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.

Acknowledgements

The calculations reported herein were performed on the WFU DEAC cluster, which is partially supported by start-up funds from the Department of Physics at Wake Forest University to FRS.

This paper is in honour of Professor Robert A. Harris, my former graduate advisor. I was a joint student between him and Alexander Pines in the Department of Chemistry at Berkeley from 1995–1999, working on density functional theory with magnetic fields; BDFT. My interactions with him can only be described as incredible; a true mentorship. He always insisted that I was working with me, not for him, and it was true. I had incredible intellectual freedom working with him, and our work was truly collaborative. I especially recall during my first and second year at Berkeley slipping notes underneath his office at night, sometimes daily, for him to look at. Even when the ideas were somewhat suspect, he was always willing to look over my ideas, to talk with me and to work closely with me, sometimes for hours. He also did a wonderful job of encouraging me to solidify my background in physics, without which I could not have continued into biophysics and now the Physics department at Wake Forest. When towards the end of my third year, I was looking ahead towards graduation and was considering moving into studying biological molecules for my post-doc, and Bob couldn't advise me specifically on my post-doc, he turned me towards other faculty who could, and was very supportive of my interests. After finishing at Berkeley, I really started to appreciate how incredibly supportive Bob had been. Even now I continually realize, how much I learned, and how much fun I had, working with, and taking classes with Bob. I would not be the scientist I am now without Bob's mentorship.