Abstract
One of the key elements in protein structure prediction is the ability to distinguish between good and bad candidate structures. This distinction is made by estimation of the structure energy. The energy function used in the best state-of-the-art automatic predictors competing in the most recent CASP (Critical Assessment of Techniques for Protein Structure Prediction) experiment is defined as a weighted sum of a set of energy terms designed by experts. We hypothesised that combining these terms more freely will improve the prediction quality. To test this hypothesis, we designed a genetic programming algorithm to evolve the protein energy function. We compared the predictive power of the best evolved function and a linear combination of energy terms featuring weights optimised by the Nelder–Mead algorithm. The GP based optimisation outperformed the optimised linear function. We have made the data used in our experiments publicly available in order to encourage others to further investigate this challenging problem by using GP and other methods, and to attempt to improve on the results presented here.
Similar content being viewed by others
Notes
Protein domain is an independent part of a protein chain that folds into distinct structural region. Its average size is around 100 amino acids in length [45].
From the original set of 56 protein we have excluded 1ogwA (it contains LEF—a non-standard amino acid) and 1cy5A (by omission).
References
C. Anfinsen, Principles that govern the folding of protein chains. Science 181(4096), 223–230 (1973). doi:10.1126/science.181.4096.223
J. Bacardit, M. Stout, N. Krasnogor, J. Hirst, J. Blazewicz, Coordination number prediction using learning classifier systems: performance and interpretability. In Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation (GECCO ’06). (ACM Press, 2006), pp. 247–254. doi:10.1145/1143997.1144041
D. Barthel, J.D. Hirst, J. Blazewicz, N. Krasnogor, ProCKSI: a decision support system for protein (structure) comparison, knowledge, similarity and information. BMC Bioinform. 8(1), 416 (2007). doi:10.1186/1471-2105-8-416
J.N.D. Battey, J. Kopp, L. Bordoli, R.J. Read, N.D. Clarke, T. Schwede, Automated server predictions in CASP7. Proteins Struct. Funct. Bioinform. 69(S8), 68–82 (2007). doi:10.1002/prot.21761
H.M. Berman, The protein data bank: a historical perspective. Acta Crystallographica Sect. A 64(1), 88–95 (2008). doi:10.1107/S0108767307035623
P.E. Bourne, Structural bioinformatics, chap. CASP and CAFASP experiments and their findings (Wiley-Liss, New York, 2003), pp. 499–505. doi:10.1002/0471721204.ch24
E. Burke, S. Gustafson, G. Kendall, Diversity in genetic programming: an analysis of measures and correlation with fitness. IEEE Trans. Evol. Comput. 8(1), 47–62 (2004). doi:10.1109/TEVC.2003.819263
E. Burke, S. Gustafson, G. Kendall, N. Krasnogor, Advanced population diversity measures in genetic programming. In 7th International Conference Parallel Problem Solving from Nature, Springer Lecture Notes in Computer Science, vol. 2439, ed. by H.G.B.J.L.F.V.H.P.S.J.J. Merelo Guervós, P. Adamidis (PPSN, Springer Berlin/Heidelberg, Granada, Spain, 2002), pp. 341–350. doi:10.1007/3-540-45712-7_33
H. Chen, H.X. Zhou, Prediction of solvent accessibility and sites of deleterious mutations from protein sequence. Nucleic Acids Res. 33(10), 3193–3199 (2005). doi:10.1093/nar/gki633
D. Chivian, CASP7 server ranking for FM category (GDT MM) (2006). http://robetta.bakerlab.org/CASP7_eval/CASP7.FR_A-NF.Best-GDT_MM.html
E.A. Coutsias, C. Seok, K.A. Dill, Using quaternions to calculate RMSD. J. Comput. Chem. 25(15), 1849–1857 (2004). doi:10.1002/jcc.20110
S. Cristobal, A. Zemla, D. Fischer, L. Rychlewski, A. Elofsson, A study of quality measures for protein threading models. BMC Bioinform. 2(1), 5 (2001). doi:10.1186/1471-2105-2-5. http://www.biomedcentral.com/1471-2105/2/5
V. Cutello, G. Narzisi, G. Nicosia, A multi-objective evolutionary approach to the protein structure prediction problem. J. R. Soc. Interface 3(6), 139–151 (2006). doi:10.1098/rsif.2005.0083. Applies MOO for CHARMM27 energy (computed with TINKER)
