R E S E A R C H A R T I C L E
Protein structure model refinement in CASP12 using short and
long molecular dynamics simulations in implicit solvent
Genki Terashi1 | Daisuke Kihara1,2
1
Department of Biological Sciences, Purdue
University, West Lafayette, Indiana 47907
2
Department of Computer Science, Purdue
University, West Lafayette, Indiana 47907
Correspondence
Daisuke Kihara, Department of Biological
Sciences, Purdue University, West
Lafayette, Indiana 47907,
Email: dkihara@purdue.edu
Funding information
Division of Biological Infrastructure, Grant
number: DBI1262189; National Institute of
General Medical Sciences, Grant number:
R01GM123055; Division of Information
and Intelligent Systems, Grant number:
IIS1319551; Division of Integrative
Organismal Systems, Grant number:
IOS1127027; Division of Mathematical
Sciences, Grant number: DMS1614777
Abstract
Protein structure prediction has matured over years, particularly those which use structure templates
for building a model. It can build a model with correct overall conformation in cases where
appropriate templates are available. Models with the correct topology can be practically useful for
limited purposes that need residue-level accuracy, but further improvement of the models can
allow the models to be used in tasks that need detailed structures, such as molecular replacement
in X-ray crystallography or structure-based drug screening. Thus, model refinement is an important
final step in protein structure prediction to bridge predictions to real-life applications. Model
refinement is one of the categories in recent rounds of critical assessment of techniques in protein
structure prediction (CASP) and has recently been drawing more attention due to its realized
importance. Here we report our group’s performance in the refinement category in CASP12. Our
method is based on inexpensive short molecular dynamics (MD) simulations in implicit solvent.
Our performance in CASP12 was among the top, which was consistent with the previous round,
CASP11. Our method with short MD runs achieved comparable performance with other methods
that used longer simulations. Detailed analyses found that improvements typically occurred in
entire regions of a structure rather than only in flexible loop regions. The remaining challenge in
the structure refinement includes large conformational refinement which involves substantial
motions of secondary structure elements or domains.
K E Y W O R D S
CASP, computational method, molecular dynamics, protein structure prediction, protein structure
refinement, structure modeling, template-based modeling
1 | INTRODUCTION
Methodology of protein structure prediction has been intensively studied
over decades from various angles, such as bioinformatics, physics,
chemistry, statistics, and robotics. Although there are still some areas
that need further development, for example, template-free (often also
called ab initio or de novo) modeling,1,2
structure prediction has
become practical in several situations, which include cases where structures
can be modeled using templates (template-based modeling).3–5
The progress of the protein structure modeling field has been objectively
monitored in the critical assessment of techniques for protein
structure prediction (CASP) from 1994,6
a community-wide assessment
of prediction methods that is held every 2 years. In CASP, participating
prediction groups/methods are evaluated based on structure models
they build for protein target sequences, which are presented by the
organizers before determination of their tertiary structures. From
CASP7 in 2006, assessors’ evaluation reports show that performance
of template-based modeling has not changed much partly reflecting
maturity of the methods.4,7–10
Now, biologists routinely use structure
prediction to interpret or design experiments.11,12
In the case of template-based modeling, obtaining a structure
model of the correct fold, that is, a structure that has a root-mean
square deviation (RMSD) of 3–6 Å, can be expected if the template
structures found in a structure library has a reasonably high confidence
score.5,13
Improving the structure model further through model refinement,
an additional procedure to gain a couple of more angstroms in
RMSD to the native structure, is critical for bringing a computational
model with the correct fold to a level that it is practically useful in various
applications. For example, a model at a 5 Å RMSD would be only
used for indicating residue positions in the protein such as interpreting
Proteins. 2018;86:189–201. wileyonlinelibrary.com/journal/prot VC 2017 Wiley Periodicals, Inc. | 189
Received: 21 June 2017 | Revised: 1 August 2017 | Accepted: 18 August 2017
DOI: 10.1002/prot.25373
and designing residue mutagenesis experiments. However, if the model
was refined to within 1.5 Å RMSD, it can be used for molecular
replacement in experimental structure determination, virtual drug
screening, and investigating enzymatic reactions.14
Thus, model refinement
has been one of the foci of recent method developments in the
CASP community.4,15
However, model refinement is still not easy. It is well known that
running naïve molecular dynamics (MD) simulations on a structure
model do not improve model consistently. Rather, it deteriorates the
model for almost half of the cases.16
In CASP, until CASP9 held in
2010, there were no methods that could refine models consistently
with statistical significance.17
This situation changed in CASP10, when
the FEIG and Seok groups showed improvements on the starting models
in majority of their cases.18
Particularly, the FEIG group significantly
outperformed all the other groups in their Global Distance Test-High
Accuracy (GDT-HA) score19
improvement. The FEIG’s approach was
based on MD: from the MD trajectories starting of a model to be
refined, structures were chosen that did not deviate much from the initial
structure to avoid degraded structures and further filtered by using
additional scoring function.20
In CASP11, many top performing groups,
including FEIG,15,21
used MD-based approaches with some variations,
for example, using support vector machine (a machine learning method)
to select models after MD,22
remodeling using multiple templates
before MD-based refinement,23
taking consensus with homologous
structures,24
or using multiple rounds of relaxation.25
Here, we report our group’s method and performance in the model
refinement category in CASP12. Our approach is based on MD trajectories,
following the FEIG group’s success, with several critical differences:
We used an implicit solvent model rather than explicit water
molecules in simulation, and moreover, the length of the trajectories is
significantly shorter than those used in the FEIG approach. In spite of
the computationally inexpensive strategy, our approach was ranked high
among participants in CASP1115
as well as in CASP12. Differences of
our approach in CASP11 and CAS12 are that we optimized parameters
of the method carefully for CASP12 and also changed the implicit solvent
model used in the MD simulations. In CASP12, our approach
refined 29 out of 42 targets successfully in terms of the GDT-HA score
and 24 in terms of the CASP12 assessors’ score that is a linear combination
of five scores (http://predictioncenter.org/casp12/zscores_final_
refine.cgi?formula5 assessors) . We showed that the refinement
occurred not only at loop regions but also overall in structures cores,
and the approach mainly expanded structures (showing that the
improvement of structure evaluation scores are not merely due to compression
of structures). Drawbacks of the approach are also discussed.
