TREATMENT OF ELECTROSTATIC EFFECTS IN PROTEINS - MULTIGRID-BASED NEWTON ITERATIVE METHOD FOR SOLUTION OF THE FULL NONLINEAR POISSON-BOLTZMANN EQUATION

The nonlinear Poisson-Boltzmann equation (NPBE) provides a continuum d escription of the electrostatic field in an ionic medium around a macr omolecule. Here, a novel approach to the solution of the full NPBE is developed. This robust and efficient algorithm combines multilevel tec hniques with a damped inexact Newton's method. The CPU time required f or solution of the full NPBE, which is less than that for standard sin gle-grid approaches in solving the corresponding Linearized equation, is proportional to the number of unknowns enabling applications to ver y large macromolecular systems. Convergence of the method is demonstra ted for a variety of protein systems. Comparison of the solutions to t he linearized Poisson-Boltzmann equation shows that the damping of the electrostatic field around the charge is increased and that the poten tial scales logarithmically with charge. The inclusion of the full non linearity thus reduces the impact of highly charged residues on protei n surfaces and provides a more realistic representation of electrostat ic effects. This is demonstrated through calculation of potential arou nd the active site regions of the 1,266-residue tryptophan synthase di mer and in the computation of rate constants from Brownian dynamics ca lculations in the superoxide dismutase-superoxide and antibody-antigen systems. (C) 1994 Wiley-Liss, Inc.