  Electrostatic forces play many important roles in molecular biology, but are
hard to model due to the complicated interactions between biomolecules and the
surrounding solvent, a fluid composed of water and dissolved ions. Continuum
model have been surprisingly successful for simple biological questions, but
fail for important problems such as understanding the effects of protein
mutations. In this paper we highlight the advantages of boundary-integral
methods for these problems, and our use of boundary integrals to design and
test more accurate theories. Examples include a multiscale model based on
nonlocal continuum theory, and a nonlinear boundary condition that captures
atomic-scale effects at biomolecular surfaces.