2 | MATERIALS AND METHODS
2.1 | Overview of the refinement protocol
Our refinement protocol used in CASP12 is shown in Figure 1. Figure
1A shows the overall flowchart. We performed short and long MD simulations
after the energy minimization was applied to a structure model
to refine. The short MD consists of sixty 1.2 nanosecond (ns) MD simulations
with restraints of increasing strength (0.1, 0.2, 0.4
kcal mol21
Å22
) applied to Ca atom positions, which was increased
every 400 pico seconds (ps). The long MD consists of twenty 20 ns
MD simulations with weak restraints (0.05 kcal mol21
Å22
)21
on Ca
atoms positions. After the MD simulations, a subset of structures in
FIGURE 1 The model refinement protocol of the Kiharalab group in CASP12. A, the flow chart of our refinement protocol. Before
performing MD simulations, the energy of the staring model was minimized, and then subjected to the next heating and equilibration step.
The equilibrated structure was used as the starting model for the two types of production MD runs (short MD and long MD simulations). In
the filtering step, subset of models extracted from the MD trajectories were selected by the filtering criteria. The coordinates of selected
models were averaged and then relaxed. B, Definition of the parameters used in the filtering step. The x axis is the Z score of GDT-HA of a
model from the initial structure and the y axis is the Z score of the DFIRE scoring function. The distribution shown is from extracted models
from short MD trajectories of TR520. Red points represent selected models by the filtering with r 5 2.0, u 5 310, and g 5 35
190 | TERASHI AND KIHARA
the trajectories were selected by considering the deviation from the
starting model and the statistical potential score (Figure 1B). The
selected models were averaged on the Cartesian coordinates of atoms,
which were then minimized and relaxed with a10 ps MD simulation.
2.2 | Setting of MD simulation
MD runs were performed by CHARMM MD program version 38b2
with CHARM22/CMAP force field. We used a 2 femto seconds (fs)
time step for all of simulations. The non-bond interactions were listed
using a 14 Å cutoff. Electrostatic interactions were calculated with a
shifting function applied to the potential energy at 12 Å. van der Waals
interactions were calculated with a switching function applied to the
potential energy between 10 and 12 Å. The solvent effect was computed
by the FACTS implicit solvent model26
with its default parameters.
In CASP11, we used SCPISM27
for implicit solvent but changed it
to FACTS following a comparison study of implicit solvents by Hua
et al.28
Before running MD simulations, hydrogen atoms were added to
the starting model by the CHARMM HBUIld command. To fix the
length of bonds involving hydrogen atoms, the CHARMM SHAKE command
was used. Energy minimization was performed in total of 12,100
steps of the Adopted Basis Newton-Raphson (ABNR) method. In the
first 100 steps of the minimization, the position of all non-hydrogen
atoms was fixed, and then we applied harmonic constants that were
subsequently decreased from 20.0, 10.0, 5.0, 2.0, 1.0, to 0.5
kcal mol21
Å22
for every 2 000 steps (4 ps). The minimized protein
model was subjected to the next heating and equilibration step. The
temperature of the system was gradually increased from 50 K to 298 K
in 200 000 steps (400 ps) with harmonic restraints of 0.05
kcal mol21
Å22
on Ca atom positions. Then, the equilibrated structure
was used as the starting model for production MD runs. All trajectories
were calculated with the leapfrog verlet algorithm at 298 K. Model
structures are saved every 500 steps (1ps) in each trajectory. In the
short and the long MDs, a total of 72 000 (1200*60) and 400 000
(20 000*20) models were extracted from trajectories, respectively.
2.3 | Model filtering
Following the FEIG method,20,21
extracted models from MD trajectories
were cross-evaluated by a statistical knowledge-based potential
(we used DFIRE29
). We have also calculated the GDT-HA between the
starting model and the extracted models after MD (denoted as
iGDT_HA). These two parameters for the filtering are illustrated in Figure
1B. The DFIRE score and iGDT_HA of each selected model were
normalized by computing Z score, using a distribution of structures
from each MD trajectory as follows:
FIGURE 2 Results of model selection from MD trajectories with different parameter settings, r, u, and g. For the explanation of the
parameters, see Figure 1B. The distribution of the average dGDT-HA of selected models from the short MD (left) and the long MD (right)
trajectories are shown in a color scale from dark red to purple for negatively large dGDT-HA, 23 to over 20.5. dGDT-HA is the difference
of the GDT-HA to the native structure of the initial model to that of the average of the selected models using a corresponding parameter
set. A white region means that no models exist for the corresponding parameter combinations
TERASHI AND KIHARA | 191
Z iGDT HAm5
iGDT HAm2iGDT HA
riGDT HA
(1)
Z DFIREm5
DFIREm2DFIRE
rDFIRE
(2)
where iGDT HA and DFIRE are average values, and riGDT HA and
rDFIRE are standard deviations of iGDT_HA and DFIRE. For DFIRE,
structures with negative Z scores are those which are more geometrically
favorable than the average (Z score 5 0). For iGDT-HA, structures
with a positive value are those which are more similar to the initial
structure than the average.
To select models, we applied a filter (Figure 1B) that extracts a pieshaped
area between angle u6g degree and the radial distance r from
the center of distribution of Z iGDTHAm and Z DFIREm. The criteria for
selecting model m were
Z iGDT HAm
2
1Z DFIREm
2
> r (3)
and
arccos
Z iGDT HAmcosu1Z DFIREmcosu
Z iGDT HAm
2
1Z DFIREm
2
 
< g (4)
which corresponds to the lower-right region in red in Figure 1B. Thus,
the intention is that, among models from MD trajectories, we would
like to select those which have relatively low (better) statistical potential
and less deviation from the initial model.
For the extracted models from the Short MD trajectories, we used
r5 2.0, u 5 310 and g 5 35 in the filtering step. For the Long MD, we
used r5 1.5, u 5 325 and g 5 30. These parameters were chosen
based on a benchmark study performed on the CASP11 dataset (discussed
in Results). After the filtering, 1 0004 500 and 1 00025 000
models were selected from the short MD and the long MD trajectories.
Selected models were averaged, which were subject to the structure
relaxation and energy minimization (Model 1 and Model 2 in Figure 1A).
This protocol is different from the FEIG method21
used in CASP11
in the following ways: First, the MD runs in our protocol were much
shorter. We used 1.2 ns * 60 trajectories (the short MD runs) and 20 ns *
20 trajectories (the long MD runs), thus in total of 472 ns MD runs, while
the FEIG method used 1200 ns long runs (40 ns * 30). Second, we used
an implicit solvent model while the FEIG method used explicit solvent.
