Abstract
We derive a new numerical approach to solving the linearized Poisson Boltzmann equation (PBE) by representing the protein surface as a collection of spheres in which the surface charges can then be iteratively solved by new analytical multipole methods previously introduced by us [Lotan & Head-Gordon, 2006]. We show that our Poisson Boltzmann semi-analytical method, PB-SAM, realizes better accuracy, more flexible memory management, and at reduced cost relative to either finite difference or boundary element method PBE solvers. We provide two new benchmarks of PBE solution accuracy to test the numerical PBE solutions based on (1) arrays of up to hundreds of spherical low dielectric geometries with asymmetric charges in which mutual polarization is treated exactly, and (2) two overlapping spheres with increasing charge asymmetry by solving the PB-SAM method to very high pole order. We illustrate the strength of the PB-SAM approach by computing the potential profile of an array of 60 T1-particle forming monomers of the bromine mosaic virus.