POISSON-BOLTZMANN EQUATION

The 'Poisson-Boltzmann equation' is a differential equation that describes electrostatic interactions between molecules in ionic solutions. The equation is important in the fields of molecular dynamics and biophysics because it can be used in modeling implicit solvation, an approximation of the effects of solvent on the structures and interactions of proteins, DNA, RNA, and other molecules in solutions of different ionic strength. It is often difficult to solve the Poisson-Boltzmann equation for complex systems, but several computer programs have been created to solve it numerically.
The equation can be written as:
:$$
ec{
abla}left[epsilon(ec{r})ec{
abla}Psi(ec{r})
ight] = -4pi
ho^{f}(ec{r}) - 4pisum_{i}c_{i}^{infty}z_{i}lambda(ec{r})qe^{rac{-z_{i}qPsi(ec{r})}{k_B T}}

where represents the position-dependent dielectric, represents the electrostatic potential, $$
ho^{f}(ec{r}) represents the charge density of the solute, $c\_\{i\}^\{infty\}$ represents the concentration of the ion ''i'' at a distance of infinity from the solute, $z\_\{i\}$ is the charge of the ion, ''q'' is the charge of a proton, $k\_B$ is the Boltzmann constant, ''T'' is the temperature, and is a factor for the position-dependent accessibility of position ''r'' to the ions in solution. If the potential is not large, the equation can be linearized to be solved more efficiently.^[1]

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References

External links

References

1. Fogolari F, Brigo A, Molinari H. (2002). The Poisson-Boltzmann equation for biomolecular electrostatics: a tool for structural biology. ''J Mol Recognit'' 15(6):377-92. (See this paper for derivation.)

External links

★ APBS PB solver

★ Zap - A Poisson-Boltzmann electrostatics solver.

★ DelPhi DelPhi, canonical Finite Difference Poisson-Boltzmann Solver for protein, now is free