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

TLDR

Atomic Born radii are used in the generalized Born equation to approximate the electrical polarization component of solvation free energy. The authors propose a simple analytical formula to compute Born radii rapidly and accurately. The formula employs a pairwise rij‑4 treatment with empirically optimized parameters derived from over 10,000 numerically computed Born radii across diverse molecules, and integrates with the GB/SA solvation model to yield a fully analytical, computationally efficient method that provides first and second derivatives. Tests show that the new analytical Born radii produce GB/SA solvation free energies comparable to those from Poisson–Boltzmann calculations and align well with experimental data for small water‑soluble molecules.

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.