149

DEVELOPMENT OF A NEW META-SCORE FOR PROTEINSTRUCTURE PREDICTION FROM SEVEN ALL-ATOM DISTANCE
DEPENDENT POTENTIALS USING SUPPORT VECTOR REGRESSION
MATSUYUKI SHIROTA1,2
mshirota@hgc.jp

TAKASHI ISHIDA1
t-ishida@hgc.jp

KENGO KINOSHITA1,2
kinosita@hgc.jp
1

Human Genome Center, Institute of Medical Science, University of Tokyo, 4-6-1
Shirokanedai, Minato-ku, Tokyo 108-8639, Japan
2
Institute for Bioinformatics Research and Development, Japan Science and Technology
Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, JapanAn accurate scoring function is required for protein structure prediction. The
scoring function should distinguish the native structure among model structures(decoys) and it also should have correlation with the quality of the decoys.
However, we had observed the trade-off between the two requirements forseven all-atom distance dependent potentials in the previous study, where thenative structure could be discriminated by examining the fine atomic details,
whereas the correlation could be improved by examining coarse-grainedinteractions. To overcome this problem, in this study, we tried to make an
improved scoring function by combining the seven potentials. First, the sevenpotentials were normalized by the expected energy values of the native andreference states of the target protein. Second, the relationship between the sevennormalized energies and the quality (GDT_TS) of the structure were learned
using support vector regression with the decoy sets of CASP6 as the training set.
Then the meta-score was obtained as the predicted GDT_TS and it was tested
with the decoys of the CASP7 experiment. The meta-score showed
improvement in correlations with the GDT_TS and in the Z-score of the native
structure. It also showed comparable performances in the ΔGDT and enrichment
criteria, with the best component potentials. The meta-score could be also usedas the absolute quality of the structures. Our study suggests the benefit ofcombining several different scoring functions for model evaluation.
Keywords: protein structure prediction; statistical potential; support vector regression; quality
assessment

1.

Introduction

Predicting the native structure of a protein molecule from its amino acid sequence is stilla very challenging task in structural bioinformatics. The process of structure prediction
consists of the following two steps; (i) enumerating a lot of possible model structures, or150 M. Shirota , T. Ishida & K. Kinoshita
decoys, of the target protein and (ii) selecting the most likely structure among them. For
the success of the second process, an accurate scoring function of protein structures is
now required. There have been a large number of attempts for the development of theevaluation function of a protein structure. A large part of the studies relied on theanalysis of known protein structures in the Protein Data Bank [2] to find the mostappropriate structure of the target protein. They are called knowledge-based potentials or
statistical potentials [8, 13, 17, 23, 26]. Statistical potentials are constructed by counting
the occurrence of protein conformations in the PDB, comparing the observed frequency
with the expected one and calculating the energy of the conformation by the log-ratio of
the observed and expected occurrences by assuming of the Boltzmann distribution.
Various structural elements can be used for statistical potentials, such as burial andexposure of residues [7, 19], secondary structures [3], amino acid or atomic contacts [9,25], distances between amino acids or atoms [8, 12-14, 18, 26]. In spite of many efforts
that have been made, a community-wide experiment of protein structure prediction(CASP) showed that it is still difficult to pick up a few suitable models from the sampled
structures [10].
There will be two requirements for a scoring function of model structures. One isto evaluate the native structure as the lowest energy among the non-native structures.
This is expected from the thermodynamic hypothesis of protein folding which states thatthe native state of a protein molecule is the one with the lowest free energy of the system[1]. The other requirement is the correlation between the energy and the quality of thestructures, which originates from the funnel-like potential energy landscape of the protein
molecule [20].
Although it is desirable to fulfill these two requirements, it may be difficult to
optimize the performances of native discrimination and correlation simultaneously. Thisis because the native structure can be discriminated by examining the fine atomic details
such as Van der Waals interactions, whereas the near-native decoys and bad ones can beseparated by examining coarse-grained interactions such as hydrophobicity.
We had observed that there was no single potential that could work best in these two
performances among seven all-atom distance dependent statistical potentials withdifferent reference states [15]. To overcome the trade-off, in this study, we tried to makean improved scoring function that satisfied these two requirements. The new scoring
function, the meta-score, was developed as a predictor of the structural similarity to thenative structure (GDT_TS [22]) by combining the energy values of the seven potentials
with a support vector regression (SVR). The SVR was trained with the CASP6 decoy
sets and tested with the CASP7 decoy sets.
2.

