An implicit boundary integral method for computing electric potential of macromolecules in solvent

TL;DR

This paper introduces an implicit boundary integral method utilizing level set techniques and fast multipole acceleration to efficiently compute the electrostatic potential of macromolecules in solvent, improving numerical accuracy and speed.

Contribution

It presents a novel implicit boundary integral approach combined with level set and fast multipole methods for solving Poisson-Boltzmann equations in molecular electrostatics.

Findings

Accurate electrostatic potential calculations demonstrated on standard test cases.

Method outperforms some existing approaches in computational efficiency.

Numerical results validate the effectiveness of the proposed approach.

Abstract

A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equations that arise in mathematical models for the electrostatics of molecules in solvent. The proposed method used an implicit boundary integral formulation to derived a linear system defined on Cartesian nodes in a narrowband surrounding the closed surface that separate the molecule and the solvent. The needed implicit surfaces is constructed from the given atomic description of the molecules, by a sequence of standard level set algorithms. A fast multipole method is applied to accelerate the solution of the linear system. A few numerical studies involving some standard test cases are presented and compared to other existing results.