Robust Biased Brownian Dynamics for Rate Constant Calculation

75 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002.A reaction probability is required to calculate the rate constant of a diffusion-dominated reaction. Due to the complicated geometry and potentially high dimension of the reaction probability problem, it is usually solved by Brownian dynamics simulations, which is also known as a random walk or path integral method, instead of solving the equivalent partial differential equation by a discretization method. In this thesis, a robust importance sampling algorithm for Brownian dynamics, biased Brownian dynamics with weight control, is developed to overcome the high energy and entropy barriers in biomolecular association reactions. The biased Brownian dynamics steers sampling by a biasing force, and the weight control algorithm controls sampling by a target weight. This algorithm is optimal if the biasing force and the target weight is constructed from the solution of the reaction probability. In reality, an approximate reaction probability has to be used to construct the biasing force and the target weight. Thus, how close the algorithm is to optimal depends on the quality of the approximate solution. Here, an a priori method and an a posteriori method are given to calculate the approximate solution. The a priori method is based on the selection of a reaction coordinate and the variational formulation of the reaction probability problem. The a posteriori method improves the approximate solution by collecting reaction probability information during the Brownian dynamics simulations. The algorithm is proved to be effective by numerical tests. The numerical tests for bovine SOD, Escherichia coli SOD, and anti-sweetener antibody NC6.8 show speedups of 16, 36, and 42, respectively. The numerical test for reactions between two model proteins with orientations shows speedups of 2578 for one set of configurations and 3484 for another set of configurations.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD