Genetic Programming and Evolvable Machines

, Volume 11, Issue 1, pp 61–88 | Cite as

GP challenge: evolving energy function for protein structure prediction

  • Paweł Widera
  • Jonathan M. Garibaldi
  • Natalio Krasnogor
Original Paper


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.


Genetic programming Protein structure prediction Protein energy function 



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.


  1. 1.
    C. Anfinsen, Principles that govern the folding of protein chains. Science 181(4096), 223–230 (1973). doi: 10.1126/science.181.4096.223 CrossRefGoogle Scholar
  2. 2.
    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
  3. 3.
    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 CrossRefGoogle Scholar
  4. 4.
    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 CrossRefGoogle Scholar
  5. 5.
    H.M. Berman, The protein data bank: a historical perspective. Acta Crystallographica Sect. A 64(1), 88–95 (2008). doi: 10.1107/S0108767307035623 Google Scholar
  6. 6.
    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 Google Scholar
  7. 7.
    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 CrossRefGoogle Scholar
  8. 8.
    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
  9. 9.
    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 CrossRefMathSciNetGoogle Scholar
  10. 10.
    D. Chivian, CASP7 server ranking for FM category (GDT MM) (2006).
  11. 11.
    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 CrossRefGoogle Scholar
  12. 12.
    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.
  13. 13.
    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)Google Scholar
  14. 14.
    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 CrossRefGoogle Scholar
  15. 15.
    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
  16. 16.
    K.A. Dill, Dominant forces in protein folding. Biochemistry 29(31), 7133–7155 (1990). doi: 10.1021/bi00483a001 CrossRefGoogle Scholar
  17. 17.
    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 CrossRefGoogle Scholar
  18. 18.
    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
  19. 19.
    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 CrossRefGoogle Scholar
  20. 20.
    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. 69–93Google Scholar
  21. 21.
    E. Jones, T. Oliphant, P. Peterson, et al., SciPy: open source scientific tools for Python (2001–).
  22. 22.
    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 CrossRefGoogle Scholar
  23. 23.
    W.R. Knight, A computer method for calculating Kendall’s tau with ungrouped data. J. Am. Stat. Assoc. 61(314), 436–439 (1966)zbMATHCrossRefGoogle Scholar
  24. 24.
    A. Kolinski, Protein modeling and structure prediction with a reduced representation. Acta Biochimica Polonica 51(2), 349–371 (2004).
  25. 25.
    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 CrossRefGoogle Scholar
  26. 26.
    J.R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection and Genetics (MIT Press, Cambridge, 1992)zbMATHGoogle Scholar
  27. 27.
    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. 99–117Google Scholar
  28. 28.
    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 CrossRefGoogle Scholar
  29. 29.
    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. 1569–1601Google Scholar
  30. 30.
    V.I. Levenshtein, Binary codes capable of correcting deletions, insertions, and reversals. Soviet Physics Dokl. 10(8), 707–710 (1966)MathSciNetGoogle Scholar
  31. 31.
    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 CrossRefGoogle Scholar
  32. 32.
    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.
  33. 33.
    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 CrossRefGoogle Scholar
  34. 34.
    K.I.M. McKinnon, Convergence of the Nelder–Mead simplex method to a nonstationary point. SIAM J. Optim. 9, 148–158 (1999)CrossRefMathSciNetGoogle Scholar
  35. 35.
    J. Nelder, R. Mead, A simplex method for function minimization. Comput. J. 7, 308–313 (1964)Google Scholar
  36. 36.
    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 CrossRefGoogle Scholar
  37. 37.
    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 CrossRefGoogle Scholar
  38. 38.
    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 CrossRefGoogle Scholar
  39. 39.
    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 CrossRefGoogle Scholar
  40. 40.
    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 Google Scholar
  41. 41.
    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 CrossRefGoogle Scholar
  42. 42.
    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. 94–101Google Scholar
  43. 43.
    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 Google Scholar
  44. 44.
    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 CrossRefGoogle Scholar
  45. 45.
    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 CrossRefGoogle Scholar
  46. 46.
    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 CrossRefGoogle Scholar
  47. 47.
    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 CrossRefGoogle Scholar
  48. 48.
    Y. Zhang, CASP7 server ranking for FM category (TM-Score) (2006).
  49. 49.
    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 CrossRefGoogle Scholar
  50. 50.
    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 CrossRefGoogle Scholar
  51. 51.
    Y. Zhang, A. Kolinski, J. Skolnick, TOUCHSTONE II: a new approach to ab initio protein structure prediction. Biophys. J. 85(2), 1145–1164 (2003). Google Scholar
  52. 52.
    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 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Paweł Widera
    • 1
  • Jonathan M. Garibaldi
    • 1
  • Natalio Krasnogor
    • 1
  1. 1.School of Computer ScienceUniversity of NottinghamNottinghamUK

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