Analysis of errors in Still's equation for macromolecular electrostatic solvation energies

Abstract

The generalized Born (GB) solvation model is a simple dielectric model for the calculation of molecular electrostatic solvation energies. There are two distinct steps in the model: the calculation of Born radii from self-energies, and the calculation of interaction energies using an interpolation formula, such as Still's equation. The first step, the calculation of the Born radii, has been solved to high-accuracy in recent work by this author and others [M. S. Lee, F. R. Salsbury Jr, and M. A. Olson, J. Comput. Chem. 25, 1967 (2004)], so that the errors in the interpolation formula need to be considered to further improve GB theory. We examine the errors in the interpolation formula by calculating Born radii and atomic interaction energies using Poisson theory, and determining the errors associated with Still's equation. We then verify that a slight modification reduces the error in the interaction energies. We also explore alternative formulations of Still's equation, and the combinations rules for Born radii. We conclude that the Gaussian portion of Still's equation should be modified. Although additional generalizations of Still's equation do not further reduce the errors inherent to generalized Born theory substantially, there is considerable flexibility in the form of the interpolation equations which can be used in GB theory.