Chapter 2 Materials and Methods
2.8 Training procedure of GEM
GEM is a multi-operator approach that combines three mutation operators:
decreasing-based Gaussian mutation, self-adaptive Gaussian mutation, and self-adaptive Cauchy mutation. It incorporates family competition and adaptive rules for controlling step sizes to construct the relationship among these three operators. To balance the search power of exploration and exploitation, each of operators is designed to compensate for the disadvantages of the other. The details of GEM were described as previous works [21, 23], and had been successfully applied for some specific problems, such as protein-ligand docking, drug screening, and protein side-chain prediction [18-20, 22, 23].
Here, we provide an outline of our GEM for predicting protein-protein interaction sites, which can be represented by adjustable variables of atomic and structure parameters (Table 2) as
where δ is the atomic parameter and σ is the structure parameter of surface residue scoring function. The values of parameters are then used in the surface residue scoring function and predicting results are presented as specificity and success rate. In order to determine that the performance of adjustable parameters, we use a fitness function which combines specificity and success rate for GEM training. In this work, we use GEM to look for the most suitable atomic and structure parameters for identifying protein interfaces by minimizing a fitness function which is described as fellow
,
where N is total number of training proteins. ψp is the specificity of predicting results of the protein p based on the training values of atomic parameters. In order to raise success rate of prediction, we add information of success rate to our fitness function
18
(ωp). The value of ωp is depend on ψp. When ψp is over 0.5 or equal to 0, than ωp
would be set to -1 or 0.5, respectively. If ψp is lower than 0.5 and not equal to 0, then
ω
p would be set to 0.Generally, the method use global continuous-search mechanisms based on Gaussian mutations. And the steps involved are as follows:
1. Initialize the atomic and structure parameters of surface residue scoring function.
The initial values for the parameters are selected from the feasible region (-300, 300). Repeat this N times to generate the initial population of N parameters for a surface residue scoring function. Evaluate the objective value of each parameters based on the fitness function.
2. Change the value of atomic and structure parameters by genetic operators to generate offspring. Evaluate the objective values of the offspring.
3. Use selection operators to select N solutions from the atomic and structure parameters of both parent and offspring solutions.
4. Repeat steps 2 and 3 until one of the terminating conditions is satisfied.
The GEM parameters used in this paper are listed in Table 3 such as population size, initial step sizes of Gaussian mutations, recombination probability, and family competition length in this work. The GEM optimization stops when either the convergence is below certain threshold value or the iterations exceed a maximal preset value which was set to 200. These parameters were selected after many attempts to predict interaction sites for test proteins with various initial values.
Table 3. Gaussian Evolutionary Method parameters
Parameter Value
Population size 200
Step size of Gaussian mutations ν = 0.2 and λ= 0.8 (in radius) Recombination probability 0.2
Family competition length L = 3 Number of maximum generations 200
3 Results
3.1 Training results
The results of the GEM method for the training set are summarized in Table 4.
GEM is able to predict the location of the interface on 65.4% (68/104) proteins in the training dataset. The average specificity and sensitivity are 57.8% and 27.8%, respectively. If we only train atomic parameters by GEM and use optimized atomic parameters to predict training set, the success of prediction is decreasing to 51.0% and the average specificity and sensitivity are 44.9% and 27.6%, respectively. In addition, if we used atomic parameters based on Fernandez-Recio et al. [13] without any optimization, the performance of prediction is the worse. Combination of physical–chemical properties and using computational methods to assist the finding of best parameters are useful for predicting protein-protein interaction sites.