Materials and Methods

2.1. Decoy Sets
The performance of the potentials was evaluated using the decoy sets of the 6th and 7th
CASP (Critical Assessment on the techniques for protein Structure Prediction)
experiments [10, 11]. All of the native and model structures were obtained via the CASP

Meta-Score for Protein Structures 151
web site (http://predictioncenter.org/). We considered protein domains as the unit offolding and employed the definitions of the CASP organizers. The CASP6 and CASP7
decoy sets included 90 and 122 domains, respectively. The model structures with any
missing atoms, for which the corresponding atoms were observed in the native structure,
were removed from the decoy set.
2.2. Quality of the Structure
We defined the quality of a model structure by its structural similarity to the native
structure, measured by the GDT_TS [22]. GDT_TS is the average of the fraction ofmatched residues between the native and model structures within various distancethresholds after global structural superimposition. This score was scaled within [0,1], sothat it approached 1 for good decoys and 0 for bad ones. The GDT_TSs of all the native
structures are 1. We used TM-score program [24] to calculate the GDT_TS.
2.3. Component Statistical Potentials
All the seven all-atom distance dependent potentials have been described previously, andthey were classified according to the hydrophobic and attractive characteristics [15]. A
hydrophobic potential evaluates the clustering of atoms of hydrophobic residues
favorably, whereas an attractive potential prefers compact globular structures. The sevenpotentials were called RAPDF [13], AKBP [8], DFIRE [26], SHELL, BALL, FAR andDS [5]. Briefly, RAPDF is a potential without hydrophobic or attractive characteristics.
SHELL, AKBP and FAR are the potentials in which hydrophobic characteristics areadded to RAPDF. BALL is a potential which consist of RAPDF + attractive
characteristics and DFIRE has both the hydrophobic and attractive characteristics added
to RAPDF. DS has a similar characteristic to RAPDF. These characteristics of potentials
were shown to influence on their performance. The hydrophobic characteristic improved
the correlation with the GDT_TS, but decreased the ability to discriminate the native
structures. An attractive potential worked well for decoys relatively similar to the native
structure, but poor for decoys whose similarities to the native structures were low.
The seven potentials were calculated from the statistics of the non-redundant set of
1,788 SCOP domains. We considered 167 atom types, by treating all of the nonhydrogen atoms to have different types when they are in different amino acid residues[13]. We used the distance intervals described by Zhou and Zhou [26] to count thefrequency at each distance r. The width of the bin was 2 Å for r <2 Å, 0.5 Å for 2 < r < 8
Å, and 1 Å for 8 < r < 15 Å. The atom pairs with more than 15Å separation were notconsidered in the calculation of potentials.
Using these potentials, the raw energy of the model structure was calculated bymodel
E model   nab
 E ab r abr

152 M. Shirota , T. Ishida & K. Kinoshita, where nabmodel is the occurrence of atom pair ab at a distance r in the model structure.
E ab r  is the atom pair interaction energy of the statistical potentials. The atom pair typeab takes 167 x 167 types and the distance r takes 3.5 Å < r < 15 Å. For AKBP and FAR
potentials which have the strongest hydrophobic characteristics, the distance of energy
evaluation was shortened to 3.5 Å < r < 6.5 Å to reduce the hydrophobicity [15] and they
were called AKBP’ and FAR’, respectively.
2.4. Normalization of the All-Atom Distance Dependent Potentials
The potential energies of the model structures calculated above could be compared witheach other, only if all the structures had the same amino acid sequence, because thenumbers and the compositions of the atom pairs in a structure vary with its sequence.
This fact causes some problems in the regression of the quality of structures from theenergies, because different models for various targets with similar GDT_TSs can havequite diverse raw potential values, which are not suitable for regression. The relationshipbetween the energies and the GDT_TS would be different for each target. Therefore, theenergy values should be normalized according to the amino acid sequence for regression.
For this purpose, each of the potentials was normalized as,







