Implicit Solvation - Generalized Born

The Generalized Born (GB) model is an approximation to the exact (linearized) Poisson-Boltzmann equation. It is based on modeling the protein as a set of spheres whose internal dielectric constant differs from the external solvent. The model has the following functional form:

G_{s} = \frac{1}{8\pi}\left(\frac{1}{\epsilon_{0}}-\frac{1}{\epsilon}\right)\sum_{i,j}^{N}\frac{q_{i}q_{j}}{f_{GB}}

where

f_{GB} = \sqrt{r_{ij}^{2} + a_{ij}^{2}e^{-D}}

and D = \left(\frac{r_{ij}}{2a_{ij}}\right)^{2}, a_{ij} = \sqrt{a_{i}a_{j}}

where is the permittivity of free space, is the dielectric constant of the solvent being modeled, is the electrostatic charge on particle i, is the distance between particles i and j, and is a quantity (with the dimension of length) known as the effective Born radius. The effective Born radius of an atom characterizes its degree of burial inside the solute; qualitatively it can be thought of as the distance from the atom to the molecular surface. Accurate estimation of the effective Born radii is critical for the GB model.

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