Table 4. Summary of training results from 104 unbound proteins
Atomic and 2nd parameters Success Specificity Sensitivity Success Specificity Sensitivity Success Specificity Sensitivity
Enzyme
a
The parameters which are optimized by GEM
b
The parameters which are based on Fernandez-Recio et al.[13]
20
3.2 Testing results
The overall accuracy of GEM in predicting the protein-protein interaction sites of 50 test proteins is shown in Table 5. In order to test our performance of predicting protein-protein interaction sites, we tested our parameters against a accompanying paper of Fernandez-Recio et al. [13] and found that our Atomic Parameters had performed at least as well as their Atomic Solvation Parameters. The results of this test are summarized in Table 5, in which it can be seen that our method can predict 98% proteins among whole testing set and have 42.3% average specificity, better than Fernandez-Recio’s results which can predict 60% protein among whole testing set and have 37.8% average specificity.
Table 5. Prediction specificities of 50 unbound proteins PDB GEM Fernandez
Recio PDB GEM Fernandez
Recio PDB GEM Fernandez Recio
a*. — means that there are no results of prediction
3.3 Rigid-body protein-protein docking using GEMDOCK
(A) 1AVW (A:B) (B) 1FBI (LH:X) (C) 2BTF (A:P)
Figure 3. Good test cases for GEMDOCK. Hits within 2.0 Å RMSD were found
for (a) 1AVW, (b) 1FBI, (c) 2BTF. The bound receptor surface is shown. The best ranked hit is shown in blue, the original bound ligand is shown in red.We have modified GEMDOCK for rigid-body protein-protein docking and using original empirical scoring function which works well in protein-ligand docking. The former combines both discrete and continuous global search strategies with local search strategies to speed up convergence, whereas the latter results in rapid recognition of possible protein-protein interacting conformations. We have tested on 52 bound protein complexes which are used in our training set and the results are listed on Table 6. The results show that modified GEMDOCK predicts 3 times for each complex and the performance of enzyme-inhibitor (50%) better than antibody-antigen (11%) and others (27%). Figure 3 shows that modified GEMDOCK could give us confident binding conformations in some good test cases, and RMSD of these cases are smaller than 2Å. However, the overall performance is not satisfied
22
since scoring function using here is for protein-ligand docking, fortunately, the search strategies of GEMDOCK is work for protein-protein docking. In the future, we will improve scoring function of GEMDOCK for protein-protein docking and develop soft-body protein-protein docking strategies for solving unbound-unbound protein docking problems.
Table 6. Results of protein-protein docking using GEMDOCK
Complexes ∆ASA
a(Å
2) R2Å
bR5Å
cBest RMSD
d(Å)
1WEJ(LH:F) 1180 0 0 49.428
a∆ASA: change in accessible surface area (ASA) on complex formation was calculated, by using the program NACCESS.[53]
bR2Å: Number of predictions with RMSD smaller than 2 Å among 3 rounds
cR5Å: Number of predictions with RMSD smaller than 5 Å among 3 rounds
dBest RMSD: The smallest RMSD among 3 rounds
24
4 Discussion
Figure 4 shows six examples of the prediction outcome of the training set (figure 4a, 4b and 4c) and testing set (figure 4d, 4e and 4f). Predicted interface and
non-interface residues, identified by the GEM, are shown as color coded patches as follows: Red spheres = true positives (TP), actual interface residues that are predicted as such; Blue strands = true negatives (TN), non-interface residues that are predicted as such; Yellow spheres = false negatives (FN), interface residues that are misclassified as non-interface residues; Green spheres = false positives (FP), non-interface residues that are misclassified as interface residues. From the figure 4, one clearly sees that not all the interface was predicted, but that the predicted part fits the interface well.(a) (b) (c)
(d) (e) (f)
True Positives False Positives False Negatives True Negatives
Figure 4. Prediction results of training set and testing set. The partner molecule(s)
in the bound conformation after superimposition of the corresponding molecule in the complex is represented in ribbon. (a) Prediction on 1dqj_r of the Hyhel-63 Fab, (b) prediction on 1dfj_r of the ribonuclease inhibitor, (c) prediction on 1acb_r of the α-Chymotrypsin, (d) prediction on 2cpl of the Cyclophilin a, (e) prediction on 1ctm of the Cytochrome f, (f) prediction on 1a19A of the Barstar.(c) (d)
(a) (b)
Figure 5. Case study of limitations. (a) 1ahw_l, green : prediction area, yellow :
interface, blue : others, red block : fibronectin type III modules; (b) The target protein 1wej_l is shown in ribbons, green : prediction area, yellow : interface, blue : others, purple : heme; (c) pink : 1noc A chain, green : 1noc B chain and grey : 1nos; (d) 1pco, green : prediction area, yellow : interface, blue : others; and 1eth A chain (ribbon with pink color).