These two differences make our protocol more computationally inexpensive
and affordable. There are also other technical differences, described
in the following. Third, as mentioned above, we applied Ca restraints in
the MD runs that increased over time from 0.1 to 0.4 kcal mol21
Å22
where FEIG used a constant value of 0.05 kcal mol21
Å22
. Fourth, the
interval of structure snap shots taken was 1 ps in our protocol, while
FEIG used 40 ps. Fifth, for the filtering (Figure 1B), we used iGDT-HA
and DFIRE, while the FEIG method used iRMSD and RW1.30
2.4 | Structure relaxation and energy minimization
Averaged models underwent energy minimization with 500 steps of
the steepest descent algorithm and 4 500 steps of ABNR. The minimized
models were relaxed with a 40 ps MD simulation. In the minimization
and relaxation, we used strong harmonic restraints of 100
kcal mol21
Å22
on C-a atom positions. The model 3–5 were selected
from all extracted models with the lowest DFIRE, the lowest GOAP31
score and the highest iGDT-HA (Figure 1A).
2.5 | Computational costs
For a 200-residues target protein, the single 0.4 ns equilibration and
1.2 ns MD simulation took about 13.2 and 40 CPU hours, respectively.
The total computational cost of the short MD simulations (60 trajectories)
was about 3,200 CPU hours per target (2.7 hours on 1 200 cores
of Intel Xeon-E5 CPU). A single 20 ns MD simulation took about 640
CPU hours. Consequently, the total computational costs of the long
MD (20*20 ns MDs) was about 12,800 CPU hours for a refinement
target (64 hours on 200 cores of Intel Xeon-E5 CPU).
3 | RESULTS AND DISCUSSIONS
First we describe benchmark results on the CASP11 refinement dataset,
then show the results of our group in CASP12.
3.1 | Parameter optimization for model selection using
the CASP11 dataset
As a preparation for participating in CASP12, we optimized parameters,
r, u, and g that were used in the filtering protocol (Figure 1B) on the 36
TABLE 1 Average performance of our protocol in comparison with
top10 groups in CASP11
Groupa
Group ID GDT-TS GDT-HA RMS_CA
FEIG 288 74.63 56.45 3.58
Seok 296 72.45 53.71 3.62
Seok-refine 423 72.61 53.56 3.59
Schroderlab 396 73.27 55.07 3.67
PRINCETON_TIGRESS 106 72.75 53.98 3.65
Kiharalab 333 72.88 54.22 3.57
LEE 169 72.14 53.31 3.65
BAKER 64 71.20 52.25 3.86
nns 038 71.57 52.51 3.66
Seok-server 011 72.66 53.93 3.64
Average of all 53 Groups 　n/a 69.13 50.08 3.99
Starting model n/a 71.96 53.03 3.69
Short MD n/a 73.26 54.27 3.62
Long MDa
n/a 70.48 50.82 3.84
The names of top 10 groups were obtained ranked according to the
CASP11 web site, assessors’ formula.
(http://predictioncenter.org/casp11/zscores_final_refine.cgi?
formula 5 assessors).
a
The results are for 31 out of the 36 targets for which the long MD
runs finished before the CASP12 has started to release refinement
targets.
192 | TERASHI AND KIHARA
refinement targets from CASP11. The dataset included the target
TR217 to TR857 excluding TR795, whose native structure was not
available at the time of the work. The starting models and the native
structure of these targets were downloaded from the CASP11 website
(http://predictioncenter.org/casp11/). The size of the target proteins
ranged from 62 to 288 residues (average: 155). The Ca RMSD of the
starting models to their native structures ranged from 1.45 to 12.45 Å
(average: 3.69 Å), GDT-TS ranged from 46.17 to 90.24 (average:
71.96), and GDT-HA were from 29.10 to 73.51 (average: 53.03).
The parameter optimization was performed separately for the
short and the long MD runs. For the short MD runs we generated forty
1.2 ns-long trajectories while for the long MD runs we computed up to
three 20 ns-long trajectories for the starting models of the targets.
Long MD runs were finished only for 31 out of 36 targets before the
first refinement target was released in CASP12.
We first tested in total of 3888 (5 3*72*18) combinations of the
three parameters (r, u, g) for selecting models (Figure 1B), which come
from three values, 1.0, 1.5, and 2.0 for r, 72 values from 0 to 355 with
an interval of 5 for u, and 18 values from 5 to 90 with an interval of 5
for g. We examined the average change of GDT-HA of the selected
models with each parameter set from that of the initial model (dGDTHA).
The results are visualized with a color scale in Figure 2. Higher in
the color scale, purple to blue, are better than dark red that is at the
bottom of the scale. Several important trends were observed: (1) Interestingly,
as shown in Figure 2, none of the parameter combination
gave on average better GDT-HA (i.e., positive dGDT-HA) than the
starting model. However, as we show later, averaging structures
selected by a good parameter set improved GDT-HA from the starting
model. (2) Also, it was evident that the short MD runs (left panels) gave
better results than the long MD runs (right panels). (3) The parameter
space that gave better results locates at the right bottom corner of the
panel, where u is around 300 to 350 and g is around 0 to 30 degrees.
This region corresponds to the red regions in Figure 1B. (4) For this
region, using a larger radius r gave better results. (5) The parameter
space that did not perform well are at the middle bottom of the panel,
where u is around 150 and g is around 0 to 50 degrees. This is the
opposite region from the good performing region shown in red in Figure
1B.
We selected 76 and 40 parameter combinations with largest
dGDT-HA for the short and long MD runs. Then, for each parameter
combination, we generated an averaged structure model from the
selected models by the combination. The generated models were evaluated
by dGDT-HA. A combination of r 5 2.0, u 5 310, and g 5 35
was found to be optimal for the short MD trajectories and a r 5 1.5, u
5 325, and g 5 30 combination was best for the long MD runs.
3.2 | Refinement results on the CASP11 targets
Table 1 summarizes the performance of our protocol using the optimized
refinement protocol with short and long MDs (Figure 1) on the
CASP11 refinement targets. For comparison, results of the top 10
groups in CASP11 including our group (Kiharalab) are shown. Results
are on the first model (Model 1) of the groups. In the table, the average
value of three scores, GDT-TS, GDT-HA, and Ca-RMSD (RMS_CA) are
shown, which were major evaluation scores used by the CASP assessors.
