Protein electrostatics: rapid multigrid-based Newton algorithm for solution of the full nonlinear Poisson-Boltzmann equation.

Abstract

A new method for solving the full nonlinear Poisson-Boltzmann equation is outlined. This method is robust and efficient, and uses a combination of the multigrid and inexact Newton algorithms. The novelty of this approach lies in the appropriate combination of the two methods, neither of which by themselves are capable of solving the nonlinear problem accurately. Features of the Poisson-Boltzmann equation are fully exploited by each component of the hybrid algorithm to provide robustness and speed. The advantages inherent in this method increase with the size of the problem. The efficacy of the method is illustrated by calculations of the electrostatic potential around the enzyme Superoxide Dismutase. The CPU time required to solve the full nonlinear equation is less than half that needed for a conjugate gradient solution of the corresponding linearized Poisson-Boltzmann equation. The solutions reveal that the field around the active sites is significantly reduced as compared to that obtained by solving the corresponding linearized Poisson-Boltzmann equation. This new method for the nonlinear Poisson-Boltzmann equation will enable fast and accurate solutions of large protein electrostatics problems.