There are some limitations in the current implementation of the method. Figure 5 shows the limitations in the performance between the training set (figure 5a and figure
5b) and testing set (figure 5c and figure 5d). Figure 5a shows the structure of 1ahw_l.
Although our prediction area is far from the interface, this structure consists of two fibronectin type III modules whose hydrophobic cores merge in the domain-domain interface and our prediction is almost invariably symmetrical. Figure 5b shows the structure of 1wej_l. The prediction of our method is located nearby heme propionate, this result may due to the residues nearby the heme are more hydrophobic than protein-protein interaction site. Figure 5c shows the structures of bound protein complex : 1noc A chain and B chain and unbound protein : 1nos. After structure
26
alignment of 1noc A chain and 1nos, unfortunately, contact residues between 1nos and 1noc B chain are less than the bound protein complex, and it is difficult for our method to identify interaction site of 1nos. Figure 5d shows the structure of 1pco and 1eth A chain. The surface of 1eth A chain (colipase) can be divided into a rather hydrophilic part, interacting with 1pco (lipase), and a more hydrophobic part, formed by the tips of the fingers [60]. This suggests that interface of 1pco is more hydrophilic than the surface, and our method do not prove to be very useful in this case.
5 Conclusion
We have developed a method for predicting protein-protein binding sites using GEM. To train the GEM and to test the prediction method we collected dataset of 104 unbound proteins—the nonredundant benchmark for testing protein-protein docking algorithms. We were able to successfully predict the location of the binding site on 65.4% of the 104 proteins in training set. In addition, we tested GEM to predict 50 unbound proteins and had 46% successfully prediction in testing set. The performance were achieved using only 18 attributes so prediction results should be improved when more properties that distinguish between interfaces and the rest of the protein surface become available.
This method can be further improved on several aspects. First, we notice that hydrophilic effect may be main force of protein-protein interaction in some cases (figure 5d), and our predictions are poor. This is due to the fact that most interfaces of training set are hydrophobic and our parameters perform this characteristic faithfully.
Therefore, it may be useful to classify interfaces of training set according to hydrophobic or hydrophilic, and each protein has two predicting areas which are hydrophobic patch and hydrophilic patch. Second, sequence conservation tends to be important attribute to identify protein-protein interface [35]. Third, the effect of 2nd structure information is not very clear, therefore, we intend to understand it of our model. Finally, we will apply our approach to other data set and to study the behavior of our model. In the future, we will combine protein-protein interaction sites prediction into GEMDOCK and improve scoring function of GEMDOCK for protein-protein docking and develop soft-body protein-protein docking strategies for solving unbound-unbound protein docking problems.
28
Reference
[1] A. C. Gavin, M. Bosche, R. Krause, P. Grandi, M. Marzioch, A. Bauer, J.
Schultz, J. M. Rick, A. M. Michon, C. M. Cruciat, M. Remor, C. Hofert, M.
Schelder, M. Brajenovic, H. Ruffner, A. Merino, K. Klein, M. Hudak, D.
Dickson, T. Rudi, V. Gnau, A. Bauch, S. Bastuck, B. Huhse, C. Leutwein, M.
A. Heurtier, R. R. Copley, A. Edelmann, E. Querfurth, V. Rybin, G. Drewes, M.
Raida, T. Bouwmeester, P. Bork, B. Seraphin, B. Kuster, G. Neubauer, and G.
Superti-Furga, "Functional organization of the yeast proteome by systematic analysis of protein complexes," Nature, vol. 415, pp. 141-7, 2002.