GDT-TS (Global Distance Test-Total Score) and GDT-HA (Global
Distance Test-High Accuracy) are the average of the percentage of Ca
FIGURE 3 Comparison of the refined models by the short MD
protocol on the CASP11 refinement targets. Models were
evaluated by GDT-TS in the left column and by GDT-HA in the
right column. A, refined models by the short MD in comparison
with starting models. B, the short MD results compared with the
long MD results. C, The refined models with the short MD runs
compared with models submitted by Kiharalab (Group number 333)
in CASP11. D, the short MD results compared with models by
FEIG (Group number 288) in CASP11
TERASHI AND KIHARA | 193
atoms within four distance cutoffs from the corresponding Ca atoms in
the native structure after structure superimposition. GDT-TS uses 1.0,
2.0, 4.0, and 8.0 Å while GDT-HA uses 0.5, 1.0, 2.0, and 4.0 Å for the
distance cutoffs. Both scores ranges from 0 to 100 where 100 is the
best score for a model. RMS_CA is RMSD of Ca atoms of a model to
the native, which was calculated with the LGA program.32
Seven groups, FEIG, Seok, Seok-refine, Schroderlab, PRINCETON_TIGRESS,
Kiharalab, and Lee showed improvement over the
starting model in terms of all three scores, GDT-TS, GDT-HA, and
RMS_CA (Table 1). In CASP11, our group (Kiharalab) used twenty10 ns
MD runs with the Screened Coulomb Potential implicit solvent model
(SCPISM). The current protocol using the short and long MD runs are
shown at the bottom of the table. The Short MD runs performed very
well, ranking the third in terms of GDT-HA (54.27) and GDT-TS (73.26)
and the fourth for RMS_CA (3.62). The long MD runs performed worse
than the short runs. On average, it failed to improve the starting models
and ranked lower than the top 10 groups when GDT-TS and GDTHA
were considered, and was ranked ninth for RMS_CA.
In Figure 3, we examined refinement results with the short MD
protocol in comparison with other refinement protocols. Figure 3A
shows that short MD improved from the starting models in majority of
the cases, 26 (72.2%) and 21 (58.3%) out of 36 targets in terms of GDTTS
and GDT-HA, respectively. It is also observed in Figure 3A that
improvement by the short MD did not depend on the initial quality of
the starting models. Next, we compared with the results with the long
MD runs (Figure 3B). Consistent with the data shown in Table 1 and Figure
2, the short MD performed substantially better than the long MD. In
terms of GDT-TS and GDT-HA, the models of the short MD were better
for 26 and 27 targets (83.9% and 87.1%) than the long MD models
among the 31 targets for which we had data with the long MD runs. In
the next two panels, we compared the short MD refinement with the
models submitted in CASP11 by Kiharalab (Figure 3C) and FEIG (Figure
3D). Compared with CASP11 Kiharalab models, the short MD’s results
were comparable. For about half of targets (17/36 targets), the short
MD models had better GDT-TS and GDT-HA than the Kiharalab models.
On the other hands, for only 7 (19.4%) targets the short MD models had
better GDT-TS and GDT-HA than the FEIG models (Figure 3D). However,
it is worth noting that the computational cost for the short MD
protocol is much smaller than FEIG. The former used in total of 48 ns
(40*1.2 ns) MD runs with implicit solvent while the latter used 1.2 ls
MD runs with the TIP3P explicit solvent model.21
3.3 | Results in CASP12
Now we discuss our group’s performance in CASP12. In CASP12, we
applied our refinement protocol to all 42 refinement targets from
TR520 to TR948. The starting models were obtained from CASP website
(http://predictioncenter.org/casp12/). The residue length of the
targets were 54–414 residues (average: 193). The initial quality of the
starting models ranged from 1.15 to 13.86 Å Ca RMSD (average: 5.5
Å), 37.03 to 92.07 in terms of GDT-TS (average: 66.93), and GDT-HA
ranged from 24.33 to 78.36 (average: 49.76).
First we see our performance in CASP12 relative to other groups.
Table 2 summarize the average performance of top10 groups in
TABLE 2 Average performances of the top10 groups in the CASP12 refinement targets
Groupa
Group ID Assessors’ formulab
GDT-TS GDT-HA RMS_CA MolProbityc
SphGrd
QCSe
GOAL 220 21.79 67.08 50.13 5.14 2.06 69.05 80.23
Seok 023 18.39 67.79 50.93 5.43 1.11 68.37 81.22
BAKER 247 17.73 67.11 50.48 5.36 0.87 69.28 81.02
Seok-server 250 16.91 67.40 50.34 5.42 1.11 68.05 78.57
SVMQA 208 15.01 67.72 51.01 5.48 1.71 67.30 80.70
FEIG 204 13.66 67.58 50.89 5.51 0.94 66.67 79.81
LEEab 450 13.58 64.94 47.42 5.37 1.83 68.13 78.53
Kiharalab 102 12.38 67.33 50.46 5.52 1.45 66.80 80.44
GOAL_COMPLEX 430 11.87 67.33 50.78 5.52 1.80 66.67 80.45
LEE 011 11.75 65.76 48.42 5.32 1.80 67.66 80.21
Average of All
39 Groups
n/a　 211.57 62.85 45.85 6.14 2.08 62.87 76.14
Starting model n/a n/a 66.93 49.76 5.50 1.77 66.99 79.74
a
The names of Top 10 groups were obtained from CASP12 result page (http://predictioncenter.org/casp12/zscores_final_refine.cgi?formula 5 assessors)
ranked by the assessors’ formula.
b
Combined Z score of GDT-HA, RMS_CA, SphGr, QCS and MolProbity score defined as;
0:17ZGDT2HA20:46ZRMSC A10:20ZSphGr10:15ZQCS20:02ZMolProbity.
c
MolProbity considers the number of steric clashes and the percentages of outliers in rotamer and backbone conformations. A low MolProbity score
indicates that a model is more physically favorable.
d
SphereGrinder evaluates local structural similarity between a model and the native structure.
e
Quality Control Score. QCS evaluates the correctness of secondary structure element predictions in a model.
194 | TERASHI AND KIHARA
CASP12. Refined model quality was evaluated by GDT-TS, GDT-HA,
RMS_CA, MolProbity,33
SphereGrinder (SphGr),34
and Quality Control
Score (QCS),35
which were the scores used in assessors’ evaluation.
Kiharalab was ranked eighth according to the asessors’ formula (see
Table 2 caption). In terms of individual scores, we were ranked fifth in
GDT-TS, sixth in GDT-HA, ninth in RMS_CA, fifth in MolProbity, eighth
in SphGr, and fifth in QCS. These ranking results are slightly worse
than in CASP11, where our group was ranked at fourth (the CASP11
evaluation paper,15
Table 2).
