SOLVING THE FINITE-DIFFERENCE, NONLINEAR, POISSON-BOLTZMANN EQUATION UNDER A LINEAR-APPROACH

Electrostatic interactions are among the key factors in determining th e structure and function of biomolecules. Simulating such interactions involves solving the Poisson equation and the Poisson-Boltzmann (P-B) equation in the molecular interior and exterior region, respectively. The P-B equation is a nonlinear partial differential equation. The ce ntral processing unit (CPU) time for solving the full nonlinear P-B eq uation has been severalfold greater than the equivalent Linear case. H ere a simple method is proposed to solve the full nonlinear P-B equati on under a linear approach, which has been tested both on a spherical case and on small molecules. Results show that our method converges ra pidly even under highly charged cases. With this method, the CPU time for solving the full nonlinear P-B equation is somewhat less than the equivalent linear case in our calculations. (C) 1995 by John Wiley and Sons, Inc.