Accurate, robust and reliable calculations of Poisson-Boltzmann binding energies

TL;DR

This paper evaluates the impact of grid spacing on the accuracy of Poisson-Boltzmann calculations of electrostatic energies, proposing optimal grid sizes for reliable and efficient biophysical computations.

Contribution

It systematically investigates grid dependence in PB calculations, identifying grid spacings that balance accuracy and computational efficiency for solvation and binding free energies.

Findings

Grid spacing of 0.6 Å ensures accurate ΔΔG_el calculations.

Grid spacing of 1.1 Å is sufficient for high throughput screening.

Relative error in ΔG_el is less than 0.2% at 1.0 Å grid compared to 0.2 Å.

Abstract

Poisson-Boltzmann (PB) model is one of the most popular implicit solvent models in biophysical modeling and computation. The ability of providing accurate and reliable PB estimation of electrostatic solvation free energy, $\Delta G_{\text{el}}$, and binding free energy, $\Delta\Delta G_{\text{el}}$, is of tremendous significance to computational biophysics and biochemistry. Recently, it has been warned in the literature (Journal of Chemical Theory and Computation 2013, 9, 3677-3685) that the widely used grid spacing of $0.5$ \AA $ $ produces unacceptable errors in $\Delta\Delta G_{\text{el}}$ estimation with the solvent exclude surface (SES). In this work, we investigate the grid dependence of our PB solver (MIBPB) with SESs for estimating both electrostatic solvation free energies and electrostatic binding free energies. It is found that the relative absolute error of $\Delta G_{\text{el}}$ obtained at the grid spacing of $1.0$ \AA $ $ compared to $\Delta G_{\text{el}}$ at $0.2$ \AA $ $ averaged over 153 molecules is less than 0.2\%. Our results indicate that the use of grid spacing $0.6$ \AA $ $ ensures accuracy and reliability in $\Delta\Delta G_{\text{el}}$ calculation. In fact, the grid spacing of $1.1$ \AA $ $ appears to deliver adequate accuracy for high throughput screening.