It is noted that the differences of individual scores between the
top 10 groups are small. Interestingly, the difference between Kiharalab
and FEIG is very small, and indeed became smaller in CASP12 relative
to CASP11. For example, the average difference of GDT-HA between
Kiharalab and FEIG was 2.23 in CASP11, which became as small as
0.43 this time. To reveal the significance of the differences of the
group performance, we applied the paired Student’s t test on the
common set of predicted targets in CASP12. Table 3 shows the results
on GDT-TS and GDT-HA. According to the test, our group (Kiharalab,
Group ID: 102) showed significantly better results (P values < 0.05)
than LEEab (Group ID: 450), LEE (Group ID: 011), and the starting
model for both GDT-TS and GDT-HA. On the other hands, only
SVMQA (Group ID: 208) performed significantly better than our group,
and the other seven groups were indistinguishable in this test with our
group.
3.4 | Analyses of short MD (model 1) models in
CASP12
From this section, we analyze our submitted models in details. In Figure
4, we examined our Model 1 models generated by the short MD protocols.
First we checked how many cases the Model 1 improved over
starting models (Figure 4A). When evaluated by GDT-TS and GDT-HA,
TABLE 3 Head-to-head comparison of the top 10 groups in CASP12
(A) Paired t-test on GDT-TS
ID 220 023 247 250 208 204 450 102 430 011 Starting model
220 – 0.84 0.52 0.68 0.82 0.75 0.02 0.65 0.65 0.02 0.40
023 0.16 – 0.18 0.03 0.38 0.31 0.00 0.05 0.04 0.00 0.00
247 0.48 0.82 – 0.67 0.82 0.74 0.01 0.64 0.63 0.03 0.39
250 0.32 0.97 0.33 – 0.87 0.65 0.01 0.40 0.40 0.00 0.04
208 0.18 0.63 0.18 0.13 – 0.34 0.00 0.01 0.00 0.00 0.00
204 0.25 0.69 0.26 0.35 0.66 – 0.01 0.22 0.21 0.00 0.05
450 0.99 1.00 0.99 0.99 1.00 1.00 – 0.99 0.99 0.90 0.98
102 0.35 0.95 0.36 0.60 0.99 0.78 0.01 – 0.48 0.00 0.03
430 0.35 0.96 0.37 0.60 1.00 0.79 0.01 0.52 – 0.00 0.01
011 0.98 1.00 0.98 1.00 1.00 1.00 0.10 1.00 1.00 – 0.98
Starting model 0.60 1.00 0.61 0.96 1.00 0.95 0.02 0.97 0.99 0.02 –
(B) Paired t test on GDT-HA
ID 220 023 247 250 208 204 450 102 430 011 Starting model
220 – 0.86 0.66 0.61 0.87 0.81 0.01 0.69 0.82 0.01 0.30
023 0.14 – 0.29 0.01 0.61 0.47 0.00 0.09 0.31 0.00 0.00
247 0.34 0.71 – 0.43 0.76 0.69 0.00 0.49 0.67 0.01 0.18
250 0.39 0.99 0.58 – 0.98 0.81 0.00 0.66 0.92 0.00 0.04
208 0.13 0.39 0.24 0.02 – 0.40 0.00 0.02 0.13 0.00 0.00
204 0.19 0.53 0.31 0.19 0.60 – 0.00 0.17 0.41 0.00 0.03
450 1.00 1.00 1.00 1.00 1.00 1.00 – 1.00 1.00 0.94 0.99
102 0.31 0.91 0.51 0.34 0.99 0.83 0.00 – 0.92 0.00 0.02
430 0.18 0.69 0.34 0.08 0.87 0.59 0.00 0.08 – 0.00 0.00
011 0.99 1.00 0.99 1.00 1.00 1.00 0.06 1.00 1.00 – 0.97
Starting model 0.71 1.00 0.82 0.97 1.00 0.97 0.01 0.98 1.00 0.03 –
The performances of the top 10 groups were compared using paired Student’s t-tests. Statistically significant wins (P values < 0.05) of the group listed
in the first column from the left against each group listed in the first raw are shown in bold.
TERASHI AND KIHARA | 195
25 (59.5%) and 29 (69.0%) out of 42 targets were improved, respectively.
These fractions of improved targets are similar to those
observed on the CASP11 dataset (Figure 3A). Consistent with what
was observed in the CASP11 dataset (Figure 3A), improvements were
observed to starting models of various initial quality.
When compared with models from the long MD runs, which were
submitted as Model 2 models, the short MD models were better for 30
(71.4%) and 33 (78.6%) out of 42 targets. This result is qualitatively
consistent with the observation on the CASP11 dataset, but the fractions
of the wins by the short MD models are lower than before (Figure
3B). To understand the better performance of the short MD over
the long MD, we performed short-MD-based refinement using the
constraints of 0.05 kcal mol21
Å22
, the relatively weak constraint we
used in the long-MD refinement. This comparison was performed on
FIGURE 4 Comparison of short MD models submitted as Model 1 with other models in CASP12. GDT-TS (on the left column) and GDTHA
(right) are used for evaluation. A, comparison with the starting models. B, compared with refined models with the long MD runs that
were submitted as Model 2. C, comparison with Model 1 models from the FEIG group
196 | TERASHI AND KIHARA
36 CASP12 refinement targets that had their native structures available.
TR944 had its native structure in PDB but was excluded from the
analysis because its trajectory files used in CASP12 were corrupted
and could not be used at the time of the post-analysis. With the
increasing constraint strength of 0.1, 0.2 to 0.4 kcal mol21
Å22
, which
was used in CASP12, the average GDT-TS and GDT-HA obtained for
the 36 targets were 67.32 and 50.11, respectively. These values were
decreased to 66.29, and 48.60 for GDT-TS and GDT-HA, respectively,
when the constant 0.05 kcal mol21
Å22
was used. Thus, we would
have obtained better results with long-MD-based refinement if a stronger
constraint had been used.
Long MD performed substantially worse than short MD for highquality
targets whose initial GDT-HA were >70 (Figure 5). This is probably
because moving target structures far away from initial structures
by the long MD was more harmful for targets that were already in high
quality.
