Skip to main content

Advertisement

Log in

Optimized Evolutionary Strategies in Conformational Sampling

  • Original Paper
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Novel genetic algorithm (GA)-based strategies, specifically aimed at multimodal optimization problems, have been developed by hybridizing the GA with alternative optimization heuristics, and used for the search of a maximal number of minimum energy conformations (geometries) of complex molecules (conformational sampling). Intramolecular energy, the targeted function, describes a very complex nonlinear response hypersurface in the phase space of structural degrees of freedom. These are the torsional angles controlling the relative rotation of fragments connected by covalent bonds. The energy surface of cyclodextrine, a macrocyclic sugar molecule with N = 65 degrees of freedom served as model system for testing and tuning the herein proposed multimodal optimization strategies. The success of GAs is known to depend on the peculiar hypotheses used to simulate Darwinian evolution. Therefore, the conformational sampling GA (CSGA) was designed such as to allow an extensive control on the evolution process by means of tunable parameters, some being classical GA controls (population size, mutation frequency, etc.), while others control the herein designed population diversity management tools or the frequencies of calls to the alternative heuristics. They form a large set of operational parameters, and a (genetic) meta-optimization procedure was used to search for parameter configurations maximizing the efficiency of the CSGA process. The specific impact of disabling a given hybridizing heuristics was estimated relatively to the default sampling behavior (with all the implemented heuristics on). Optimal sampling performance was obtained with a GA featuring a built-in tabu search mechanism, a “Lamarckian” (gradient-based) optimization tool, and, most notably, a “directed mutations” engine (a torsional angle driving procedure generating chromosomes that radically differ from their parents but have good chances to be “fit”, unlike offspring from spontaneous mutations). “Biasing” heuristics, implementing some more elaborated random draw distribution laws instead of the ‘flat’ default rule for torsional angle value picking, were at best unconvincing or outright harmful. Naive Bayesian analysis was employed in order to estimated the impact of the operational parameters on the CSGA success. The study emphasized the importance of proper tuning of the CSGA. The meta-optimization procedure implicitly ensures the management, in the context of an evolving operational parameterization, of the repeated GA runs that are absolutely mandatory for the reproducibility of the sampling of such vast phase spaces. Therefore, it should not be only seen as a tuning tool, but as the strategy for actual problem solving, essentially advocating a parallel exploration of problem space and parameter space.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

GA:

Genetic algorithm

CSGA:

Conformational sampling GA

μGA:

Meta-GA (used for parameter setup optimization)

μF:

Meta-fitness score (target function of the μGA) a measure of success of conformational sampling

References

  1. Bäck T (1996) Evolutionary algorithms in theory and practice. Oxford University Press, Oxford

    MATH  Google Scholar 

  2. Brunger AT, Clore GM, Gronenborn AM, Saffrich R, Nilges M (1993) Assessing the quality of solution nuclear magnetic resonance structures by complete cross-validation. Science 261: 328–331

    Article  Google Scholar 

  3. Calland PY (2003) On the structural complexity of a protein. Protein Eng 16:79–86

    Article  Google Scholar 

  4. Damsbo M et al (2004) Application of evolutionary algorithm methods to polypeptidic folding: comparison with experimental results for unsolvated Ac-(Ala-Gly-Gly)5-LysH+. Proc Natl Acad Sci USA 101:7215–7222

    Article  Google Scholar 

  5. Davy M, Del Moral P, Doucet A (2003) Méthodes Monte Carlo Séquentielles pour l’analyse Spectrale Bayésienne, Proceeding of the GRETSI Conference, Paris

  6. De Jong KA, Potter MA, Spears WM (1997) Using a problem generator to explore the effects of epistasis. In: Proceedings of the 7th international conference on genetic algorithms. Morgan Kaufmann, San Fransisco, pp 338–345

  7. De Jong KA, Spears WM, Gordon DF (1994) Using Markov chains to analyse GAFOs. In: Foundations of genetic algorithms 94, Morgan Kaufmann, San Fransisco, pp 115–137

  8. Del Moral P, Doucet A (2002) Sequential Monte Carlo samplers. technical report 443, Cambridge University Press, Cambridge

    Google Scholar 

  9. Discover simulation package, Accelrys, San Diego, CA, http://www.accelrys.com/insight/discover.html

  10. Glen WG, Dunn WJ, Scott DR (1989) Principal components analysis and partial least squares regressions. Tetrahedron Comput Technol 2:349–376

    Article  Google Scholar 

  11. Glover F (1989) Tabu Search, Part I. ORSA J Comput 1(3):190–206

    MATH  Google Scholar 

  12. Glover F (1990) Tabu Search, Part II. ORSA J Comput 2(1):4–32

    MATH  Google Scholar 

  13. Goldberg DE (1989) Genetic algorithms in Search, optimization and machine learning. Addison-Wesley, Reading

    MATH  Google Scholar 

  14. Goto H, Osawa E (1993) An efficient algorithm for searching low-energy conformers of cyclic and acyclic molecules. J Chem Soc Perkin Trans 2:187–198

