Advertisement

Computational Optimization and Applications

, Volume 32, Issue 3, pp 285–297 | Cite as

Iterative Convex Quadratic Approximation for Global Optimization in Protein Docking

  • Roummel F. Marcia
  • Julie C. Mitchell
  • J. Ben Rosen
Article

Abstract

An algorithm for finding an approximate global minimum of a funnel shaped function with many local minima is described. It is applied to compute the minimum energy docking position of a ligand with respect to a protein molecule. The method is based on the iterative use of a convex, general quadratic approximation that underestimates a set of local minima, where the error in the approximation is minimized in the L1 norm. The quadratic approximation is used to generate a reduced domain, which is assumed to contain the global minimum of the funnel shaped function. Additional local minima are computed in this reduced domain, and an improved approximation is computed. This process is iterated until a convergence tolerance is satisfied. The algorithm has been applied to find the global minimum of the energy function generated by the Docking Mesh Evaluator program. Results for three different protein docking examples are presented. Each of these energy functions has thousands of local minima. Convergence of the algorithm to an approximate global minimum is shown for all three examples.

Keywords

global optimization protein docking convex underestimator docking mesh evaluator potential energy 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    N. Baker, M. Holst, and F. Wang, “Adaptive multilevel finite element solution of the Poisson-Boltzmann equation II: Refinement at solvent accessible surfaces in biomolecular systems,” J. Comput. Chem., vol. 21, pp. 1343–1352, 2000.CrossRefGoogle Scholar
  2. 2.
    K.A. Dill, A.T. Phillips, and J.B. Rosen, CGU: An algorithm for molecular structure prediction, in Large-scale optimization with applications, Part III (Minneapolis, MN, 1995), vol. 94 of IMA Vol. Math. Appl., Springer: New York, 1997, pp. 1–21.Google Scholar
  3. 3.
    P.E. Gill, W. Murray, M.A. Saunders, and M.H. Wright, “User's guide for NPSOL (version 4.0): A Fortran package for nonlinear programming,” Tech. Rep. SOL-86-2, Systems Optimization Laboratory, Stanford University, Stanford, CA, 1986.Google Scholar
  4. 4.
    D.S. Goodsell and A.J. Olson, “Automated docking of substrates to proteins by simulated annealing,” Proteins: Struct. Fun. Gen., vol. 8, pp. 195–202, 1990.CrossRefGoogle Scholar
  5. 5.
    M. Holst, N. Baker, and F. Wang, “Adaptive multilevel finite element solution of the Poisson-Boltzmann equation I: Algorithms and examples,” J. Comput. Chem., vol. 21, pp. 1319–1342, 2000.CrossRefGoogle Scholar
  6. 6.
    R. Hooke and T. A. Jeeves, “Direct search solution of numerical and statistical problems,” J. Assoc. Comput. Mach., vol. 8, pp. 212–229, 1961.Google Scholar
  7. 7.
    J. Janin, “Welcome to CAPRI: A critical assessment of predicted interactions,” Proteins: Struct. Func. Genet., vol. 47, no. 3, p. 257, 2002.CrossRefGoogle Scholar
  8. 8.
    E.C. Meng, B.K. Shoichet, and I.D. Kuntz, “Automated docking with grid-based energy evaluation,” J. Comp. Chem., vol. 13, pp. 505–524, 1992.CrossRefGoogle Scholar
  9. 9.
    J.C. Mitchell, J.B. Rosen, A.T. Phillips, and L.F. Ten Eyck, “Coupled optimization in protein docking,” in Proceedings of the Third Annual International Conference on Computational Molecular Biology, ACM Press, 1999, pp. 280–284.Google Scholar
  10. 10.
    J.B. Rosen, K.A. Dill, and A.T. Phillips, “Protein structure and energy landscape dependence on sequence using a continuous energy function,” J. Comp. Biol., vol. 4, pp. 227–239, 1997.Google Scholar
  11. 11.
    J.B. Rosen and R.F. Marcia, “Convex quadratic approximation,” Comput. Optim. Appl., vol. 28, pp. 173–184, 2004.CrossRefGoogle Scholar
  12. 12.
    J.B. Rosen, H. Park, J. Glick, and L. Zhang, “Accurate solution to overdetermined linear equations with errors using L sb 1 norm minimization,” Comput. Optim. Appl., vol. 17, pp. 329–341, 2000.CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Roummel F. Marcia
    • 1
  • Julie C. Mitchell
    • 2
  • J. Ben Rosen
    • 3
  1. 1.Departments of Biochemistry and MathematicsUniversity of Wisconsin-MadisonMadison
  2. 2.Department of Biochemistry and MathematicsUniversity of Wisconsin-MadisonMadison
  3. 3.Department of Computer Science and EngineeringUniversity of CaliforniaSan Diego, La Jolla

Personalised recommendations