[2] L. Giot, J. S. Bader, C. Brouwer, A. Chaudhuri, B. Kuang, Y. Li, Y. L. Hao, C.
E. Ooi, B. Godwin, E. Vitols, G. Vijayadamodar, P. Pochart, H. Machineni, M.
Welsh, Y. Kong, B. Zerhusen, R. Malcolm, Z. Varrone, A. Collis, M. Minto, S.
Burgess, L. McDaniel, E. Stimpson, F. Spriggs, J. Williams, K. Neurath, N.
Ioime, M. Agee, E. Voss, K. Furtak, R. Renzulli, N. Aanensen, S. Carrolla, E.
Bickelhaupt, Y. Lazovatsky, A. DaSilva, J. Zhong, C. A. Stanyon, R. L. Finley, Jr., K. P. White, M. Braverman, T. Jarvie, S. Gold, M. Leach, J. Knight, R. A.
Shimkets, M. P. McKenna, J. Chant, and J. M. Rothberg, "A protein interaction map of Drosophila melanogaster," Science, vol. 302, pp. 1727-36, 2003.
[3] Y. Ho, A. Gruhler, A. Heilbut, G. D. Bader, L. Moore, S. L. Adams, A. Millar, P. Taylor, K. Bennett, K. Boutilier, L. Yang, C. Wolting, I. Donaldson, S.
Schandorff, J. Shewnarane, M. Vo, J. Taggart, M. Goudreault, B. Muskat, C.
Alfarano, D. Dewar, Z. Lin, K. Michalickova, A. R. Willems, H. Sassi, P. A.
Nielsen, K. J. Rasmussen, J. R. Andersen, L. E. Johansen, L. H. Hansen, H.
Jespersen, A. Podtelejnikov, E. Nielsen, J. Crawford, V. Poulsen, B. D.
Sorensen, J. Matthiesen, R. C. Hendrickson, F. Gleeson, T. Pawson, M. F.
Moran, D. Durocher, M. Mann, C. W. Hogue, D. Figeys, and M. Tyers,
"Systematic identification of protein complexes in Saccharomyces cerevisiae by mass spectrometry," Nature, vol. 415, pp. 180-3, 2002.
[4] S. Li, C. M. Armstrong, N. Bertin, H. Ge, S. Milstein, M. Boxem, P. O.
Vidalain, J. D. Han, A. Chesneau, T. Hao, D. S. Goldberg, N. Li, M. Martinez, J. F. Rual, P. Lamesch, L. Xu, M. Tewari, S. L. Wong, L. V. Zhang, G. F. Berriz, L. Jacotot, P. Vaglio, J. Reboul, T. Hirozane-Kishikawa, Q. Li, H. W. Gabel, A.
Elewa, B. Baumgartner, D. J. Rose, H. Yu, S. Bosak, R. Sequerra, A. Fraser, S.
E. Mango, W. M. Saxton, S. Strome, S. Van Den Heuvel, F. Piano, J.
Vandenhaute, C. Sardet, M. Gerstein, L. Doucette-Stamm, K. C. Gunsalus, J.
W. Harper, M. E. Cusick, F. P. Roth, D. E. Hill, and M. Vidal, "A map of the interactome network of the metazoan C. elegans," Science, vol. 303, pp. 540-3,
2004.
[5] P. Uetz, L. Giot, G. Cagney, T. A. Mansfield, R. S. Judson, J. R. Knight, D.
Lockshon, V. Narayan, M. Srinivasan, P. Pochart, A. Qureshi-Emili, Y. Li, B.
Godwin, D. Conover, T. Kalbfleisch, G. Vijayadamodar, M. Yang, M. Johnston, S. Fields, and J. M. Rothberg, "A comprehensive analysis of protein-protein interactions in Saccharomyces cerevisiae," Nature, vol. 403, pp. 623-7, 2000.
[6] S. Jones and J. M. Thornton, "Principles of protein-protein interactions,"
Proceedings of the National Academy of Sciences of the United States of America, vol. 93, pp. 13-20, 1996.
