  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.
