Dielectric saturation of the ion hydration shell and interaction between two double helices of DNA in mono- and multivalent electrolyte solutions: foundations of the epsilon-modified Poisson-Boltzmann theory

Potentials of mean force between single Na+, Ca2+, and Mg2+ cations and a highly charged spherical macroion in SPC/E water have been determined using molecular dynamics simulations. Results are compared to the electrostatic energy calculations for the primitive polarization model (PPM) of hydrated cations describing the ion hydration shell as a dielectric sphere of low permittivity (Gavryushov, S.; Linse, P. J. Phys. Chem. B 2003, 107, 7135). Parameters of the ion dielectric sphere and radius of the macroion/water dielectric boundary were extracted by means of this comparison to approximate the short-range repulsion of ions near the interface. To explore the counterion distributions around a simplified model of DNA, the obtained PPM parameters for Na+ and Ca2+ have been substituted into the modified Poisson-Boltzmann (MPB) equations derived for the PPM and named the epsilon-MPB (epsilon-MPB) theory. epsilon-MPB results for DNA suggest that such polarization effects are important in the case of 2:1 electrolyte and highly charged macromolecules. The three-dimensional implementation of the epsilon-MPB theory was also applied to calculation of the energies of interaction between two parallel macromolecules of DNA in solutions of NaCl and CaCl2. Being compared to results of MPB calculations without the ion polarization effects, it suggests that the ion hydration shell polarization and inhomogeneous solvent permittivity might be essential factors in the experimentally known hydration forces acting between charged macromolecules and bilayers at separations of less than 20 A between their surfaces.