Electrostatic potential and free energy of proteins: A comparison of the Poisson-Boltzmann and the Bogolyubov-Born-Green-Yvon equations

The Bogolyubov-Born-Green-Yvon (BBGY) equations have been applied to study ionic and mean electrostatic potential distributions around a macromolecule of arbitrary shape and charge distribution. Results for the lysozyme molecule are compared with those obtained by classical Poisson-Boltzmann (PB) calculations. It is found that ion-image charge interactions and interionic correlations which are neglected by the PB equation have a weak effect on the electrostatic potential near charged groups of the protein, but they notably change electrostatic potential and ionic atmosphere at significant separation from the macromolecule. It is also shown that even for diluted solutions of electrolyte only a part of the observed macromolecule's free energy dependence on salt concentration might originate from long-range electrostatic forces, The rest comes from polarization forces within a very thin shell(similar to 2 Angstrom) around the macromolecule's surface, where macroscopic description of electrostatics cannot be used.