    Google Scholar 

  15. Grefenstette JJ (1986) Optimisation of control parameters for genetic algorithms. IEEE Trans SMC 16:122–128

    Google Scholar 

  16. Hagler AT, Huler E, Lifson S (1974) Energy functions for peptides and proteins: I. Derivation of a consistent force field including the hydrogen bond from amide crystals. J Am Chem Soc 96: 5319–5327

    Google Scholar 

  17. Hart WE, Belew RK (1991) Optimizing an arbitrary function is hard for the genetic algorithm. In: Booker LB (eds) Proceedings of the 4th international conference on the genetic algorithms. Morgan Kaaufmann, San Mateo, pp 190–195

    Google Scholar 

  18. Herrera F, Lozano M (2001) Adaptative genetic operators based on coevolution with fuzzy behaviors. IEEE Trans Evol Comput 2:149–165

    Article  Google Scholar 

  19. Heudin JC (1994) La vie artificielle. Hermès Editions, Paris

    MATH  Google Scholar 

  20. Hornak V, Simmerling C (2003) Generation of accurate protein loop conformations through low-barrier molecular dynamics. Proteins 51:577–590

    Article  Google Scholar 

  21. Horvath D (1997) A virtual screening approach applied to the search of trypanothione reductase inhibitors. J Med Chem 15:2412–2423

    Article  Google Scholar 

  22. Horvath D, Jeandenans C (2003) Neighborhood behavior of in silico structural spaces with respect to in vitro activity spaces – a novel understanding of the molecular similarity principle in the context of multiple receptor binding profiles. J Chem Inf Comp Sci 43:680–690

    Article  Google Scholar 

  23. Jarvis BB (2002) http://www.chem.umd.edu/courses/jarvis/chem 233spr04/Chapter04Notes.pdf

  24. Kolossvary I, Guida WC (1996) Low mode search. An efficient, automated computational method for conformational analysis: Application to cyclic and acyclic alkanes and cyclic peptides. J Am Chem Soc 118:5011–5019

    Google Scholar 

  25. Kubota N, Fukuda T (1997) Genetic algorithms with age structure. Soft Comput 1:155–161

    Google Scholar 

  26. Michalewicz Z (1994) Genetic algorithms + data structure = evolution programs, 2nd edn. Springer, Berlin Heidelberg New York

    Google Scholar 

  27. Morris GM, Goodsell DS, Halliday RS, Huey R, Hart WE, Belew RE, Olson AJ (1998) Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function. J Comp Chem 19:1639–1662

    Article  Google Scholar 

  28. Ochoa G, Harvey J, Buxton H (1999) On recombination and Optimal Mutation Rates. In: Proceedings of genetic and evolutionary computation conference (GECCO-99), Morgan Kaufmann, San Francisco, pp 488–495

  29. Packer MJ, Hunter CA (2001) Sequence-structure relationships in DNA oligomers: a computational approach. J Am Chem Soc 123:7399–7406

    Article  Google Scholar 

  30. Pipeline Pilot version 3.0, available from SciTegic, Inc, at http://www.scitegic.com

  31. Prebys EK (1999) The genetic algorithm in computer science. MIT Undergraduate J Math 1:165–170

    Google Scholar 

  32. Renders JM (1995) Algorithmes Génétiques et Réseaux de Neurones. Hermès Editions, Paris

    MATH  Google Scholar 

  33. Shetty RP, De Bakker PI, DePristo MA, Blundell TL (2003) Advantages of fine-grained side chain conformer libraries. Protein Eng 16:963–969

    Article  Google Scholar 

  34. Spears WM (1992) Adapting crossover in a genetic algorithm, technical report AIC-92–025, Navy Center for Applied Research in AI, http://www.aic.nrl.navy.mil/∼spears/papers/adapt.crossover.pdf

  35. Spears WM (1994) Simple subpopulation schemes. In: Proceedings of the third annual conference on evolutionary programming, Evolutionary Programming Society, San Diego, pp 296–307

  36. Spears WM, De Jong KA (1996) Analysing GAs using Markov models with semantically ordered and lumped states. In: Foundations of genetic algorithms 96, Morgan Kaufmann, San Fransisco, pp 95–100

  37. Stein EG, Rice LM, Brunger AT (1997) Torsion-angle molecular dynamics as a new efficient tool for NMR structure calculation. J Magn Reson 124:154–164

    Article  Google Scholar 

  38. Tai K (2004) Conformational sampling for the impatient. Biophys Chem 107:213–220

    Article  Google Scholar 

  39. Teghem J (2003) Résolution de problèmes de RO par les métaheuristiques. Ed Hermès Sciences/Lavoisier, Paris

    Google Scholar 

  40. Vertanen K Genetic (1998) Adventures in parallel: towards a good island model under PVM. Oregon State University

  41. Xia X, Maliski EG, Gallant P, Rogers D (2004) Classification of kinase inhibitors using a Bayesian model. J Med Chem 47:4463–4470

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dragos Horvath.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Parent, B., Kökösy, A. & Horvath, D. Optimized Evolutionary Strategies in Conformational Sampling. Soft Comput 11, 63–79 (2007). https://doi.org/10.1007/s00500-006-0053-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-006-0053-y

Keywords

Navigation