Accuracy of continuum electrostatic calculations based on three common dielectric boundary definitions

We investigate the influence of three common definitions of the solute/solvent dielectric boundary (DB) on the accuracy of the electrostatic solvation energy Delta G(el) computed within the Poisson-Boltzmann (PB) and the generalized Born (GB) models of implicit solvation. The test structures include small molecules, peptides and small proteins; explicit solvent Delta G(el) are used as accuracy reference. For common atomic radii sets BONDI, PARSE (and ZAP9 for small molecules) the use of van der Waals (vdW) DB results, on average, in considerably larger errors in Delta G(el) than the molecular surface (MS) DB. The optimal probe radius rho(w) for which the MS DB yields the most accurate Delta G(el) varies considerably between structure types. The solvent accessible surface (SAS) DB becomes optimal at rho(w) similar to 0.2 angstrom(exact value is sensitive to the structure and atomic radii), at which point the average accuracy of Delta G(el) is comparable to that of the MS-based boundary. The geometric equivalence of SAS to vdW surface based on the same atomic radii uniformly increased by rho(w) gives the corresponding optimal vdW DB. For small molecules, the optimal vdW DB based on BONDI + 0.2 angstrom radii can yield Delta G(el) estimates at least as accurate as those based on the optimal MS DB. Also, in small molecules, pairwise charge-charge interactions computed with the optimal vdW DB are virtually equal to those computed with the MS DB, suggesting that in this case the two boundaries are practically equivalent by the electrostatic energy criteria. In structures other than small molecules, the optimal vdW and MS dielectric boundaries are not equivalent: the respective pairwise electrostatic interactions in the presence of solvent can differ by upto 5 kcal/mol for individual atomic pairs in small proteins, even when the total Delta G(el) are equal. For small proteins, the average decrease in pairwise electrostatic interactions resulting from the switch from optimal MS to optimal vdW DB definition can be mimicked within the MS DB definition by doubling of the solute dielectric constant. However, the use of the higher interior dielectric does not eliminate the large individual deviations between pairwise interactions computed within the two DB definitions. It is argued that while the MS-based definition of the DB is more physically correct in some types of practical calculations, the choice is not so clear in some other common scenarios.