An Adaptive,Finite Difference Solver for the Nonlinear Poisson-Boltzmann Equation with Applications to Biomolecular Computations

We present a solver for the Poisson-Boltzmann equation and demonstrate its applicability for biomolecular electrostatics computation.The solver uses a level set framework to represent sharp,complex interfaces in a simple and robust manner.It also uses non-graded,adaptive octree grids which,in comparison to uniform grids,drastically decrease memory usage and runtime without sacrificing accuracy.The basic solver was introduced in earlier works[16,27],and here is extended to address biomolecular systems.First,a novel approach of calculating the solvent excluded and the solvent accessible surfaces is explained;this allows to accurately represent the location of the molecule’s surface.Next,a hybrid finite difference/finite volume approach is presented for discretizing the nonlinear Poisson-Boltzmann equation and enforcing the jump boundary conditions at the interface.Since the interface is implicitly represented by a level set function,imposing the jump boundary conditions is straightforward and efficient.