The GB/SA Continuum Model for Solvation. A Fast Analytical Method for the Calculation of Approximate Born Radii

Abstract

Atomic Born radii (α) are used in the generalized Born (GB) equation to calculate approximations to the electrical polarization component (Gpol) of solvation free energy. We present here a simple analytical formula for calculating Born radii rapidly and with useful accuracy. The new function is based on an atomic pairwise rij-4 treatment and contains several empirically determined parameters that were established by optimization against a data set of >10 000 accurate Born radii computed numerically using the Poisson equation on a diverse group of organic molecules, molecular complexes, oligopeptides, and a small protein. Coupling this new Born radius calculation with the previously described GB/SA solvation treatment provides a fully analytical solvation model that is computationally efficient in comparison with traditional molecular solvent models and also affords first and second derivatives. Tests with the GB/SA model and Born radii calculated with our new analytical function and with the accurate but more time-consuming Poisson−Boltzmann methods indicate that comparable free energies of solventlike dielectric polarization can be obtained using either method and that the resulting GB/SA solvation free energies compare well with the experimental results on small molecules in water.