Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators.

摘要: In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing operators fact that their eigenfunctions are surface harmonics. To introduce uncommon calculations separable geometries, first re-derive Kirkwood's classic results protein surrounded concentrically by pure-water ion-exclusion (Stern) layer then dilute electrolyte, which is modeled with linearized Poisson-Boltzmann equation. The eigenfunction-expansion provides computationally efficient way test some implications of models, including estimating reasonable range length-scale parameter λ. suggest solvent response may help reduce need very high dielectric constants calculating pH-dependent behavior, though more sophisticated models needed resolve question full. An open-source MATLAB implementation our freely available online.