Analysis of integral expressions for effective Born radii

Generalized Born (GB) models provide a computationally efficient means of representing the electrostatic effects of solvent and are widely used, especially in molecular dynamics (MD). Accurate and facile computation of the effective Born radii is a key for the performance of GB models. Here, we examine a simple integral prescription, R6, based on the exact solution of the Poisson-Boltzmann (PB) equation for a perfect sphere. Numerical tests on 22 molecules representing a variety of structural classes show that R6 may be more accurate than the more complex integral-based approaches such as GBMV2. At the same time, R6 is computationally less demanding. Fundamental limitations of current integration-based methods for calculating effective radii, including R6, are explored and the deviations from the numerical PB results are correlated with specific topological and geometrical features of the molecular surface. A small systematic bias observed in the R6-based radii can be removed with a single, transferable constant offset; when the resulting effective radii are used in the "classical" (Still et al.'s) GB formula to compute the electrostatic solvation free energy, the average deviation from the PB reference is no greater than when the "perfect" (PB-based) effective radii are used. This deviation is also appreciably smaller than the uncertainty of the PB reference itself, as estimated by comparison to explicit solvent.