~
~
~
E normalized  E model  E reference E native  E reference~ native~ reference, where E
and E
are the estimated potential values for the native andreference state structures, respectively, of the same protein. The normalized energies are
expected to have a constant relationship to the quality of the structure for different
proteins. The details about the normalization will be described elsewhere.
2.5. Development of the Meta-Score
We developed a new meta-score of protein structures by combining the information fromseven normalized energies of the all-atom distance dependent statistical potentials. Thismeta-score can be regarded as a predicted GDT-TS of a structure estimated by aregression from the seven normalized energies. The underlying assumption for thisattempt is that the relationship between the normalized energies and the quality(GDT_TS) would be universal for proteins of various amino acid sequences. This
assumption can be reasonable from the viewpoint that both the normalized energies andthe GDT_TS indicate the energetic and structural distance to the native structure,
respectively, between 0 and 1, regardless of amino acid sequence.
For the purpose, we employed the support vector regression (SVR) algorithm, which
was implemented using the libsvm package [4] with the regression mode. SVR can solve
nonlinear regression problems using the kernel functions. In this study, the Gaussianradial basis function (RBF) was selected as the kernel function. We adjusted two
parameters, the width γ of the Gaussian function and the regularization parameter C. γ
controls how peaked Gaussian functions were and C controls the cost for the regression
errors. These parameters were optimized by the leave-one-out jackknife method using

Meta-Score for Protein Structures 153
CASP6 decoy sets. The meta-scores were trained with various width γ and theregularization parameter C using all but one decoy sets of CASP6, and the resulting
meta-scores were subjected to evaluate the model structures of the remaining decoy set.
Then the correlation coefficients between the meta-score and the GDT_TS were
calculated. All the 90 decoy sets were evaluated in this manner and the parameter set, γ
and C, that yielded the highest averaged correlation coefficient was selected. After thisparameter optimization, a meta-score was trained using all of the 90 CASP6 decoy sets of
17,184 structures with the optimized parameters. The meta-score was tested by the
decoys of CASP7.
2.6. Assessment of Potentials
Five criteria were used for the assessment of the potentials or the meta-score (in thefollowing, the potential values and the meta-scores are simply referred to as scores) as in
the previous study [15]: (1) PCC, the Pearson’s correlation coefficient between the score
and the GDT_TS of the decoys; (2) Z-score, the difference between the native score andthe average of the decoy scores in units of their standard deviation; (3) ΔGDT, thedifference between the GDT_TS of the best decoy and that of the best-scored decoy; and(4, 5), 10% and 20% enrichments; x% enrichment is the relative frequency of the mostaccurate x% models in the GDT_TS among the x% best scored models and x%.
2.7. Statistical Significance of the Difference in Performance
These five assessment measures were calculated for each target domain of CASP7, using
each of the scores, and they were averaged for 104 template-based modeling (TBM)
targets and 18 free modeling (FM) targets. The statistical significance of the difference inperformance between the scores for the TBM and FM categories was assessed by the
Wilcoxon signed rank test [16] with a threshold of p<0.01. More precisely, for a single
decoy set k, the difference in performance between two scores X and Y was determinedby using a bootstrap approach, as follows. Half of the decoys were sampled randomly
100 times, and the performances were calculated for both X and Y. Then, we define thedifferenceinperformance
for
the
decoy
set
k
to
be
dk (X,Y )  (m k (X)  m k (Y )) /( k (X)   k (Y )) , where mk  X  and  k  X  are
the mean and the standard deviation of the performance of X. Finally, the distributiond k  X , Y  (k=1,…, n, where n is the number of decoy sets) was evaluated by the
Wilcoxon signed rank test.
3.

Results and Discussion

3.1. Performances for the Training Set
Table 1 shows the assessment results for the seven all-atom distance dependent statisticalpotentials and the meta-score averaged over 90 CASP6 decoy sets. Among the seven154 M. Shirota , T. Ishida & K. Kinoshita
component potentials, DFIRE showed the largest PCC, whereas RAPDF showed thelargest Z-score and BALL showed the best ΔGDT and the largest 10% and 20%
enrichment values.
These results of the seven potentials for the training set were basically the same as
the results reported in the previous article [15]. A non-hydrophobic potential, RAPDF,
has the highest Z-score of the native structure, but smaller PCC with the GDT_TS thanthe hydrophobic potentials, AKBP’, SHELL, FAR’. The attractive characteristics areusually effective as observed for DFIRE and BALL. DS has a similar characteristic with,
but a little worse performance than RAPDF. In short, seven potentials had their own
advantages and disadvantages in model evaluation and none of them outperformed othersin all the assessment criteria.
On the other hand, the assessments of the meta-score with the training CASP6 decoy
sets showed improvements overall the seven potentials in both PCC and Z-score. The
improvements were also observed in ΔGDT and enrichment criteria. Thus, the metascore has combined the strong points of the component potentials, although these results
are for the training sets.
Table 1. Results of the assessment of the seven normalized energies (columns 2-8) and themeta-score (column 9) with the CASP6 decoy sets. The meta-score was calculated using theJackknife-method as described in the text. The rows 2-6 correspond to the five assessment
criteria. PCC: Pearson’s correlation coefficient between score and the GDT_TS, Z-score:
the deviation of the native energy from the mean energy of the decoys in units of standard
deviation, ΔGDT: the difference between the best GDT_TS among the decoys and the
GDT_TS of the best-scored decoy, Enr 10%, 20%: 10% and 20% enrichments respectively.
These assessment values were calculated for all of the 90 decoy sets of CASP6 and theaverages were listed.
PCC
Z
ΔGDT
Enr10
Enr20