[7] S. Jones and J. M. Thornton, "Prediction of protein-protein interaction sites using patch analysis," Journal of Molecular Biology, vol. 272, pp. 133-143, 1997.
[8] S. Jones and J. M. Thornton, "Analysis of protein-protein interaction sites using surface patches," Journal of Molecular Biology, vol. 272, pp. 121-132, 1997.
[9] I. M. Nooren and J. M. Thornton, "Diversity of protein-protein interactions,"
EMBO Journal, vol. 22, pp. 3486-3492, 2003.
[10] I. A. Vakser and C. Aflalo, "Hydrophobic docking: a proposed enhancement to molecular recognition techniques," Proteins: Structure, Function and Genetics, vol. 20, pp. 320-329, 1994.
[11] L. Young, R. L. Jernigan, and D. G. Covell, "A role for surface hydrophobicity in protein-protein recognition," Protein Science, vol. 3, pp. 717-729, 1994.
[12] J. Fernandez-Recio, M. Totrov, and R. Abagyan, "Identification of protein-protein interaction sites from docking energy landscapes," Journal of
Molecular Biology, vol. 335, pp. 843-865, 2004.
[13] J. Fernandez-Recio, M. Totrov, C. Skorodumov, and R. Abagyan, "Optimal docking area: a new method for predicting protein-protein interaction sites,"
Proteins: Structure, Function, and Bioinformatics, vol. 58, pp. 134-143, 2005.
[14] P. Fariselli, F. Pazos, A. Valencia, and R. Casadio, "Prediction of protein--protein interaction sites in heterocomplexes with neural networks,"
European Journal of Biochemistry, vol. 269, pp. 1356-1361, 2002.
[15] M. Keil, T. E. Exner, and J. Brickmann, "Pattern recognition strategies for molecular surfaces: III. Binding site prediction with a neural network,"
Journal of Computational Chemistry, vol. 25, pp. 779-789, 2004.
[16] H. Neuvirth, R. Raz, and G. Schreiber, "ProMate: a structure based prediction program to identify the location of protein-protein binding sites," Journal of
Molecular Biology, vol. 338, pp. 181-199, 2004.
[17] H. X. Zhou and Y. Shan, "Prediction of protein interaction sites from sequence
30
profile and residue neighbor list," Proteins: Structure, Function and Genetics, vol. 44, pp. 336-343, 2001.
[18] J. M. Yang, "Development and evaluation of a generic evolutionary method for protein-ligand docking," Journal of Computational Chemistry, vol. 25, pp.
843-857, 2004.
[19] J. M. Yang and C. C. Chen, "GEMDOCK: a generic evolutionary method for molecular docking," Proteins: Structure, Function, and Bioinformatics, vol. 55, pp. 288-304, 2004.
[20] J. M. Yang, J. T. Horng, and C. Y. Kao, "A genetic algorithm with adaptive mutations and family competition for training neural networks," International
Journal of Neural Systems, vol. 10, pp. 333-352, 2000.
[21] J. M. Yang and C. Y. Kao, "A family competition evolutionary algorithm for automated docking of flexible ligands to proteins," IEEE Transactions on
Information Technology in Biomedicine, vol. 4, pp. 225-237, 2000.
[22] J. M. Yang and T. W. Shen, "A pharmacophore-based evolutionary approach for screening selective estrogen receptor modulators," Proteins: Structure,
Function, and Bioinformatics, vol. 59, pp. 205-220, 2005.
[23] J. M. Yang, C. H. Tsai, M. J. Hwang, H. K. Tsai, J. K. Hwang, and C. Y. Kao,
"GEM: a Gaussian Evolutionary Method for predicting protein side-chain conformations," Protein Science, vol. 11, pp. 1897-1907, 2002.
[24] W. Kabsch and C. Sander, "Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features," Biopolymers, vol.
22, pp. 2577-2637, 1983.
