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The application of the genetic algorithm to the minimization of potential energy functions

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Abstract

We adapted the genetic algorithm to minimize the AMBER potential energy function. We describe specific recombination and mutation operators for this task. Next we use our algorithm to locate low energy conformation of three polypeptides (AGAGAGAGA, A9, and [Met]-enkephalin) which are probably the global minimum conformations. Our potential energy minima are −94.71, −98.50, and −48.94 kcal/mol respectively. Next, we applied our algorithm to the 46 amino acid protein crambin and located a non-native conformation which had an AMBER potential energy ∼150 kcal/mol lower than the native conformation. This is not necessarily the global minimum conformation, but it does illustrate problems with the AMBER potential energy function. We believe this occurred because the AMBER potential energy function does not account for hydration.

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References

  • Ackley, D. (1987),A Connectionist Machine for Genetic Hillclimbing, Kluwer, Boston.

    Google Scholar 

  • Anfinsen, C. (1959),The Molecular Basis of Evolution, John Wiley & Sons, New York.

    Google Scholar 

  • Anfinsen, C. (1961), The kinetics of formation of native ribonuclease during oxidation of the reduced polypeptide chain,PNAS 47(9), 1309–1314.

    Google Scholar 

  • Anflnsen, C. (1973), Principles that govern the folding of protein chains,Science 181, 223–230.

    Google Scholar 

  • Ankenbrandt, C. (1991), An extension to the theory of convergence and a proof of the time complexity of genetic algorithms, inFoundations of Genetic Algorithms, Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Baldwin, R. (1989), How does protein folding get started?,Trends Biochem. Sci. 14, 291–294.

    Google Scholar 

  • Baldwin, R. and Eisenberg, D. (1987), Protein stability, inProtein Engineering, Alan R. Liss, Inc., NY.

    Google Scholar 

  • Billeter, M., Havel, T. F., and Wüthrich, K. (1987), The ellipsoid algorithm as a method of determination of polypeptide conformations from experimental distance constraints and energy minimization,J. Comp. Chem. 8(2), 132–141.

    Google Scholar 

  • Bohr, H., Bohr, J., Brunak, S., Cotterill, R., Lautrup, B., Norskov, L., Oslen, O., and Petersen, S. (1988), Protein secondary structure and homology by neural networks: The a-helices in rhodopsin,FEBS Letters 241, 223–228.

    Google Scholar 

  • Booker, L. (1987), Improving search in genetic algorithms, inGenetic Algorithms and Simulated Annealing, Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Brooks, B., Bruccoleri, R., Olafson, B., States, D., Swaminathan, S., and Karplus, M. (1983), CHARMM: A program for macromolecular energy, minimization, and dynamics calculations,J. Comp. Chem. 4, 187–217.

    Google Scholar 

  • Brooks, C., III, Karplus, M., and Montgomery Pettitt, B. (1988),Proteins: A Theoretical Perspective of Dynamics, Structure and Thermodynamics, Wiley Interscience, New York.

    Google Scholar 

  • Chakrabarty, A., Schellman, J. A., and Baldwin, R. L. (1991), Large differences in the helix propensities of alanine and glycine,Nature 351, 586–588.

    Google Scholar 

  • Chou, P. and Fasman, G. (1974), Prediction of protein conformation,Biochemistry 13, 222–244.

    Google Scholar 

  • Cleveland, G. and Smith, S. (1989), Using genetic algorithms to schedule flow shop releases, inProceedings of the Third International Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Cohen, F. and Kuntz, I. (1989), Tertiary Structure Prediction, inPrediction of Protein Structure and the Principles of Protein Conformation, Plenum Press, New York.

    Google Scholar 

  • Crippen, G. (1977), A novel approach to calculation of conformation: distance geometry,J. Comp. Phys. 24, 96–107.

    Google Scholar 

  • Crippen, G. and Havel, T. (1990), Global energy minimization by rotational energy embedding,J. Chem. Inf. Comp. Sci. 30, 222–227.

    Google Scholar 

  • Davidor, Y. (1989), Analogous crossover, inProceedings of the Third International Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Davis, L. (1989), Adapting operator probabilities in genetic algorithms, inProceedings of the Third International Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo, SA.

    Google Scholar 

  • Davis, T. and Principe, J. (1991), A simulated annealing like convergence theorem for the simple genetic algorithm, inProceedings of the Fourth International Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Dudek, J. and Scheraga, H. (1990), Protein structure prediction using a combination of sequence homology and global energy minimization I. Global energy minimization of surface loops,J. Comp. Chem. 11, 121–151.

    Google Scholar 

  • Eisenberg, D. and McLachlan, A. D. (1986), Solvation energy in protein folding and binding,Nature 319, 199–203.

    Google Scholar 

  • Fasman, G. (1989), Development of the prediction of protein structure, inPrediction of Protein Structure and the Principles of Protein Conformation, Plenum Press, New York.

    Google Scholar 

  • Ferrin, T. E. (1988), The MIDAS display system,J. Mol. Graphics 6, 13–27.

