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Novel Applications of Optimization to Molecule Design

  • J. C. Meza
  • T. D. Plantenga
  • R. S. Judson
Chapter
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 94)

Abstract

We present results from the application of two conformational search methods: genetic algorithms (GA) and parallel direct search methods for finding all of the low energy conformations of a molecule that are within a certain energy of the global minimum. Genetic algorithms are in a class of biologically motivated optimization methods that evolve a population of individuals where individuals who are more “ fit ” have a higher probability of surviving into subsequent generations. The parallel direct search method (PDS) is a type of pattern search method that uses an adaptive grid to search for minima. In addition, we present a technique for performing energy minimization based on using a constrained optimization method.

Key words

global optimization constrained optimization nonlinear programming molecular conformation 

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References

  1. [1]
    R. Abagyan, M. Totrov, and D. Kuznetsov, ICM—a new method for protein modeling and design: applications to docking and structure prediction from the distorted native conformation, J. Comp. Chem., 15:488–506, 1994.CrossRefGoogle Scholar
  2. [2]
    H. Abe, W. Braun, T. Noguti, and N. Go, Rapid calculation of first and second derivatives of conformational energy with respect to dihedral angles for proteins: general recurrent equations, Comp. and Chem., 8:239–247, 1984.CrossRefGoogle Scholar
  3. [3]
    M.P. Allen and D.J. Tildesley, Computer Simulation of Liquids, New York: Oxford UP, 1987.zbMATHGoogle Scholar
  4. [4]
    G. Box and K. Wilson, On the experimental attainment of optimum conditions, J. Royal Statistical Society, Series B, 13 (1951), pp. 1–45.MathSciNetGoogle Scholar
  5. [5]
    B.R. Brooks, R.E. Bruccoleri, B.D. Olafson, D.J. States, S. Swaminatha, and M. Karplus, CHARMM: a program for macromolecular energy, minimization, and dynamics calculations, J. Comp. Chem., 4:187–217, 1983.CrossRefGoogle Scholar
  6. [6]
    R.H. Byrd, Robust trust region methods for constrained optimization, Third SIAM Conference on Optimization, Houston, 20 May 1987.Google Scholar
  7. [7]
    R. Byrd, E. Eskow, and R. Schnabel, A new large-scale global optimization method and its application to Lennard-Jones problems, Tech. Report CU-CS-630-92, University of Colorado at Boulder, 1992.Google Scholar
  8. [8]
    R. Byrd, E. Eskow, R. Schnabel, and S. Smith, Parallel global optimization: Numerical methods, dynamic scheduling methods, and applications to molecular configuration, Tech. Report CU-CS-553-91, University of Colorado at Boulder, 1991.Google Scholar
  9. [9]
    R.H. Byrd, J. Nocedal, R.B. Schnabel, Representations of quasi-Newton matrices and their use in limited memory methods, Math. Prog. (Ser. A), 63:129–156, 1994.MathSciNetzbMATHCrossRefGoogle Scholar
  10. [10]
    G. Ciccotti, M. Ferrario, and J.-P. Ryckaert, Molecular dynamics of rigid systems in cartesian coordinates: a general formulation, Molec. Phys., 47:1253–1264, 1982.CrossRefGoogle Scholar
  11. [11]
    D. Cvijovic and J. Klinowski, Taboo search: An approach to the multiple minima problem, Science, 267 (1995), p. 664.MathSciNetCrossRefGoogle Scholar
  12. [12]
    J. Dennis and V. Torczon, Direct search methods on parallel machines, SIAM J. Optimization, 1 (1991), pp. 448–474.MathSciNetzbMATHCrossRefGoogle Scholar
  13. [13]
    J.J. Dongarra, J.R. Bunch, C.B. Moler, and G.W. Stewart, LINPACK User’s Guide, Philadelphia: SIAM, 1979.CrossRefGoogle Scholar
  14. [14]
    R. Fletcher, Practical Methods of Optimization, Second ed., Chichester, UK: Wiley & Sons, 1990.Google Scholar
  15. [15]
    P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization, London: Academic Press-Harcourt, 1981.zbMATHGoogle Scholar
  16. [16]
    N. Go and H.A. ScHeraga, Ring closure and local conformational deformations of chain molecules, Macromolecules, 3:178–187, 1970.CrossRefGoogle Scholar
  17. [17]
    D. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, 1989.Google Scholar
  18. [18]
    G. H. Golub and C. F. Van Loan., Matrix Computations, Second ed., Baltimore: Johns Hopkins UP, 1991.Google Scholar
  19. [19]
    M.R. Hoare, Structure and dynamics of simple microclusters, Adv. Chem. Phys., 40:49–135, 1979.CrossRefGoogle Scholar
  20. [20]
    R. Hooke and T. Jeeves, Direct search solution of numerical and statistical problems, J. Assoc. Comp. Mach., 8 (1961), pp. 212–229.zbMATHCrossRefGoogle Scholar
  21. [21]
    A. Howard and P. Kollman, An analysis of current methodologies for conformational searching of complex molecules, J. Med. Chem., 31 (1988), pp. 1669–1675.CrossRefGoogle Scholar
  22. [22]
    R. Judson, D. Barsky, T. Faulkner, D. Mcgarrah, C. Melius, J. Meza, E. Mori, and T. Plantenga, CCEMD-Center for Computational Engineering molecular dynamics: Theory and users’ guide, version 2.2, Tech. Report SAND95-8258, Sandia National Laboratories, 1995.Google Scholar
  23. [23]
