A boundary-integral approach for the Poisson-Boltzmann equation with polarizable force fields

TL;DR

This paper introduces a boundary-integral method for solving the Poisson-Boltzmann equation with polarizable force fields like AMOEBA, demonstrating improved efficiency and accuracy over traditional methods, especially when utilizing GPU acceleration.

Contribution

The work implements and validates a boundary integral solver for polarizable force fields, overcoming limitations of mesh transfer issues seen in finite-difference approaches, and assesses its performance and accuracy.

Findings

Boundary integral approach performs similarly to volumetric methods on CPU.

GPU implementation offers significant speedup.

Polarizability influences cooperative effects in binding energy calculations.

Abstract

Implicit-solvent models are widely used to study the electrostatics in dissolved biomolecules, which are parameterized using force fields. Standard force fields treat the charge distribution with point charges, however, other force fields have emerged which offer a more realistic description by considering polarizability. In this work, we present the implementation of the polarizable and multipolar force field AMOEBA, in the boundary integral Poisson-Boltzmann solver \texttt{PyGBe}. Previous work from other researchers coupled AMOEBA with the finite-difference solver APBS, and found difficulties to effectively transfer the multipolar charge description to the mesh. A boundary integral formulation treats the charge distribution analytically, overlooking such limitations. We present verification and validation results of our software, compare it with the implementation on APBS, and assess the efficiency of AMOEBA and classical point-charge force fields in a Poisson-Botlzmann solver. We found that a boundary integral approach performs similarly to a volumetric method on CPU, however, it presents an important speedup when ported to the GPU. Moreover, with a boundary element method, the mesh density to correctly resolve the electrostatic potential is the same for stardard point-charge and multipolar force fields. Finally, we saw that polarizability plays an important role to consider cooperative effects, for example, in binding energy calculations.