Optimizing the Poisson dielectric boundary with explicit solvent forces and energies: Lessons learned with atom-centered dielectric functions

Accurate implicit solvent models require parameters that have been optimized in a system- or atom-specific manner on the basis of experimental data or more rigorous explicit solvent simulations. Models based on the Poisson or Poisson-Boltzmann equation are particularly sensitive to the nature and location of the boundary which separates the low dielectric solute from the high dielectric solvent. Here, we present a novel method for optimizing the solute radii, which define the dielectric boundary, on the basis of forces and energies from explicit solvent simulations. We use this method to optimize radii for protein systems defined by AMBER ff99 partial charges and a spline-smoothed solute surface. The spline-smoothed surface is an atom-centered dielectric function that enables stable and efficient force calculations. We explore the relative performance of radii optimized with forces alone and those optimized with forces and energies. We show that our radii reproduce the explicit solvent forces and energies more accurately than four other parameter sets commonly used in conjunction with the AMBER force field, each of which has been appropriately scaled for spline-smoothed surfaces. Finally, we demonstrate that spline-smoothed surfaces show surprising accuracy for small, compact systems but may have limitations for highly solvated protein systems. The optimization method presented here is efficient and applicable to any system with explicit solvent parameters. It can be used to determine the optimal continuum parameters when experimental solvation energies are unavailable and the computational costs of explicit solvent charging free energies are prohibitive.