Iterative Convex Quadratic Approximation for Global Optimization in Protein Docking |
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| Authors: | Roummel F Marcia Julie C Mitchell J Ben Rosen |
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| Institution: | (1) Departments of Biochemistry and Mathematics, University of Wisconsin-Madison, Madison, WI;(2) Department of Biochemistry and Mathematics, University of Wisconsin-Madison, Madison, WI;(3) Department of Computer Science and Engineering, University of California, San Diego, La Jolla, CA |
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| 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. |
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| Keywords: | global optimization protein docking convex underestimator docking mesh evaluator potential energy |
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