R. Das, B. Qian, S. Raman, R. Vernon, J. Thompson, P. Bradley, S. Khare, M.D. Tyka, D. Bhat, D. Chivian, D.E. Kim, W.H. Sheffler, L. Malmström, A.M. Wollacott, C. Wang, I. Andre, D. Baker, Structure prediction for CASP7 targets using extensive all-atom refinement with Rosetta@home. Proteins Struct. Funct. Bioinform. 69(S8), 118–128 (2007). doi:10.1002/prot.21636
R.O. Day, G.B. Lamont, R. Pachter, Protein structure prediction by applying an evolutionary algorithm. In Proceedings of the 17th International Symposium on Parallel and Distributed Processing (IEEE Computer Society, 2003), p. 155.1. doi:10.1109/IPDPS.2003.1213291
K.A. Dill, Dominant forces in protein folding. Biochemistry 29(31), 7133–7155 (1990). doi:10.1021/bi00483a001
D.P. Djurdjevic, M.J. Biggs, Ab initio protein fold prediction using evolutionary algorithms: influence of design and control parameters on performance. J. Comput. Chem. 27(11), 1177–1195 (2006). doi:10.1002/jcc.20440
C. Dwork, R. Kumar, M. Naor, D. Sivakumar, Rank aggregation methods for the Web. In Proceedings of the 10th international conference on World Wide Web (ACM, Hong Kong, 2001), pp. 613–622. doi:10.1145/371920.372165
C. Gagné, M. Parizeau, Genericity in evolutionary computation software tools: principles and case-study. Int. J. Artif. Intell. Tools 15(2), 173–194 (2006). doi:10.1142/S021821300600262X
D.E. Goldberg, K. Deb, A comparative analysis of selection schemes used in genetic algorithms. In Foundations of Genetic Algorithms, ed. by G.J.E. Rawlins (Morgan Kaufmann, San Francisco, CA, 1990), pp. 69–93
E. Jones, T. Oliphant, P. Peterson, et al., SciPy: open source scientific tools for Python (2001–). http://www.scipy.org/
W. Kabsch, A discussion of the solution for the best rotation to relate two sets of vectors. Acta Crystallographica Sect. A 34(5), 827–828 (1978). doi:10.1107/S0567739478001680
W.R. Knight, A computer method for calculating Kendall’s tau with ungrouped data. J. Am. Stat. Assoc. 61(314), 436–439 (1966)
A. Kolinski, Protein modeling and structure prediction with a reduced representation. Acta Biochimica Polonica 51(2), 349–371 (2004). http://www.actabp.pl/html/2_2004/349.html
A. Kolinski, J. Skolnick, Assembly of protein structure from sparse experimental data: an efficient Monte Carlo model. Proteins Struct Funct Genet 32(4), 475–494 (1998). doi:10.1002/(SICI)1097-0134(19980901)32:4<475::AID-PROT6>3.0.CO;2-F
J.R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection and Genetics (MIT Press, Cambridge, 1992)
J.R. Koza, Scalable learning in genetic programming using automatic function definition. In Advances in Genetic Programming, Chap. 5, ed. by K.E.J. Kinnear (MIT Press, Cambridge, 1994), pp. 99–117
N. Krasnogor, B. Blackburnem, J. Hirst, E. Burke, Multimeme algorithms for protein structure prediction. In Parallel Problem Solving from Nature—PPSN VII, Springer Lecture Notes in Computer Science, vol. 2439, ed. by J.J. Merelo, P. Adamidis, H.G. Beyer (Springer, Berlin, 2002), pp. 769–778. doi:10.1007/3-540-45712-7_74
N. Krasnogor, W. Hart, J. Smith, D. Pelta, Protein structure prediction with evolutionary algorithms. In International Genetic and Evolutionary Computation Conference (GECCO99), ed. by Banzhaf, Daida, Eiben, Garzon, Honovar, Jakiela, Smith (Morgan Kaufmann, San Francisco, CA, 1999), pp. 1569–1601
V.I. Levenshtein, Binary codes capable of correcting deletions, insertions, and reversals. Soviet Physics Dokl. 10(8), 707–710 (1966)
A. Liwo, S. Oldziej, C. Czaplewski, U. Kozlowska, H. Scheraga, Parametrization of backbone-electrostatic and multibody contributions to the UNRES force field for protein-structure prediction from ab initio energy surfaces of model systems. J. Phys. Chem. B 108(27), 9421–9438 (2004). doi:10.1021/jp030844f
S. Luke, L. Panait, A survey and comparison of tree generation algorithms. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), ed. by L. Spector, E.D. Goodman, A. Wu, W.B. Langdon, H.M. Voigt, M. Gen, S. Sen, M. Dorigo, S. Pezeshk, M.H. Garzon, E. Burke (Morgan Kaufman, San Francisco, CA, 2001), pp. 81–88. http://en.scientificcommons.org/453130
J.A. MacKerell, Empirical force fields for biological macromolecules: overview and issues. J. Comput. Chem. 25(13), 1584–1604 (2004). doi:10.1002/jcc.20082
K.I.M. McKinnon, Convergence of the Nelder–Mead simplex method to a nonstationary point. SIAM J. Optim. 9, 148–158 (1999)
J. Nelder, R. Mead, A simplex method for function minimization. Comput. J. 7, 308–313 (1964)