    R. Judson, M. Colvin, J. Meza, A. Huffer, and D. Gutierrez, DO intelligent configuration search techniques outperform random search for large molecules?, International Journal of Quantum Chemistry, 44 (1992), pp. 277–290.CrossRefGoogle Scholar
  24. [24]
    R. Judson, E. Jaeger, A. Treasurywala, and M. Peterson, Conformational searching methods for small molecules II: A genetic algorithm approach, J.Comp.Chem., 14 (1993), p. 1407.CrossRefGoogle Scholar
  25. [25]
    J. Kostrowicki, L. Piela, B. Cherayil, and H. ScHeraga, Performance of the diffusion equation method in searches for optimum structures of clusters of Lennard-Jones atoms, J.Phys.Chem., 95 (1991), p. 4113.CrossRefGoogle Scholar
  26. [26]
    M. Lalee, J. Nocedal, and T. Plantenga, On the implementation of an algorithm for large-scale equality constrained optimization, Submitted to SIAM J. Optimization, 1993.Google Scholar
  27. [27]
    S.M. Legrand and K.M. Merz JR., The application of the genetic algorithm to the minimization of potential energy functions, Journal of Global Optimization, Vol. 3.1 (1993), pp. 49–66.MathSciNetCrossRefGoogle Scholar
  28. [28]
    D.C. Liu and J. Nocedal, On the limited memory BFGS method for large scale optimization, Math. Prog. (Ser. B), 45:503–525, 1989.MathSciNetzbMATHCrossRefGoogle Scholar
  29. [29]
    R. Maier, J. Rosen, and G. Xue, Discrete-continuous algorithm for molecular energy minimization, Tech. Report 92-031, AHPCRC, 1992.Google Scholar
  30. [30]
    C. Maranas and C. Floudas, A deterministic global optimization approach for molecular structure determination, J.Chem.Phys., 100 (1994), p. 1247.CrossRefGoogle Scholar
  31. [31]
    A.K. Mazur, V.E. Dorofeev, and R.A. Abagyan, Derivation and testing of explicit equations of motion for polymers described by internal coordinates, J.Comput. Phys., 92:261–272, 1991.zbMATHCrossRefGoogle Scholar
  32. [32]
    J. Meza, R. Judson, T. Faulkner, and A. Treasurywala, A comparison of a direct search method and a genetic algorithm for conformational searching, Tech. Report SAND95-8225, Sandia National Laboratories, 1995. To appear in the J. Comp. Chem., 1996.Google Scholar
  33. [33]
    J. Meza and M. Martinez, Direct search methods for the molecular conformation problem, Journal of Computational Chemistry, 15 (1994), pp. 627–632.CrossRefGoogle Scholar
  34. [34]
    F.A. Momany, R.F. Mcguire, A.W. Burgess, and H.A. Scheraga, Geometric parameters, partial atomic charges, nonbonded interactions, hydrogen bond interactions, and intrinsic torsional potentials for the naturally occurring amino acids, J. Phys. Chem., 79:2361–2381, 1975.CrossRefGoogle Scholar
  35. [35]
    J. Nelder and R. Mead, A simplex method for function minimization, Comput. J., 7 (1965), pp. 308–313.zbMATHGoogle Scholar
  36. [36]
    E.O. Omojokun, Trust region algorithms for optimization with nonlinear equality and inequality constraints, Diss., Dept. of Computer Science, University of Colorado, 1989.Google Scholar
  37. [37]
    P.M. Pardalos, D. Shalloway, and G. Xue (EDITORS), Optimization Methods for Computing Global Minima of Nonconvex Potential Energy Functions, Journal of Global Optimization, Vol. 4.2 (1994), pp. 117–133.MathSciNetCrossRefGoogle Scholar
  38. [37]
    P.M. Pardalos, D. Shalloway, and G. Xue (EDITORS), Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding, DIMACS Series, Vol. 23, American Mathematical Society (1996).Google Scholar
  39. [39]
    T.D. Plantenga, Large-scale nonlinear constrained optimization using trust regions, Diss., Dept. of Electrical Engineering and Computer Science, Northwestern University, 1994.Google Scholar
  40. [40]
    T. PLantenga and R. Judson, Energy minimization along dihedrals in cartesian coordinates using constrained optimization, Tech. Report SAND95-8724, Sandia National Laboratories, 1995.Google Scholar
  41. [41]
    QUANTA/CHARMM, Molecular Simulations, Inc. (Waltham MA, 1993). The results published were generated in part using the program QUANTA. This program was developed by Molecular Simulations, Inc.Google Scholar
  42. [42]
    M. Saunders, Stochastic search for the conformations of icyclic hydrocarbons, J.Comp.Chem., 10 (1989), p. 203.CrossRefGoogle Scholar
  43. [43]
    M. Saunders, K. Houk, Y.-D. Wu, W. C. Still, M. Lipton, G. Chang, and W. C. Guida, Conformations of cycloheptadecane. A comparison of methods for conformational searching, J. Am. Chem. Soc, 112 (1990), pp. 1419–1427.CrossRefGoogle Scholar
  44. [44]
    S. Sunada and N. Go, Small-amplitude protein conformational dynamics: second-order analytic relation between Cartesian coordinates and dihedral angles, J. Comp. Chem., 16:328–336, 1995.CrossRefGoogle Scholar
  45. [45]
    S. Wilson and W. Cui, Applications of simulated annealing to peptides, Biopoly-mers, 29 (1990), pp. 225–235.CrossRefGoogle Scholar
  46. [46]
    G. Xue, Improvement on the Nortkby algorithm for molecular conformation: Better solutions, Tech. Report 92-055, University of Minnesota, 1992.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • J. C. Meza
    • 1
  • T. D. Plantenga
    • 1
  • R. S. Judson
    • 1
  1. 1.Scientific Computing DepartmentMS 9214, Sandia National LaboratoriesLivermoreUSA

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