Finite Difference Poisson-Boltzmann FDPB

To solve the PB equation for arbitrary geometries requires some type of discretization, to convert the partial differential equation into a set of difference equations. Finite difference methods divide space into a cubic lattice, with the potential, charge density, and ion accessibility defined at the lattice points (or grid points ) and the permittivity defined on the branches (or grid lines ). Equation [1] becomes a system of simultaneous equations referred to as the finite difference Poisson-Boltzmann (FDPB) equation ... 

Table 1 Free Energies of Hydration (kcal/mol) for Organic Molecules Calculated with the Finite Difference Poisson-Boltzmann (FDPB) Method and Experimental Results...

These FDPB-based methods might be further improved by using a position-dependent dielectric function that treats distinct regions of the protein differently (e.g., surface, interior, polar, nonpolar, charged, flexible, rigid, etc.), as has been mentioned by Warshel and others. These methods, as they mature, can be applied to questions of protein stability versus pH, the pH-dependent binding of inhibitors, and so on. The availability of these fast and automated methods makes the finite difference Poisson-Boltzmann method a useful predictive tool for the computational chemist. 

---