Mediating role of multivalent cations in DNA electrostatics: an epsilon-modified Poisson-Boltzmann study of B-DNA-B-DNA interactions in mixture of NaCl and MgCl2 solutions.

Potentials of mean force acting between two ions in SPC/E water have been determined via molecular dynamics simulations using the spherical cavity approach ( J. Phys. Chem. B 2006 , 110 , 10878 ). The potentials were obtained for Me(2+)-Me(+) pairs, where Me(2+) means cations Mg(2+) and Ca(2+) and Me(+) denotes monovalent ions Li(+), Na(+), and K(+). The hard-core interaction distance for effective Me(2+)-Me(+) potentials appears to be of about 5 A that looks like a sum of the effective radii of a Me(2+) ion (3 A) and of an alkali metal ion Me(+) (about 2 A). These ion-ion interaction parameters were used in the epsilon-Modified Poisson-Boltzmann (epsilon-MPB) calculations ( J. Phys. Chem. B 2007 , 111 , 5264 ) of ionic distributions around DNA generalized for the arbitrary mixture of different ion species. Ionic distributions around an all-atom geometry model of B-DNA in solution of a mixture of NaCl and MgCl(2) were obtained. It was found that even a small fraction of ions Mg(2+) led to sharp condensation of Mg(2+) near the phosphate groups of DNA due to polarization deficiency of cluster [Mg(H(2)O)(6)](2+) in an external field. The epsilon-MPB calculations of the B-DNA-B-DNA interaction energies suggest that adding 1 mM of Mg(2+) to 50 mM solution of NaCl notably affects the force acting between the two macromolecules. Being compared to Poisson-Boltzmann results and to MPB calculations for the primitive model of ions, the epsilon-MPB results also indicate an important contribution of dielectric saturation effects to the mediating role of divalent cations in the DNA-DNA interaction energies.