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

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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.

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