RAPDF
0.38
3.02
0.13
2.53
1.92

AKBP’
0.41
2.77
0.12
2.64
2.03

DFIRE SHELL
0.56
0.47
2.47
2.88
0.15
0.11
3.00
2.73
2.24
2.09

BALL
0.53
2.93
0.11
3.11
2.25

FAR’
0.43
2.74
0.12
2.65
2.06

DS
0.37
2.79
0.14
2.36
1.82

Meta
0.57
3.34
0.10
3.11
2.30

3.2. Performances for the Test Set
Table 2 shows the assessment results with the test decoy sets of CASP7. These decoy
sets were classified as either a) TBM targets or b) FM targets.
For both categories, the meta-score showed higher correlation with GDT_TS andbetter Z-score than the seven potentials. The meta-score displayed significantly better
PCC values than all potentials but DFIRE for TMB targets and SHELL for FM targets.
Significant differences in Z-score values were observed between the meta-score and thepotentials except for RAPDF for TBM modeling targets and RAPDF, AKBP’ andSHELL for FM targets by the same test. These results indicated that the meta-score could
satisfy the two requirements, the correlation and native discrimination, and overcame thetrade-off of the seven component potentials.

Meta-Score for Protein Structures 155
The meta-score demonstrated the smallest ΔGDT for TBM targets. DFIRE andBALL showed similar performances with the meta-score, indicating that the attractive
characteristics played an important role in choosing the best model from decoys. DFIRE
slightly outperformed the meta-score in ΔGDT for FM targets, although the difference
was not significant due to small sample size (18 targets).
In 10% and 20% enrichment criteria, the meta-score was not the best score either for
TBM targets or for FM targets. The results of enrichment assessment revealed thedifference between the TBM and FM decoy sets. The two attractive potentials, DFIRE
and BALL, showed good performances for TBM targets but they performed worse than
the non-attractive five potentials for FM targets. The best result for FM targets wasachieved by a hydrophobic potential SHELL. Despite these differences, the meta-scoreshowed comparable performance to the best potentials for both categories (BALL for
TBM and SHELL for FM).
The performance of these scores was also compared with the previously reported
scoring functions, DOPE [14] and Verify3D [3]. DOPE is another type of all-atom
distance dependent statistical potential based on a reference state corresponding to noninteracting atoms in a homogeneous sphere, with the radius dependent on a sample native
structure. Verify3D assesses the compatibility of each residue with its environment. The
performances of these two potentials were comparable to the seven component potentials
in the five assessment criteria for both TBM targets and FM targets. The meta-scoresignificantly outperformed these two scores in all five criteria for TBM targets. The
meta-score also outperformed these two scores for FM targets although the significancewas not clear because of the small number of targets.
Table 2. Assessments with the CASP7 decoy sets (test set) averaged over a) 104 TBM targets and b) 18
FM targets. The columns represent the seven potentials (columns 2-8), the meta-score (column 9), DOPE
[14] (column 10) and Verify3D [3] (column 11). The rows 2-6 correspond to the five assessment criteria.
The results for the seven potentials were taken from the Table III of our previous paper [15] except for
AKBP’ and FAR’. An asterisk represents the significant difference between the meta-score and the scorein the assessment of the same row. The highest performance column in each row is underlined.
a)

