Enriched Gradient Recovery for Interface Solutions of the Poisson-Boltzmann Equation

TL;DR

This paper introduces a novel numerical method that enhances the accuracy and stability of electrostatic potential and gradient calculations on molecular surfaces by enriching the potential reconstruction with Green's functions.

Contribution

A new enriched gradient recovery method for interface solutions of the Poisson-Boltzmann equation is proposed, improving accuracy over classical techniques.

Findings

Significantly more accurate potential gradients on molecular surfaces.

Enhanced stability of gradient recovery compared to classical methods.

Effective in large-scale biomolecular modeling applications.

Abstract

Accurate calculation of electrostatic potential and gradient on the molecular surface is highly desirable for the continuum and hybrid modeling of large scale deformation of biomolecules in solvent. In this article a new numerical method is proposed to calculate these quantities on the dielectric interface from the numerical solutions of the Poisson-Boltzmann equation. Our method reconstructs a potential field locally in the least square sense on the polynomial basis enriched with Green's functions, the latter characterize the Coulomb potential induced by charges near the position of reconstruction. This enrichment resembles the decomposition of electrostatic potential into singular Coulomb component and the regular reaction field in the Generalized Born methods. Numerical experiments demonstrate that the enrichment recovery produces drastically more accurate and stable potential gradients on molecular surfaces compared to classical recovery techniques.