V.S. Pande, I. Baker, J. Chapman, S.P. Elmer, S. Khaliq, S.M. Larson, Y.M. Rhee, M.R. Shirts, C.D. Snow, E.J. Sorin, B. Zagrovic, Atomistic protein folding simulations on the submillisecond time scale using worldwide distributed computing. Biopolymers 68(1), 91–109 (2003). doi:10.1002/bip.10219
C.A. Rohl, C.E.M. Strauss, K.M.S. Misura, D. Baker, Protein structure prediction using rosetta. In Numerical Computer Methods, Part D, Methods in Enzymology, vol. 383, ed. by L. Brand, M.L. Johnson (Academic Press, New York, 2004), pp. 66–93. doi:10.1016/S0076-6879(04)83004-0
R. Santana, P. Larranaga, J. Lozano, Protein folding in simplified models with estimation of distribution algorithms. IEEE Trans. Evol. Comput. 12(4), 418–438 (2008). doi:10.1109/TEVC.2007.906095
K.T. Simons, I. Ruczinski, C. Kooperberg, B.A. Fox, C. Bystroff, D. Baker, Improved recognition of native-like protein structures using a combination of sequence-dependent and sequence-independent features of proteins. Proteins Struct Funct Genet 34(1), 82–95 (1999). doi:10.1002/(SICI)1097-0134(19990101)34:1<82::AID-PROT7>3.0.CO;2-A
M. Stout, J. Bacardit, J. Hirst, R. Smith, N. Krasnogor, Prediction of topological contacts in proteins using learning classifier systems. Soft Comput. Fusion Found. Methodol. Appl. 13(3), 245–258 (2009). doi:10.1007/s00500-008-0318-8
M. Stout, J. Bacardit, J.D. Hirst, N. Krasnogor, Prediction of recursive convex hull class assignments for protein residues. Bioinformatics 24(7), 916–923 (2008). doi:10.1093/bioinformatics/btn050
G. Syswerda, A study of reproduction in generational and steady state genetic algorithms. In Foundations of Genetic Algorithms, ed. by G.J.E. Rawlins (Morgan Kaufmann, San Francisco, CA, 1990), pp. 94–101
R. Unger, Applications of Evolutionary Computation in Chemistry, Structure & Bonding, vol. 110, chap. The Genetic Algorithm Approach to Protein Structure Prediction (Springer, Berlin, 2004), pp. 2697–2699. doi:10.1007/b13936
S. Wallin, J. Farwer, U. Bastolla, Testing similarity measures with continuous and discrete protein models. Proteins Struct. Funct. Genet. 50(1), 144–157 (2003). doi:10.1002/prot.10271
S.J. Wheelan, A. Marchler-Bauer, S.H. Bryant, Domain size distributions can predict domain boundaries. Bioinformatics 16(7), 613–618 (2000). doi:10.1093/bioinformatics/16.7.613
S. Wu, J. Skolnick, Y. Zhang, Ab initio modeling of small proteins by iterative TASSER simulations. BMC Biol 5(1), 17 (2007). doi:10.1186/1741-7007-5-17
A. Zemla, LGA: a method for finding 3D similarities in protein structures. Nucl. Acids Res. 31(13), 3370–3374 (2003). doi:10.1093/nar/gkg571
Y. Zhang, CASP7 server ranking for FM category (TM-Score) (2006). http://zhang.bioinformatics.ku.edu/casp7/24.html
Y. Zhang, I.A. Hubner, A.K. Arakaki, E. Shakhnovich, J. Skolnick, On the origin and highly likely completeness of single-domain protein structures. PNAS 103(8), 2605–2610 (2006). doi:10.1073/pnas.0509379103
Y. Zhang, D. Kihara, J. Skolnick, Local energy landscape flattening: Parallel hyperbolic Monte Carlo sampling of protein folding. Proteins Struct. Funct. Genet. 48(2), 192–201 (2002). doi:10.1002/prot.10141
Y. Zhang, A. Kolinski, J. Skolnick, TOUCHSTONE II: a new approach to ab initio protein structure prediction. Biophys. J. 85(2), 1145–1164 (2003). http://www.biophysj.org/cgi/content/full/85/2/1145
Y. Zhang, J. Skolnick, Tertiary structure predictions on a comprehensive benchmark of medium to large size proteins. Biophys. J. 87(4), 2647–2655 (2004). doi:10.1529/biophysj.104.045385
Acknowledgments
We would like to thank Yang Zhang for making the decoys data available online and for explaining the details of I-TASSER energy terms implementation. This research was supported by the Marie Curie Action MEST-CT-2004-7597 under the Sixth Framework Programme of the European Community and by the UK Engineering and Physical Sciences Research Council under grant GR/T07534/01.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Widera, P., Garibaldi, J.M. & Krasnogor, N. GP challenge: evolving energy function for protein structure prediction. Genet Program Evolvable Mach 11, 61–88 (2010). https://doi.org/10.1007/s10710-009-9087-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10710-009-9087-0