PROTEIN ELECTROSTATICS - RAPID MULTIGRID-BASED NEWTON ALGORITHM FOR SOLUTION OF THE FULL NONLINEAR POISSON-BOLTZMANN EQUATION

A new method for solving the full nonlinear Poisson-Boltzmann equation is outlined. This method is robust and efficient, and uses a combinat ion of the multigrid and inexact Newton algorithms. The novelty of thi s approach lies in the appropriate combination of the two methods, nei ther of which by themselves are capable of solving the nonlinear probl em accurately. Features of the Poisson-Boltzmann equation are fully ex ploited by each component of the hybrid algorithm to provide robustnes s and speed. The advantages inherent in this method increase with the size of the problem. The efficacy of the method is illustrated by calc ulations of the electrostatic potential around the enzyme Superoxide D ismutase. The CPU time required to solve the full nonlinear equation i s less than half that needed for a conjugate gradient solution of the corresponding linearized Poisson-Boltzmann equation. The solutions rev eal that the field around the active sites is significantly reduced as compared to that obtained by solving the corresponding linearized Poi sson-Boltzmann equation. This new method for the nonlinear Poisson-Bol tzmann equation will enable fast and accurate solutions of large prote in electrostatics problems.