Three-dielectric-layer hybrid solvation model with spheroidal cavities in biomolecular simulations

This paper extends the three-dielectric-layer hybrid solvation model for treating electrostatic interactions in biomolecular simulations from the spherical geometry [Comm. Comp. Phys. 6, 955 (2009)] to the prolate/oblate spheroidal geometries. In the resulting model, the inner spheroidal cavity of a low dielectric constant epsilon(i) contains an irregular-shaped solute and some explicit solvent molecules, while the unbounded outer layer is used to implicitly model the bulk solvent as a dissimilar continuum medium of a high dielectric constant epsilon(o). The thin intermediate translation layer, which also consists of explicit solvent molecules, assumes a continuous variation of the dielectric permittivity epsilon(r) changing smoothly from epsilon(i) to epsilon(o). In particular, the so-called quasiharmonic dielectric permittivity profile is introduced based on a harmonic interpolation, thus allowing analytical series solutions of the generalized Coulomb potential and the self-polarization energy in terms of the associated Legendre functions. A key advantage of the proposed quasiharmonic dielectric model lies in the fact that it overcomes the inherent mathematical divergence in the self-polarization energy that exists in the simple and widely used steplike dielectric model. Numerical examples are included to show some simulated behaviors of the quasiharmonic dielectric model and the corresponding analytical solution.