A fast solver for nonlocal electrostatic theory in biomolecular science and engineering

Biological molecules perform their functions surrounded by water and mobile ions, which strongly influence molecular structure and behavior. The electrostatic interactions between a molecule and solvent are particularly difficult to model theoretically, due to the forces' long range and the collective response of many thousands of solvent molecules. The dominant modeling approaches represent the two extremes of the trade-off between molecular realism and computational efficiency: all-atom molecular dynamics in explicit solvent, and macroscopic continuum theory (the Poisson or Poisson--Boltzmann equation). We present the first fast-solver implementation of an advanced nonlocal continuum theory that combines key advantages of both approaches. In particular, molecular realism is included by limiting solvent dielectric response on short length scales, using a model for nonlocal dielectric response allows the resulting problem (a linear integro-differential Poisson equation) to be reformulated as a system of coupled boundary-integral equations using double reciprocity. Whereas previous studies using the nonlocal theory had been limited to small model problems, owing to computational cost, our work opens the door to studying much larger problems including rational drug design, protein engineering, and nanofluidics.