Work/Precision Tradeoffs in Continuum Models of Biomolecular Electrostatics

TL;DR

This paper explores a simplified boundary-element method for biomolecular electrostatics, modeling surface charges as discrete points, which offers better accuracy at low resolution for certain applications like drug design.

Contribution

It introduces a point-charge boundary-element approach that improves low-resolution accuracy over traditional panel-based methods in biomolecular electrostatics calculations.

Findings

Point-based BEM outperforms panel-based BEM at low resolution.

Surface sampling with point charges enhances accuracy for moderate-precision tasks.

The method is computationally simpler and effective for early-stage drug design.

Abstract

The structure and function of biological molecules are strongly influenced by the water and dissolved ions that surround them. This aqueous solution (solvent) exerts significant electrostatic forces in response to the biomolecule's ubiquitous atomic charges and polar chemical groups. In this work, we investigate a simple approach to numerical calculation of this model using boundary-integral equation (BIE) methods and boundary-element methods (BEM). Traditional BEM discretizes the protein--solvent boundary into a set of boundary elements, or panels, and the approximate solution is defined as a weighted combination of basis functions with compact support. The resulting BEM matrix then requires integrating singular or near singular functions, which can be slow and challenging to compute. Here we investigate the accuracy and convergence of a simpler representation, namely modeling the unknown surface charge distribution as a set of discrete point charges on the surface. We find that at low resolution, point-based BEM is more accurate than panel-based methods, due to the fact that the protein surface is sampled directly, and can be of significant value for numerous important calculations that require only moderate accuracy, such as the preliminary stages of rational drug design and protein engineering.