Reducing the Secondary Structure Bias in the Generalized Born Model via R6 Effective Radii

The generalized Born model (GB) provides a reasonably accurate and computationally efficient way to compute the electrostatic component (Delta G(el)) of the solvation free energy. In this work, we have developed a method to compute effective Born radii, which is intended to address the known secondary structure bias of the GB model reported earlier (Roe et al. J. Phys. Chem. B, 2007, 111, 1846-1857). Our analytical approach, termed AR6, is based on the vertical bar r vertical bar(-6) (R6) integration over an approximation to molecular volume. Within the approach, several computationally efficient corrections to the pairwise VDW-volume integration are combined to closely approximate the true molecular volume in the vicinity of each atom. The accuracy of the AR6 model in predicting relative Delta G(el) is tested on four conformational states of alanine decapeptide. Changes in Delta G(el) estimated by AR6 between various pairs of conformational states have the same RMS error relative to the explicit solvent, as do the corresponding numerical PB values; at the same time, the RMS error of the proposed model is 2 times lower than that of the popular GB_OBC model from the AMBER package. Tests against the PB treatment on 22 biomolecular structures including proteins and DNA show that the relative error of Delta G(el) is 0.58%; the RMS error of Delta G(el) computed by AR6 is 3 times lower than the corresponding value for GB_OBC. However, the computational efficiencies of the AR6 and GB_OBC models are comparable. A variant of the R6 model, NSR6, based on numerically exact integration over triangulated molecular surface is tested on a "challenge" set of small drug-like molecules (Nicholls et al. J. Med. Chem. 2008, 51, 769-779). When augmented with cavity and VDW terms to account for the nonpolar part of solvation energy, the model with only one free parameter is capable of predicting the total solvation free energy to within 1.73 kcal/mol RMS error relative to experimental data. Within the NSR6 formulation, computation of the nonpolar contribution is particularly efficient because its VDW part depends on the same vertical bar r vertical bar(-6) integrals.