We also examined if the oligomeric state of targets affected to
the refinement results. In Table 4, we show the average GDT-HA of
monomer and oligomer targets in CASP12. Both short MD and long
MD performed worse on the oligomer targets and the difference
between the short MD- and the long MD-based refinement was
smaller for the oligomer targets. Thus, it is not the case that the long
MD worked particularly worse on the oligomer targets. The reason of
the worse performance on the oligomer targets would probably
because we applied the refinement protocol to a single target protein
even for an oligomer target without considering physical interaction to
other proteins. This would mean, conversely, a structure would be better
refined when its interacting proteins, either other subunits in a
complex if there are any, or crystal contacts in the protein crystal is
considered in refinement.
Next, we compared with the Model 1 models from FEIG, which
used a similar MD-based refinement protocol (Figure 4C). The FEIG
models were better than Kiharalab in 27 (64.3%) and 25 (59.5%) out of
42 targets in terms of GDT-TS and GDT-HA, respectively. This difference
between the two groups is much smaller than on the CASP11
dataset (Figure 3D), which is consistent with the results shown as overall
average scores in Table 2 and the results in Table 3 that shows the
two groups were statistically indistinguishable.
3.5 | Examples of refined models
Examples of models with successful and failed refinement are shown in
Figure 6. Improved and deteriorated regions in a model are colored in
blue and red, the darker more substantial. Green regions are those which
did not move >0.1 Å. The first example in the top row is TR948. For this
target, the overall improvement of GDT-HA (dGDT-HA) was large, 4.70,
and this model was ranked sixth among all the first models submitted by
the 36 groups. As shown in the color code, improvement occurred at
almost all the helical regions in the structure and degradation occurred at
ends of some helices. The next one, TR912, is another successful example,
where dGDT-HA of 4.58 was achieved. This model was the best in
GDT-HA among all the 31 groups’ Model 1 models. Similar to the previous
example, improvement occurred globally, at almost all b-strands in
the structure. In TR868, the third example, there was a modest improvement
where dGDT-HA at 0.72 was observed. This model was ranked
seventh among 34 groups who submitted models for this target. In this
refined model, improved and degraded regions co-exist, mixed in the
structure, which is typically observed in models with a small improvement
of <1.0 dGDT-HA. The last one, TR891, is a case that our refinement
failed. The model had a dGDT-HA of 23.57 and ranked 18th among 36
groups. As shown, the refinement protocol moved all the b-sheets away
from the native structure. We observed failure for other three targets of
b-barrel structures, too (TR879, dGDT-HA of 25.0; TR891, 23.57;
TR928, 22.79). Overall, these examples illustrate that improvement and
deterioration occurred globally in a model including the structure core
rather than merely moving flexible loop regions.
3.6 | Relaxing or compressing?
Observing that the structural change occurs globally to a model by
our refinement protocol, we questioned whether the observed
FIGURE 5 GDT-HA difference between short MD and long MD
models relative to the initial quality of the targets. The x axis
shows GDT-HA of the starting models. The y axis shows the difference
of GDT-HA of Model 1 (short MD) and Model 2 (long MD).
The positive value indicates that GDT-HA of Model 1 was higher
than Model 2
TABLE 4 Average GDT-HA of monomer and oligomer targets in
CASP12
No. of Targets Short MD Long MD Difference
Monomers 24 52.69 49.82 2.88
Oligomers 18 47.49 46.32 1.17
Among the 48 refinement targets, the following targets are oligomers:
TR520, 594, 694, 862, 866, 870, 875, 877, 881, 887, 893, 896, 909,
912, 913, 917, 945, 947 (all IDs with TR as prefix).
TERASHI AND KIHARA | 197
improvement was due to simply compression of the structure since it
is widely known that compression of Ca coordinates of a model
decreases the radius of gyration, which contributes to apparent
improvement of some quality assessment scores, such as GDT-TS,
GDT-HA, and RMSD. To answer this question, we evaluated a compactness
of refined models and the starting models by comparing the
radius of gyration (Rg) of the structures. It is defined as:
Rg5
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
PN
i
jvi2vj2
N
v
u
u
u
t
(5)
where N is a total number of Ca atoms in the model, vi is the coordinate
of ith Ca atom, v is the average coordinate of all Ca atoms of the
model. In this calculation, we ignored largely incorrect regions in the
FIGURE 6 Examples of successful and failed refinement by our group. The left column shows the native structures (magenta) and the
starting models (cyan). The right column shows our Model 1 models that were refined with the short MD runs. The refined models are
colored according to the degree of improvement of Ca atom positions from the starting models. Improved regions in a model are colored
from light blue to dark blue for small to large improvements. On the other hand, deteriorated regions are colored from light to dark red for
slight to large deteriorations. Green represents regions that did not change >0.1 Å. Deviation of the Ca positions of a model from the
starting structure was judged after superimposing the starting structure and the model to the native structure using the LGA program with
a 4.0 Å threshold
198 | TERASHI AND KIHARA
starting model where the distance between the corresponding Ca
atom positions to the native structure was larger than 4.0 Å, because
these regions are highly unlikely to influence refined model’s GDT-TS
and more so for GDT-HA. To assess the compression or relaxation of
refined models, we computed the difference of Rg between the starting
model and the refine model (dRg), dRg 5 Rg(refined model)2 Rg(starting
model). A positive dRg indicates that the refined model was relaxed
(expanded) while a negative value shows the model was compressed
from the starting model.
In Figure 7A, the improvement of models (dGDT-HA) was presented
in a color code relative to dRg and GDT-HA of starting models.
First, by examining dRg, models for 32 out of 37 targets (five targets
were excluded from this analysis because their native structures were
not available for computing GDT-HA of their starting models) have
positive values, indicating that the refinement actually expanded (or
relaxed), not compressed the structures. This figure also shows that the
degree of the relaxation did not depend on the quality of the starting
models and larger improvement (points in blue) occurred for starting
models with a middle range GDT-HA and dRg, namely about 50 and
0.2, respectively. Figure 7B compares dGDT-HA with dRg and the deviation
of refined models from their starting structures (iGDT-HA). There
is an obvious correlation between iGDT-HA and dRg, which simply
shows that the model drifted away from the initial structure as it
expanded (larger dRg). An interesting observation is that two
FIGURE 7 Refinement results relative to the change of radius of gyration of models. Improvement of models (dGDT-HA) is shown in color
code relative to the change of the radius of gyration (dRg) by the short MD refinement protocol. dGDT-HA of over 24.0 to >4.0 is shown
in a color scale from red to blue. Each data point represents a Model 1 refined model for the 37 targets that have their native structure
available for the analysis. A, The x axis shows the quality, GDT-HA of starting models. B, The x axis is the structural deviation of refined
models form the starting model (iGDT-HA)
FIGURE 8 Improvement of GDT-HA (dGDT-HA) relative to the
quality of starting models (GDT-HA(Starting Model)). Red points
represent Model 1 models and open circles represent Model 2 to
Model 5. The best dGDT-HA models among the five models for
each target are connected with a line
TABLE 5 Average performance of Kiharalab model 1–5 in CASP12
GDT-TS GDT-HA RMS_CA MolProbity SphGr QCS
Model 1a
67.33 50.46 5.52 1.45 66.80 80.44
Model 2b
65.84 48.32 5.51 1.80 66.11 79.76
Model 3c
65.29 47.19 5.59 2.01 65.85 78.79
Model 4d
64.37 46.22 5.63 1.94 65.40 76.73
Model 5e
66.16 48.38 5.56 2.10 65.59 79.84
Starting
Model
66.93 49.76 5.50 1.77 66.99 79.74
The best result among Model 1–5 and the starting model for each score
is shown in bold.
