Continuum electrostatics, in which thesolvent is represented as a featureless dielectric medium, is an increasingly popular approach to describe solvation of polar molecules. The approximation goes back to Born (1920), Kirkwood (1934), and Onsager (1936). Continuum electrostatic approximations are based upon the Poisson Boltzmann equation for macroscopic media. The approach is of particular interest for incorporating solvent effects implicitly in atomic models of biomolecules. Numerical solutions of the PB equation based on finite-difference can be obtained routinely in the case of molecules of arbitrary irregular shapes.

One of the most important aspect of PB calculations is the atomic radii used to define the location of the solvent-protein dielectric boundary. We have determine a set of atomic Born radii for all 20 amino acids using MD/FES simulations with explicit water molecules (Nina et al, 1997).

In most practical applications, the PB equation is solved numerically for a fixed conformation of the biomolecular to obtain the electrostatic solvation free energy, shifts in pKa for specific residues, and protein-protein interactions in solution. The electrostatic solvation forces (i.e., the first derivatives of the solvation free energy with respect to the atomic coordinates of the solute), can also be calculated to implement energy minimization and dynamical algorithms. Lastly, the influence of the transmembrane potential can be incorporated into the theory easily using a modified form of the PB equation.