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An efficient algorithm combining cell multipole and multigrid methods for rapid evaluation of dipole iteration in polarizable force fields

  • Author(s): Dinh-Truong, Thuy Linh
  • et al.
Abstract

There has been continuing effort to develop polarizable force fields for computational studies of biological systems. Applications of polarizable models in molecular dynamics simulations include liquid water, ionic systems, alcohols, solvated proteins, interfacial systems and membrane systems. An overview of the advances in development of these polarizable force fields to date is presented. Recent studies have shown that the dynamic response to inhomogeneous environment represented by the explicit inclusion of polarization is necessary for more realistic descriptions of biosystems. Explicitly including polarization effects in force fields requires self- consistent iteration to evaluate induced dipole moments. However, the demanding computational cost using traditional solvers limits the system sizes that can be fully described with explicit polarization. To make this calculation more tractable for large-scale systems, an efficient method for computation of polarizable interactions is needed. An algorithm combining hierarchical cell multipole (CMM) and multigrid (MG) schemes is developed for fast computation of these interactions, using polarizable point dipoles. This scheme separates polarizable interactions into direct and indirect components, where we derived the CMM electric field terms for dipolar systems to handle long-range interactions. A fast multigrid solver is applied to further increase computational efficiency in solving these induced dipolar calculations. Performance of various iterative solvers, Jacobi, Gauss-Seidel, successive over- relaxation, conjugate gradient, and our newly developed multigrid-multipole (MG-CMM) solver are compared for test cases of varying system sizes to demonstrate the efficiency of this algorithm for a uniform distribution. The MG-CMM algorithm achieves fast convergence with reasonable accuracy. A matrix version of the cell multipole method is derived and extended to include polarizable dipoles. In order to extend MG-CMM to treat non-uniform distributions, we have casted the cell multipole method in matrix form and introduce an algebraic multigrid and matrix-based cell multipole (AMG-CMMm) scheme to reduce the number of iterations to self- consistency. For further speedup, AMG-CMMm can be parallelized and the sparse matrix storage can be optimized. An efficient implementation of this technique will significantly reduce the number of dipole iterations for large polarizable systems and help enhance the ability of force field methods to accurately describe biomolecular processes

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