a
Averaged and relaxed model generated from the subset of short MD
trajectories.
b
Averaged and relaxed model generated from the subset of long MD
trajectories.
c
The lowest DFIRE model.
d
The lowest GOAP model.
e
The highest iGDT-HA model.
TERASHI AND KIHARA | 199
unsuccessful refined models (TR879, dGDT-HA: 25.0; TR928, dGDTHA:
22.8), which are shown in red and orange, are found at high dRg
(0.47 and 0.55, respectively) and low iGDT-HA (59.7 and 73.8, respectively),
distinct from the other models, in Figure 7B. This result suggests
that models of unsuccessful refinement may be better identified by the
combination of iGDT-HA and dRg rather than only using iGDT-HA.
This idea works particularly well for distinguishing TR879 (the red data
point) from the other models that have a similar iGDT-HA value.
3.7 | What went right and what went wrong
Following the tradition of the CASP predictors’ reports, we discuss
things that worked well and those which need improvement.
One thing which clearly worked well was the ranking of the submitted
models. Table 5 summarizes the average of evaluation scores of
Model 1 to 5 and Figure 8 presents dGDT-HA of individual models relative
to the quality (GDT-HA) of the starting models. In the figure,
Model 1 models are shown in red and the best model (i.e., the model
with the largest dGDT-HA) for each target are connected with lines.
From Table 5, Model 1 models were on average the best among the
five submitted models for all the evaluation scores except for that of
the RMS_CA, where Model 1 was ranked second, following Model 2.
Figure 8 visualizes the same conclusion; 28 out of 42, of the Model 1
models were the best for the targets, and if not they were close to the
best.
Second, as discussed with Figure 4A, our refinement protocol with
short MD runs improved models for most of the cases. Additionally,
the structure sampling from short MD runs with an increasing Ca constraints,
which increased from 0.1, 0.2 to 0.4 kcal mol21
Å22
for every
400 ps, worked well. As shown in Table 6, sampling structures from different
portions of MD runs we tried all worked worse than the method
we used. Thus, overall, we can conclude that we were successful in
exploiting inexpensive short MD runs with an implicit solvent model
very effectively. This point becomes evident when our group’s results
were compared with a contrasting approach that used significantly
more expensive MD runs but had similar performance (Table 2).
On the other hand, by design our protocol could not make large
refinement to models due to the use of short MD simulations. To make
substantial corrections to a model conformation, such as rearrangement
of secondary structures or domain moves, a completely different
algorithm design, probably with a different protein model, such as a
coarse-grained model,2,36,37
is obviously needed. Indeed, this is the
challenge left for the whole CASP refinement community.
4 | CONCLUSION
We discussed our group’s performance in the CASP12 refinement category.
Our protocol makes use of inexpensive short MD simulations
with implicit solvent and successfully showed consistent improvements
to starting models regardless of the quality of the starting models. By
examining submitted models, we found that achieved improvements
are due to relaxation of structures rather than compression, which also
suggested that the degree of relaxation (dRg) could be another metric
to eliminate unsuccessful refined models. However, the protocol does
not make large conformational refinement by design due to the use of
short MD trajectories, which is still the goal of further development.
ACKNOWLEDGMENTS
The authors thank Kevin Shim for proofreading the manuscript. This
work was partly supported by National Institutes of Health
(R01GM123055) and National Science Foundation (IIS1319551,
DBI1262189, IOS1127027, DMS1614777).
ORCID
Daisuke Kihara http://orcid.org/0000-0003-4091-6614
REFERENCES
[1] Kinch LN, Li W, Monastyrskyy B, Kryshtafovych A, Grishin NV.
Evaluation of free modeling targets in CASP11 and ROLL. Proteins.
2016;84(Suppl 1):51–66.
[2] Kihara D, Lu H, Kolinski A, Skolnick J. TOUCHSTONE: an ab initio
protein structure prediction method that uses threading-based tertiary
restraints. Proc Natl Acad Sci USA. 2001;98(18):10125–10130.
[3] Modi V, Xu Q, Adhikari S, Dunbrack RL Jr.Assessment of templatebased
modeling of protein structure in CASP11. Proteins. 2016;84
(Suppl 1):200–220.
[4] Moult J, Fidelis K, Kryshtafovych A, Schwede T, Tramontano A. Critical
assessment of methods of protein structure prediction: progress
and new directions in round XI. Proteins. 2016;84(Suppl 1):4–14.
[5] Qu X, Swanson R, Day R, Tsai J. A guide to template based structure
prediction. Curr Protein Peptide Sci. 2009;10(3):270–285.
[6] Moult J, Pedersen JT, Judson R, Fidelis K. A large-scale experiment to
assess protein structure prediction methods. Proteins. 1995;23(3):2–4.
[7] Kryshtafovych A, Fidelis K, Moult J. Progress from CASP6 to
CASP7. Proteins. 2007;69(Suppl 8):194–207.
TABLE 6 Results of using different structure sampling form short
MD runs
Ca restraintsa
GDT-TS GDT-HA
Section 1 (400 ps) 0.1 66.73 49.21
Section 1, 2 (800 ps) 0.1, 0.2 67.06 49.70
Section 1, 2, 3 (1.2 ns) 0.1, 0.2, 0.4 67.32 50.11
Section 2 (400 ps) 0.2 67.11 49.78
Section 3 (400 ps) 0.4 67.27 50.08
Starting model n/a 67.06 49.80
In the short MD runs of 1.2 ns in total, as described in Methods, we
applied an increasing Ca constraints from 0.1, 0.2, to 0.4 to three 400
ps-long subsections sequentially. In this small experiment, structures are
sampled from different subsections of the MD runs, which underwent
the structure averaging and relaxing procedure to yield a final model.
