Image Charge Methods for a Three-Dielectric-Layer Hybrid Solvation Model of Biomolecules (Communications in Computational Physics, 2020)
This paper introduces a three dielectric layer hybrid solvation model fortreating electrostatic interactions of biomolecules in solvents using the Poisson-Boltzmannequation. In this model, an interior spherical cavity will contain the soluteand some explicit solvent molecules, and an intermediate buffer layer and an exteriorlayer contain the bulk solvent. A special dielectric permittivity profile is used toachieve a continuous dielectric transition from the interior cavity to the exterior layer.The selection of this special profile using a harmonic interpolation allows an analyticalsolution of the model by generalizing the classical Kirkwood series expansion. Discreteimage charges are used to speed up calculations for the electrostatic potential withinthe interior and buffer layer regions. Semi-analytical and least squares methods areused to construct an accurate discrete image approximation for the reaction field dueto solvent with or without salt effects. In particular, the image charges obtained bythe least squares method provide accurate approximations to the reaction field independentof the ionic concentration of the solvent. Numerical results are presented tovalidate the accuracy and effectiveness of the image charge methods.