A regularized Matched Interface and Boundary Method (MIB) for Solving Polarizable Multipole Poisson-Boltzmann model

Abstract

To accurately model the electron density and polarization, a polarizable multipole (PM) model using the AMOEBA force field has been introduced \cite{Ren:2003, Shi:2013} recently. In the AMOEBA force field, the traditional point atomic representation is updated with permanent multipoles including additional dipoles and quadrupoles at atom centers in terms of derivatives of delta functions. Meanwhile, the polarization of the solute is considered by the introduction of induced dipoles. The AMOEBA forcefield thus shows significantly better agreement with experimental and high-level {\it ab initio} results. Moreover, the AMOEBA force field keeps the simple atomic structure, so that it can conviniently replace the traditional partial charge model. In this paper, we address the numerical challenges associated with the Polarizable Multipole Poisson--Boltzamnnn (PM-PB) model, which couples the AMOEBA force field with a linear Poisson-Boltzmann equation for implicit solvent and polarization modeling. To solve the PM-PB model, we designed a regularized Matched Interface and Boundary (MIB) method to analytically regularizes the singular source term in the PMPB model while maintains 2nd order accuracy by rigorously treating the interface conditions. The accuracy of the method is validated on Kirkwood sphere with available analytical solutions and on proteins whose charge distribution are assigned using AMOEBA force field.