Modified Poisson–Boltzmann equations for characterizing biomolecular solvation

Abstract

Methods for computing electrostatic interactions often account implicitly for the solvent, due to the much smaller number of degrees of freedom involved. In the Poisson–Boltzmann (PB) approach the electrostatic potential is obtained by solving the Poisson–Boltzmann equation (PBE), where the solvent region is modeled as a homogeneous medium with a high dielectric constant. PB however is not exempt of problems. It does not take into account for example the sizes of the ions in the atmosphere surrounding the solute, nor does it take into account the inhomogeneous dielectric response of water due to the presence of a highly charged surface. In this paper we review two major modifications of PB that circumvent these problems, namely the size-modified PB (SMPB) equation and the Dipolar Poisson–Boltzmann Langevin (DPBL) model. In SMPB, steric effects between ions are accounted for with a lattice gas model. In DPBL, the solvent region is no longer modeled as a homogeneous dielectric media but rather as an assembly of self-orienting interacting dipoles of variable density. This model results in a dielectric profile that transits smoothly from the solute to the solvent region as well as in a variable solvent density that depends on the charges of the solute. We show successful applications of the DPBL formalism to computing the solvation free energies of isolated ions in water. Further developments of more accurately modified PB models are discussed.