Iterative Convex Quadratic Approximation for Global Optimization in Protein Docking
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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.
Keywordsglobal optimization protein docking convex underestimator docking mesh evaluator potential energy
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- 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.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
- 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
- 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.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