    Google Scholar 

  • Fogarty, T. (1989), Varying the probability of mutation in the genetic algorithm, inProceedings of the Third International Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Gamier, J., Osguthorpe, D., and Robson, B. (1978),J. Mol. Biol. 120, 97–120.

    Google Scholar 

  • Gibrat, J., Gamier, J., and Robson, B. (1987), Further developments of secondary structure prediction using information theory: New parameters and consideration of residue pairs,J. Mol. Biol. 198, 425–443.

    Google Scholar 

  • Goldberg, D. (1987), Genetic algorithms with sharing for multimodal function optimization, inGenetic Algorithms and Their Applications: Proceedings of the Second International Conference on Genetic Algorithms, Lawrence Erlbaum, Hillsdale, NJ.

    Google Scholar 

  • Goldberg, D. (1989),Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, San Mateo, CA.

    Google Scholar 

  • Grefenstette, J. and Baker, J. (1989), How genetic algorithms work: a critical look at implicit parallelism, inProceedings of the Third International Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Holland, J. (1975),Adaptation in Natural and Artificial Systems, University of Michigan Press, Ann Arbor, MI.

    Google Scholar 

  • Holley, L. and Karplus, M. (1989), Protein secondary structure prediction with a neural network,PNAS 86, 152–156.

    Google Scholar 

  • Jaenicke, R. (1991), Protein folding: Local structures, domains, subunits, and assemblies,Biochemistry 30(13), 3147–3161.

    Google Scholar 

  • Janikow, C. and Michalewicz, Z. (1991), An experimental comparison of binary and floating point representations in genetic algorithms, inProceedings of the Fourth International Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Khechinashvili, N. (1990), Thermodynamic properties of globular proteins and the principle of stabilization of their native structure,Biochimica et Biophysica Acta. 1040, 346–354.

    Google Scholar 

  • Kneller, D., Cohen, F., and Langridge, R. (1990), Improvements in protein secondary structure prediction by an enhanced neural network,J. Mol. Biol. 214, 171–182.

    Google Scholar 

  • Lambert, M. and Scheraga, H. (1989a), Pattern recognition in the prediction of protein structure. I. Tripeptide conformational probabilities calculated from the amino acid sequence,J. Comp. Chem. 10, 770–797.

    Google Scholar 

  • Lambert, M. and Scheraga, H. (1989b), Pattern recognition in the prediction of protein structure. II. Chain conformation from a probability-directed search procedure,J. Comp. Chem. 10, 798–816.

    Google Scholar 

  • Lambert, M. and Scheraga, H. (1989c), Pattern recognition in the prediction of protein structure. III. An importance-sampling minimization procedure,J. Comp. Chem. 10, 817–831.

    Google Scholar 

  • Levitt, M. (1983), Protein folding by restrained energy minimization and molecular dynamics,J. Mol. Biol. 170, 723–764.

    Google Scholar 

  • Li, Z. and Scheraga, H. (1987), Monte Carlo-minimization approach to the multiple-minima problem in protein folding,PNAS 84, 6611–6615.

    Google Scholar 

  • Li, Z. and Scheraga, H. (1988), Monte Carlo recursion evaluation of free energy,J. Phys. Chem. 92, 2633–2636.

    Google Scholar 

  • Lipton, M. and Still, W. (1988), The multiple minimum problem in molecular modeling. Tree searching internal coordinate conformation space,J. Comp. Chem. 4, 343–355.

    Google Scholar 

  • Lucasius, C. B. and Kateman, G. (1989), Application of genetic algorithms in chemometrics, inProceedings of the Third International Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Lucasius, C. B., Blommers, M. J. J., Buydens, L. M. C., and Kateman, G. (1990), A genetic algorithm for conformational analysis of DNA, inHandbook of Genetic Algorithms, Van Nostrand Reinhold, New York.

    Google Scholar 

  • Marqusee, S., Robbins, V. H., and Baldwin, R. L. (1989), Unusually stable helix formation in short alanine-based peptides,PNAS 86, 5286–5290.

    Google Scholar 

  • Momany, F., McGuire, R., Burgess, A., and Scheraga, H. (1975), Energy parameters in polypeptides. VII. Geometric parameters, partial atomic charges, nonbonded interactions, hydrogen bond interactions, and intrinsic torsional potentials for the naturally occurring amino acids,J. Phys. Chem. 79(22), 2361–2381.

    Google Scholar 

  • Montana, D. and Davis, L. (1989), Training feedforward neural networks using genetic algorithms, inProceedings of the Third International Joint Conference on Artificial Intelligence, Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Mühlenbein, H. (1989), Parallel genetic algorithms, population genetics, and combinatorial optimization, inProceedings of the Third International Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Ooi, T., Oobatake, M., Nemethy, G., and Scheraga, H. A. (1987), Accessible surface areas as a measure of the thermodynamic parameters of hydration of peptides,PNAS 84, 3086–3090.

