ZHY) [42]. The ring system
(Fig. 2) is rigid relative to the alkyl side chain, thanks to interactions
with the protein and conformational constraints imposed by the fused
rings. The increase in disorder correlates well with the expected decrease
in rigidity. The chemical stability of cholesterol disfavors the
Fig. 6. Noncovalently bound ligand vs covalent adduct. A molecule of TRIS buffer from the crystallization solution was found bound in the active site of MppR (A). The electron density does
not completely cover the molecule and its average B-factor is closer to that of the solvent than the macromolecule. MppR will react with 2-oxo-5-guanidinovaleric acid to form an imine at
Lys156 (B). The electron density is signiﬁcantly clearer in B due to the covalent attachment. Notice the small positive peak in the mFo − DFc difference map near the guanidinium group. It is
likely that a small portion of molecules in the crystal either do not have the ligand bound and have a water in that position, or there is a small population with a different conformation of
the ligand. This electron density is too weak to justify modeling either scenario.
Fig. 5. Hydrogen bonding patterns should make chemical sense. An ultra-high resolution
electron density map (0.75 Å) of the Streptomyces strain R61 D-alanyl-D-alanine carboxypeptidase/transpeptidase
showing His37, on the protein surface, making hydrogen bonding
interactions with a water molecule and an adjacent aspartate residue (unpublished
data). The modeled conformation of the imidazole ring of His37 agrees with the surrounding
network of hydrogen bonds and is further supported by the larger electron density
peaks of the two N atoms (N has one more electron than C, and at very high resolutions
this difference in visible for well-ordered atoms). The 2mFo − DFc electron density maps
are contoured at 1.5 (blue) and 4.0 σ (yellow).
266 A.L. Lamb et al. / Biochimica et Biophysica Acta 1854 (2015) 258–268
alternate hypothesis, that side chain atoms are present at fractional
occupancy due to breakdown of the ligand.
Overzealous interpretation of solvent components as ligands is particularly
hazardous in structure-based drug design [10,43]. A serious
problem arises when a buffer component or a decomposition product
is mistaken for a ligand that was desired to be present [44]. Unless
heavy atoms are part of the ligand, it can be hard to distinguish ligands
from solvent or buffer components. There are a number of tools available
to crystallographers and model users alike for validating the ﬁt of
a ligand to the electron density. Most of these rely wholly or in part on
statistical measures of map-model agreement like the real space R
value (RSR), the real space correlation coefﬁcient, or a difference density
Z score [7,45,46]. One tool, the Twilight script [21], ﬂags ligands with
low RSCC values and ranks ligand plausibility. Another piece of software,
VHELIBS [47] allows even novice users to visually assess both
the ligand and binding site.
Covalent adducts are physically linked to the protein (Fig. 6B) and
the occupancy is often known from separate analysis. Small covalent adducts,
such as an acetylated lysine residue, often have B-factors similar
to unmodiﬁed residues. Large covalent adducts, like the sugar moieties
in glycoproteins, are often rather mobile and can be as difﬁcult to model
as ligands. Polysaccharide adducts are often represented by partial
models with high B-factors.
4. Conclusions
Coordinate ﬁles downloaded from the PDB contain three dimensional
models that are built to approximate electron density maps derived
from crystallographic data. All areas of the map are not equally welldrawn,
so structure users must be careful not to base their hypothesis
on areas of the map that ancient mapmakers would have labeled
“Here Be Dragons.” Nevertheless, all areas of the model appear at ﬁrst
glance to be equally sound when looking at the coordinate ﬁle in a
graphical viewer. In order to know where the dragons lurk, the savvy
scientist must examine the map. Critical assessment of the data (in the
form of electron density maps) will assure model users that their
hypotheses and future experiments are supported by crystallographic
evidence.
Funding sources
This work was supported by the Purdue University College of Agriculture
and MB-22 from the Paciﬁc Enzyme Science Trust (T.J.K.), K02
AI093675 from the National Institute for Allergy and Infectious Disease
of the National Institutes of Health (A.L.L), and MCB7171573 from
the National Science Foundation, Directorate of Biological Sciences
(N.R.S.). Use of the Advanced Photon Source was supported by the
U. S. Department of Energy, Ofﬁce of Science, Ofﬁce of Basic Energy
Sciences, under Contract No. DE-AC02-06CH11357. Use of the LS-CAT
Sector 21 was supported by the Michigan Economic Development Corporation
and the Michigan Technology Tri-Corridor for the support of
this research program (Grant 085P1000817). Use of the Stanford Synchrotron
Radiation Lightsource, SLAC National Accelerator Laboratory,
is supported by the U.S. Department of Energy, Ofﬁce of Science, Ofﬁce
of Basic Energy Sciences under Contract No. DE-AC02-76SF00515. The
SSRL Structural Molecular Biology Program is supported by the DOE
Ofﬁce of Biological and Environmental Research, and by the National
Institutes of Health, National Institute of General Medical Sciences
(including P41GM103393). The contents of this publication are solely
the responsibility of the authors and do not necessarily represent
the ofﬁcial views of NIGMS or NIH.
Acknowledgments
We thank Drs. Aron Fenton, Andy Gulick, Joe Jez, Graham Moran,
Jeramia Ory, Emily Scott, and Courtney Starks for comments on the
manuscript and synchrotron beamline scientists across the country for
their help and advice. TJK thanks Drs. Paul Harkins, Courtney Starks,
and I. I. Mathews for encouraging an interest in crystallography. ALL
thanks Drs. Marcia Newcomer, Paula Flicker and Amy Rosenzweig for
crystallographic training. NRS thanks Drs. Judith Kelly, Karen Allen,
and Michael McDonough for training in crystallography. TJK and NRS
thank Dr. Robert Sweet and the staff of the RapiData course for providing
a solid foundation in crystallographic theory and practice.
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