Electrostatics of a DNA-like polyelectrolyte: Effects of solvent dielectric saturation and polarization of ion hydration shells

The modified Poisson-Boltzmann (MPB) equations together with the Booth's theory of water dielectric saturation and an experimental dependence of water dielectric constant on ionic concentrations have been numerically solved to calculate the mean electrostatic potential and ionic distributions around a DNA-like highly charged cylindrical polyion. The model is explored for diluted mono- and multivalent electrolyte solutions. As follows from comparisons with the MPB and Poisson-Boltzmann (PB) calculations for the uniform permittivity solvent model, the solvent dielectric saturation and ion hydration shell polarization can be a significant contributor in the mean electrostatic potential and free energy of a highly charged macromolecule. Such effects may not be neglected in the case of a multivalent electrolyte. In contrast, the influence of solvent dielectric saturation and ionic polarization is negligible for a moderately charged spherical macroion, which confirms the success of numerous PB applications to calculations of pK values of protein charged groups.