    Google Scholar 

  • Piela, L. and Scheraga, H. (1989), The multiple minima problem in the conformational analysis of molecules. Deformation of the potential energy hypersurface by the diffusion equation method,J. Phys. Chem. 93, 3339–3346.

    Google Scholar 

  • Purisima, E. and Scheraga, H. (1987), An approach to the multiple-minima problem in protein folding by relaxing dimensionality: Tests on enkephalin,J. Mol. Biol. 196, 697–709.

    Google Scholar 

  • Qian, N. and Sejnowski, T. (1988), Predicting the secondary structure of globular proteins using neural network models,J. Mol. Biol. 202, 865–884.

    Google Scholar 

  • Radcliffe, N. and Wilson, G. (1990), Natural solutions give their best,New Scientist 126, 47–50.

    Google Scholar 

  • Richards, F. (1991), The Protein Folding Problem,Sci. Am. 264, 54–63.

    Google Scholar 

  • Richardson, J. S. (1981), The anatomy and taxonomy of protein structure,Adv. Protein Chem. 34, 167–284.

    Google Scholar 

  • Richardson, J. S. and Richardson, D. C. (1990), The origami of proteins, inProtein Folding: Deciphering the Second Half of the Genetic Code, AAAS Press, Washington, D.C.

    Google Scholar 

  • Ripoli, D. R., Vasquez, M., and Scheraga, H. A. (1991), The electrostatically driven monte carlo method: Application to conformational analysis of decaglycine,Biopolymers 31, 319–330.

    Google Scholar 

  • Schaffer, J. and Morishima, A. (1987), An adaptive crossover distribution mechanism for genetic algorithms, inGenetic Algorithms and Their Applications: Proceedings of the Second International Conference on Genetic Algorithms, Lawrence Erlbaum, Hillsdale, NJ.

    Google Scholar 

  • Sirag, D. and Weisser, P. (1987), Toward a unified thermodynamic genetic operator, inGenetic Algorithms and Their Applications: Proceedings of the Second International Conference on Genetic Algorithms, Lawrence Erlbaum, Hillsdale, NJ.

    Google Scholar 

  • Skolnick, J. and Kolinski, A. (1990), Simulations of the folding of a globular protein,Science 250, 1121–1125.

    Google Scholar 

  • Stolorz, P., Lapedes, A., and Xia, Y. (1991), Predicting protein secondary structure using neural net and statistical methods, to appear inJ. Mol. Biol.

  • Tanese, R. (1989), Distributed genetic algorithms, inProceedings of the Third International Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Vajda, S. and Delisi, C. (1990), Determining minimum energy conformations of polypeptides by dynamic programming,Biopolymers 29, 1755–1772.

    Google Scholar 

  • Vasquez, M., Nemethy, G., and Scheraga, H. A. (1983), Computed conformational states of the 20 naturally occurring amino acid residues and of the prototype residue a-aminobutyric acid,Macromolecules 16, 1043–1049.

    Google Scholar 

  • Walbridge, C. (1989), Genetic algorithms: What computers can learn from Darwin,Technology Review 92, 46–53.

    Google Scholar 

  • Wayner, P. (1991), Genetic algorithms,Byte 16, Jan., 361–364.

    Google Scholar 

  • Weiner, S., Kollmann, P., Nguyen, D., and Case, D. (1986), An all atom force field for simulations of proteins and nucleic acids,J. Comp. Chem. 7(2), 230–252.

    Google Scholar 

  • Whitley, D. and Kauth, J. (1988), Sampling long schemata in genetic algorithms, Tech Report CS-88-105, Computer Science Dept., Colorado State Univ.

  • Whitley, D. and Hanson, T. (1989a), The GENITOR algorithm and selective pressure: why rank-based allocation of reproductive trials is best, inProceedings of the Third International Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Whitley, D. and Hanson, T. (1989b), Optimizing neural nets using faster, more accurate genetic search, inProceedings of the Third International Conference on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA.

    Google Scholar 

  • Whitley, D., Starkweather, T., and Bogart, C. (1990a), Genetic algorithms and neural networks: optimizing connections and connectivity,Parallel Computing 13, 347–361.

    Google Scholar 

  • Whitley, D. and Starkweather, T. (1990b), GENITOR II: a distributed genetic algorithm,J. Exp. Theor. Artif. Intell. 2, 189–214.

    Google Scholar 

  • Wilson, S. and Cui, W. (1990), Applications of simulated annealing to peptides,Biopolymers 29, 225–235.

    Google Scholar 

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  1. Department of Molecular and Cell Biology and Department of Chemistry, The Pennsylvania State University, 16802, University Park, Pennsylvania, USA

    Scott M. Le Grand & Kenneth M. Merz Jr.

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  1. Scott M. Le Grand
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  2. Kenneth M. Merz Jr.
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Le Grand, S.M., Merz, K.M. The application of the genetic algorithm to the minimization of potential energy functions. J Glob Optim 3, 49–66 (1993). https://doi.org/10.1007/BF01100239

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