TBM targets
RAPDF
PCC
0.46*
Z
2.83
ΔGDT
0.08*
Enr10
3.03*
Enr20
2.21*

FM targets
RAPDF
PCC
0.47*
Z
2.28
ΔGDT
0.10
Enr10
3.21
Enr20
2.22

AKBP’
0.48*
2.74*
0.07*
2.85*
2.21*

DFIRE SHELL
0.60
0.52*
2.32*
2.64*
0.07
0.07*
3.70
3.14*
2.52
2.31*

BALL
0.58*
2.81*
0.05
3.81
2.54

FAR’
0.49*
2.72*
0.07*
2.88*
2.24*

DS
0.44*
2.64*
0.09*
2.93*
2.16*

Meta
0.60
3.11
0.05
3.70
2.53

DOPE
0.43*
2.53*
0.06*
2.76*
2.10*

V3D
0.48*
2.34*
0.09*
2.64*
2.07*

AKBP’
0.55*
2.16
0.10
3.64
2.40

DFIRE SHELL
0.55*
0.58
2.03*
2.25
0.09
0.10
2.97
3.77
2.16
2.49

BALL
0.54*
2.47*
0.10
2.84*
2.15*

FAR’
0.56*
2.14*
0.10
3.62
2.40

DS
0.43*
2.13*
0.11
3.11
2.04*

Meta
0.61
2.78
0.10
3.55
2.44

DOPE
0.44*
2.36
0.10
2.75*
2.09*

V3D
0.54*
2.38*
0.10
3.14
2.23

b)

156 M. Shirota , T. Ishida & K. Kinoshita
3.3. Evaluation of the Meta-Score as an Absolute Quality Score for Protein
Structures
Since a meta-score was constructed as a predictor of the GDT-TS of each structure, it canalso be regarded as the absolute quality score. We checked the ability of the meta-score
to approximate the true GDT_TS.
Figure 1 shows the scatter plot of the predicted and true GDT_TS of all the nativeand decoy structures for 122 targets, totaling 33,758 structures. The overall correlation
coefficient and the root mean squared error (RMSE) between the meta-score and the true
GDT-TS were 0.84 and 0.142, respectively.
There have been some reports on estimating the absolute quality of models. Wan etal [21] developed a method to evaluate the absolute quality of a model structure as apredicted GDT_TS value using the identities between the observed and predictedstructural features of various kinds and support vector regression. They reported theoverall correlation coefficient and the RMSE for the CASP7 decoys 0.87 and 0.123,
respectively. Eramian et al [6] reported a prediction of NO3.5Å score (the fraction of Cα
atoms in a model that are within 3.5Å of the corresponding atom in the native structure
after superposition) of their 580,317 comparative modeling structures using support
vector regression which utilized various scoring functions. They reported that the PCC
between the observed and predicted NO3.5Å was 0.84. Although the direct comparison
to these reports was not appropriate due to the different model structures used in thesestudies (the decoy set of Wan et al. was not completely the same as that of ours because
their method evaluated the whole chains instead of the domains), our meta-score wasalmost comparable to these results.
We created a predictor of the absolute quality of decoys from the component
potentials. The normalization of the component potentials was the key to absolute quality
assessment. Employing other statistical potentials in their normalized form would help
improve the performance for model evaluation and increase the accuracy of theprediction of the GDT_TS.

Figure 1. The meta-score and the GDT_TS score of the CASP7 native and model structures.

Meta-Score for Protein Structures 157
4.

Conclusion

We have developed a new meta-score which combined the normalized energies of theseven all-atom distance dependent statistical potentials with support vector regression.
The meta-score performed better than or comparable to the best of the component
potentials in five assessment criteria. Therefore, the meta-score could combine theadvantages of the component potentials. In addition, it could be used as the absolute
quality score of the model structures, which had comparable accuracy with the previous
results.
Acknowledgments
This work was partially supported by a Grant-in Aid for Scientific Research on the
Priority Area "Transportsome" from the Ministry of Education, Culture, Sports, Science,
and Technology of Japan, and by a Grant-in-aid from the Institute for Bioinformatics
Research and Development, Japan Science and Technology Corporation (BIRD-JST) to
KK. Computation time was provided by the Super Computer System, Human Genome
Center, Institute of Medical Science, The University of Tokyo.
References[1] Anfinsen, C. B., Principles that govern the folding of protein chains, Science,
181(96):223-30, 1973
[2] Berman, H. M., Westbrook, J., Feng, Z., Gilliland, G., Bhat, T. N., Weissig, H.,
Shindyalov, I. N. and Bourne, P. E., The Protein Data Bank, Nucleic Acids Res,
28(1):235-42, 2000
[3] Bowie, J. U., Luthy, R. and Eisenberg, D., A method to identify protein sequencesthat fold into a known three-dimensional structure, Science, 253(5016):164-70,
1991[4] Chang, C.-C. and Lin, C.-J., LIBSVM: a library for support vector machines.
Software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm, 2001
[5] DeBolt, S. E. and Skolnick, J., Evaluation of atomic level mean force potentials
via inverse folding and inverse refinement of protein structures: atomic burial
position and pairwise non-bonded interactions, Protein Eng, 9(8):637-55, 1996
[6] Eramian, D., Eswar, N., Shen, M. Y. and Sali, A., How well can the accuracy ofcomparative protein structure models be predicted?, Protein Sci, 17(11):1881-93,
2008[7] Jones, D. T., Taylor, W. R. and Thornton, J. M., A new approach to protein foldrecognition, Nature, 358(6381):86-9, 1992
[8] Lu, H. and Skolnick, J., A distance-dependent atomic knowledge-based potential
for improved protein structure selection, Proteins, 44(3):223-32, 2001
[9] Miyazawa, S. and Jernigan, R. L., Estimation of effective interresidue contact
energies from protein crystal structures: quasi-chemical approximation. ,Macromolecules, 18:534-552, 1985