[25] Q. Dong, X. Wang, L. Lin, and Y. Guan, "Exploiting residue-level and profile-level interface propensities for usage in binding sites prediction of proteins," BMC Bioinformatics, vol. 8, pp. 147, 2007.
[26] F. Glaser, D. M. Steinberg, I. A. Vakser, and N. Ben-Tal, "Residue frequencies and pairing preferences at protein-protein interfaces," Proteins: Structure,
Function and Genetics, vol. 43, pp. 89-102, 2001.
[27] T. A. Larsen, A. J. Olson, and D. S. Goodsell, "Morphology of protein-protein interfaces," Structure, vol. 6, pp. 421-7, 1998.
[28] X. Gallet, B. Charloteaux, A. Thomas, and R. Brasseur, "A fast method to predict protein interaction sites from sequences," Journal of Molecular
Biology, vol. 302, pp. 917-26, 2000.
[29] A. Koike and T. Takagi, "Prediction of protein-protein interaction sites using support vector machines," Protein Engineering Design and Selection, vol. 17, pp. 165-73, 2004.
[30] A. P. Korn and R. M. Burnett, "Distribution and complementarity of
hydropathy in multisubunit proteins," Proteins: structure, function, and
bioinformatics, vol. 9, pp. 37-55, 1991.
[31] L. Lo Conte, C. Chothia, and J. Janin, "The atomic structure of protein-protein recognition sites," Journal of Molecular Biology, vol. 285, pp. 2177-98, 1999.
[32] S. F. Altschul, T. L. Madden, A. A. Schaffer, J. Zhang, Z. Zhang, W. Miller, and D. J. Lipman, "Gapped BLAST and PSI-BLAST: a new generation of protein database search programs," Nucleic Acids Research, vol. 25, pp.
3389-402, 1997.
[33] W. S. Valdar, "Scoring residue conservation," Proteins: structure, function,
and bioinformatics, vol. 48, pp. 227-41, 2002.
[34] J. R. Bradford and D. R. Westhead, "Asymmetric mutation rates at enzyme-inhibitor interfaces: implications for the protein-protein docking problem," Protein Science, vol. 12, pp. 2099-103, 2003.
[35] D. R. Caffrey, S. Somaroo, J. D. Hughes, J. Mintseris, and E. S. Huang, "Are protein-protein interfaces more conserved in sequence than the rest of the protein surface?" Protein Science, vol. 13, pp. 190-202, 2004.
[36] N. V. Grishin and M. A. Phillips, "The subunit interfaces of oligomeric enzymes are conserved to a similar extent to the overall protein sequences,"
Protein Science, vol. 3, pp. 2455-8, 1994.
[37] M. Guharoy and P. Chakrabarti, "Conservation and relative importance of residues across protein-protein interfaces," Proceedings of the National
Academy of Sciences of the United States of America, vol. 102, pp. 15447-52,
2005.[38] A. Porollo and J. Meller, "Prediction-based fingerprints of protein-protein interactions," Proteins: structure, function, and bioinformatics, vol. 66, pp.
630-45, 2007.
[39] C. Cole and J. Warwicker, "Side-chain conformational entropy at protein-protein interfaces," Protein Science, vol. 11, pp. 2860-70, 2002.
[40] J. L. Chung, W. Wang, and P. E. Bourne, "Exploiting sequence and structure homologs to identify protein-protein binding sites," Proteins: structure,
function, and bioinformatics, vol. 62, pp. 630-40, 2006.
[41] M. C. Lawrence and P. M. Colman, "Shape complementarity at protein/protein interfaces," Journal of Molecular Biology, vol. 234, pp. 946-50, 1993.
[42] A. J. McCoy, V. Chandana Epa, and P. M. Colman, "Electrostatic complementarity at protein/protein interfaces," Journal of Molecular Biology, vol. 268, pp. 570-84, 1997.
[43] F. B. Sheinerman, R. Norel, and B. Honig, "Electrostatic aspects of protein-protein interactions," Current Opinion in Structural Biology, vol. 10,
32
pp. 153-9, 2000.