GDT-TS and GDT-HA are average of models for 36 targets, which had
the native structure available from PDB. TR944 has its native structure
in PDB but was excluded from this data, because the trajectory files
used in CASP12 were corrupted and could not be used.
a
The unit is kcal/mol/Å2
. If more than one value is shown, each was
applied subsequently to each subsection in MD trajectories.
200 | TERASHI AND KIHARA
[8] Kryshtafovych A, Fidelis K, Moult J. CASP8 results in context of
previous experiments. Proteins. 2009;77(Suppl 9):217–228.
[9] Kryshtafovych A, Fidelis K, Moult J. CASP9 results compared to
those of previous CASP experiments. Proteins. 2011;79(Suppl 10):
196–207.
[10] Kryshtafovych A, Fidelis K, Moult J. CASP10 results compared to
those of previous CASP experiments. Proteins. 2014;82(Suppl 2):
164–174.
[11] Kihara D, ed. Protein Structure Prediction. New York: Humana Press;
2014.
[12] Padilla-Sanchez V, Gao S, Kim HR, et al. Structure-function analysis
of the DNA translocating portal of the bacteriophage T4 packaging
machine. J Mol Biol. 2014;426(5):1019–1038.
[13] Marti-Renom MA, Stuart AC, Fiser A, Sanchez R, Melo F, Sali A.
Comparative protein structure modeling of genes and genomes.
Annu Rev Biophys Biomol Struct. 2000;29:291.
[14] Baker D, Sali A. Protein structure prediction and structural
genomics. Science. 2001;294(5540):93–96.
[15] Modi V, Dunbrack RL Jr. Assessment of refinement of templatebased
models in CASP11. Proteins. 2016;84(Suppl 1):260–281.
[16] an H, Mark AE. Refinement of homology-based protein structures
by molecular dynamics simulation techniques. Protein Sci. 2004;13
(1):211–220.
[17] MacCallum JL, Perez A, Schnieders MJ, Hua L, Jacobson MP, Dill
KA. Assessment of protein structure refinement in CASP9. Proteins.
2011;79(Suppl 10):74–90.
[18] Nugent T, Cozzetto D, Jones DT. Evaluation of predictions in the
CASP10 model refinement category. Proteins. 2014;82(Suppl 2):98–
111.
[19] Kopp J, Bordoli L, Battey JN, Kiefer F, Schwede T. Assessment of
CASP7 predictions for template-based modeling targets. Proteins.
2007;69(Suppl 8):38–56.
[20] Mirjalili V, Noyes K, Feig M. Physics-based protein structure refinement
through multiple molecular dynamics trajectories and structure
averaging. Proteins. 2014;82(Suppl 2):196–207.
[21] Feig M, Mirjalili V. Protein structure refinement via moleculardynamics
simulations: What works and what does not? Proteins.
2016;84(Suppl 1):282–292.
[22] Khoury GA, Smadbeck J, Kieslich CA, et al. Princeton_TIGRESS 2.0:
High refinement consistency and net gains through support vector
machines and molecular dynamics in double-blind predictions during
the CASP11 experiment. Proteins. 2017;85(6):1078–1098.
[23] Joung I, Lee SY, Cheng Q, et al. Template-free modeling by LEE and
LEER in CASP11. Proteins. 2016;84(Suppl 1):118–130.
[24] Della Corte D, Wildberg A, Schroder GF. Protein structure refinement
with adaptively restrained homologous replicas. Proteins.
2016;84(Suppl 1):302–313.
[25] Lee GR, Heo L, Seok C. Effective protein model structure refinement
by loop modeling and overall relaxation. Proteins. 2016;84
(Suppl 1):293–301.
[26] Haberthur U, Caflisch A. FACTS: fast analytical continuum treatment
of solvation. J Computat Chem. 2008;29(5):701–715.
[27] Hassan SA, Guarnieri F, Mehler EL. A general treatment of solvent
effects based on screened coulomb potentials. J Phys Chem B.
2000;104:6478–6489.
[28] Hua DP, Huang H, Roy A, Post CB. Evaluating the dynamics and
electrostatic interactions of folded proteins in implicit solvents. Protein
Sci. 2016;25(1):204–218.
[29] Zhou H, Zhou Y. Distance-scaled, finite ideal-gas reference state
improves structure-derived potentials of mean force for structure
selection and stability prediction. Protein Sci 2002.11(11):2714–
2726.
[30] Zhang J, Zhang Y. A novel side-chain orientation dependent potential
derived from random-walk reference state for protein fold
selection and structure prediction. PloS One. 2010;5(10):e15386.
[31] Zhou H, Skolnick J. GOAP: a generalized orientation-dependent, allatom
statistical potential for protein structure prediction. Biophys J.
2011;101(8):2043–2052.
[32] Zemla A. LGA: a method for finding 3D similarities in protein structures.
Nucleic Acids Res. 2003;31(13):3370.
[33] Chen VB, Arendall WB III, Headd JJ, et al. MolProbity: all-atom
structure validation for macromolecular crystallography. Acta Crystallograph
Sect D Biol Crystallogr. 2010;66(Part 1):12–21.
[34] Kryshtafovych A, Monastyrskyy B, Fidelis K. CASP prediction center
infrastructure and evaluation measures in CASP10 and CASP ROLL.
Proteins. 2014;82(Suppl 2):7–13.
[35] Cong Q, Kinch LN, Pei J, et al. An automatic method for CASP9
free modeling structure prediction assessment. Bioinformatics. 2011;
27(24):3371–3378.
[36] Kolinski A. Protein modeling and structure prediction with a
reduced representation. Acta Biochim Pol. 2004;51(2):349–371.
[37] Sieradzan AK, Krupa P, Scheraga HA, Liwo A, Czaplewski C.
Physics-based potentials for the coupling between backbone- and
side-chain-local conformational states in the united residue (UNRES)
force field for protein simulations. J Chem Theory Computat. 2015;
11(2):817–831.
How to cite this article: Terashi G, Kihara D. Protein structure
model refinement in CASP12 using short and long molecular
dynamics simulations in implicit solvent. Proteins. 2018;86:189–
201. https://doi.org/10.1002/prot.25373
TERASHI AND KIHARA | 201