Optimal integral expressions for effective radii in the generalized Born model of molecular solvation

The goal of this paper is to derive better approximations for effective Born radii in the generalized Born model of molecular solvation by analyzing the Kirkwood-series solution of the Poisson equation for a spherical solute. The main focus is on solutes under non-conducting boundaries, where the solute dielectric constant 2in and solvent dielectric constant 2ex lead to a non-vanishing ratio δ = 2in 2in+2ex , 0 < δ ≤ 0.5. A series approximation is developed for the Born radius, in which a dominant leading term is corrected by terms of the order of O(δ). The series is further approximated by an expansion of volume integrals over the solute domain. Optimal combinations of integrals are then proposed, based on computational cost and accuracy criteria. The combinations are tested on solute molecules with non-spherical geometry including a prolate spheroidal model and a protein molecule. For finite values of δ, the proposed formulas are seen to work better than the models developed previously. The relative accuracy of integral expressions is seen to vary among spherical and non-spherical solutes.