[44] D. Xu, S. L. Lin, and R. Nussinov, "Protein binding versus protein folding: the role of hydrophilic bridges in protein associations," Journal of Molecular
Biology, vol. 265, pp. 68-84, 1997.
[45] J. R. Bradford and D. R. Westhead, "Improved prediction of protein-protein binding sites using a support vector machines approach," Bioinformatics, vol.
21, pp. 1487-1494, 2005.
[46] P. Aloy, E. Querol, F. X. Aviles, and M. J. Sternberg, "Automated structure-based prediction of functional sites in proteins: applications to assessing the validity of inheriting protein function from homology in genome annotation and to protein docking," Journal of Molecular Biology, vol. 311, pp.
395-408, 2001.
[47] G. Casari, C. Sander, and A. Valencia, "A method to predict functional residues in proteins," Nature Structural Biology, vol. 2, pp. 171-8, 1995.
[48] S. Madabushi, H. Yao, M. Marsh, D. M. Kristensen, A. Philippi, M. E. Sowa, and O. Lichtarge, "Structural clusters of evolutionary trace residues are statistically significant and common in proteins," Journal of Molecular
Biology, vol. 316, pp. 139-54, 2002.
[49] Y. Ofran and B. Rost, "Predicted protein-protein interaction sites from local sequence information," FEBS Letters, vol. 544, pp. 236-239, 2003.
[50] F. Pazos, M. Helmer-Citterich, G. Ausiello, and A. Valencia, "Correlated mutations contain information about protein-protein interaction," Journal of
Molecular Biology, vol. 271, pp. 511-23, 1997.
[51] B. Wang, P. Chen, D. S. Huang, J. J. Li, T. M. Lok, and M. R. Lyu, "Predicting protein interaction sites from residue spatial sequence profile and evolution rate," FEBS Letters, vol. 580, pp. 380-4, 2006.
[52] D. K. Gehlhaar, G. M. Verkhivker, P. A. Rejto, C. J. Sherman, D. B. Fogel, L. J.
Fogel, and S. T. Freer, "Molecular recognition of the inhibitor AG-1343 by HIV-1 protease: conformationally flexible docking by evolutionary programming," Chemistry and Biology, vol. 2, pp. 317-24, 1995.
[53] R. Chen, J. Mintseris, J. Janin, and Z. Weng, "A protein-protein docking benchmark," Proteins: Structure, Function and Genetics, vol. 52, pp. 88-91, 2003.
[54] C. Yan, D. Dobbs, and V. Honavar, "A two-stage classifier for identification of protein-protein interface residues," Bioinformatics, vol. 20 Suppl 1, pp.
I371-I378, 2004.
[55] B. Rost and C. Sander, "Conservation and prediction of solvent accessibility in protein families," Proteins: Structure, Function, and Genetics, vol. 20, pp.
216-226, 1994.
[56] S. Ansari and V. Helms, "Statistical analysis of predominantly transient protein-protein interfaces," Proteins: Structure, Function, and Bioinformatics, vol. 61, pp. 344-355, 2005.
[57] M. J. Sternberg, H. A. Gabb, and R. M. Jackson, "Predictive docking of protein-protein and protein-DNA complexes," Current Opinion in Structural
Biology, vol. 8, pp. 250-256, 1998.
[58] D. Eisenberg and A. D. McLachlan, "Solvation energy in protein folding and binding," Nature, vol. 319, pp. 199-203, 1986.
[59] L. Wesson and D. Eisenberg, "Atomic solvation parameters applied to molecular dynamics of proteins in solution," Protein Science, vol. 1, pp.
227-235, 1992.
[60] M. P. Egloff, L. Sarda, R. Verger, C. Cambillau, and H. van Tilbeurgh,
"Crystallographic study of the structure of colipase and of the interaction with pancreatic lipase," Protein Science, vol. 4, pp. 44-57, 1995.