158 M. Shirota , T. Ishida & K. Kinoshita[10] Moult, J., Fidelis, K., Kryshtafovych, A., Rost, B., Hubbard, T. and Tramontano,A., Critical assessment of methods of protein structure prediction-Round VII,
Proteins, 69 Suppl 8:3-9, 2007[11] Moult, J., Fidelis, K., Rost, B., Hubbard, T. and Tramontano, A., Criticalassessment of methods of protein structure prediction (CASP)--round 6, Proteins,
61 Suppl 7:3-7, 2005[12] Rykunov, D. and Fiser, A., Effects of amino acid composition, finite size ofproteins, and sparse statistics on distance-dependent statistical pair potentials,
Proteins, 67(3):559-68, 2007[13] Samudrala, R. and Moult, J., An all-atom distance-dependent conditional
probability discriminatory function for protein structure prediction, J Mol Biol,
275(5):895-916, 1998
[14] Shen, M. Y. and Sali, A., Statistical potential for assessment and prediction ofprotein structures, Protein Sci, 15(11):2507-24, 2006[15] Shirota, M., Ishida, T. and Kinosita, K., Analyses on hydrophobicity andattractiveness of all-atom-distance-dependent potentials, Protein Sci, 18(9):19061915, 2009[16] Siegel, S., Nonparametric Statistics for the Behavioral Sciences, McGraw-Hill
Book Company, 1956
[17] Simons, K. T., Kooperberg, C., Huang, E. and Baker, D., Assembly of protein
tertiary structures from fragments with similar local sequences using simulated
annealing and Bayesian scoring functions, J Mol Biol, 268(1):209-25, 1997[18] Sippl, M. J., Calculation of conformational ensembles from potentials of mean
force. An approach to the knowledge-based prediction of local structures in
globular proteins, J Mol Biol, 213(4):859-83, 1990
[19] Sippl, M. J., Recognition of errors in three-dimensional structures of proteins,
Proteins, 17(4):355-62, 1993[20] Skolnick, J., In quest of an empirical potential for protein structure prediction,
Curr Opin Struct Biol, 16(2):166-71, 2006[21] Wang, Z., Tegge, A. N. and Cheng, J., Evaluating the absolute quality of a single
protein model using structural features and support vector machines, Proteins,
75(3):638-47, 2009[22] Zemla, A., LGA: A method for finding 3D similarities in protein structures,
Nucleic Acids Res, 31(13):3370-4, 2003[23] Zhang, Y., Kolinski, A. and Skolnick, J., TOUCHSTONE II: a new approach to ab
initio protein structure prediction, Biophys J, 85(2):1145-64, 2003[24] Zhang, Y. and Skolnick, J., Scoring function for automated assessment of protein
structure template quality, Proteins, 57(4):702-10, 2004[25] Zhang, C., Vasmatzis, G., Cornette, J. L. and DeLisi, C., Determination of atomic
desolvation energies from the structures of crystallized proteins, J Mol Biol,
267(3):707-26, 1997[26] Zhou, H. and Zhou, Y., Distance-scaled, finite ideal-gas reference state improves
structure-derived potentials of mean force for structure selection and stability
prediction, Protein Sci, 11(11):2714-26, 2002