Poisson-Boltzmann Theory A Brief Overview

This section provides a brief overview of PB theory however, the interested reader is urged to read the much more comprehensive treatment provided by Gene Lamm in vol. 19 of this series. As mentioned, the Poisson-Boltzmann equation is obtained from a continuum description of the solvent and counterions surrounding a biomolecule. Although 

To obtain the PB equation from the Poisson equation, we need to consider the two types of charge distributions present in biomolecular systems. First, the partial atomic charges are usually modeled as a fixed charge distribution  

The full or nonlinear form of the problem given in Eq. [5] is often simplified to the linearized PB equation by replacing the sinhtp(x) term with its first-order approximation, sinh p(x) p(x), to give  

Solutions to the PB equation generally calculate either energies or forces. Electrostatic free energies are obtained by integration of solutions to the PB equation over the domain of interest  

As with the PB equation, the energy can be linearized by noting coshcp(x) — 1 cp (x)/2 for small cp(x) to give the simplified expression. A 

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