Monovalent and divalent salt effects on electrostatic free energies defined by the nonlinear Poisson-Boltzmann equation: Application to DNA binding reactions

We have extended the finite-difference Poisson-Boltzmann (FDPB) equation method to incorporate the treatment of mixed salts (i.e. NaCl/MgCl2). In this context, we have derived an expression for the total electrostatic free energy for mixed salt systems. We use the theory to study nonspecific mixed salt effects on the binding free energies of the minor groove binding antibiotic DAPI, and lambda repressor, with DNA. We find that in a pure salt solution the electrostatic contribution to binding varies linearly with log[Mn+], (where Mn+ represents an n-valent cation) and that the effect is uncorrelated with either the valence of the binding ligand or the number of counterions in the binding site. In mixed salt solution, the monovalent and divalent counterions ''compete'' for the immediate vicinity of the DNA. As experimentally observed in mixed salt solutions, a pronounced curvature appears in the plot of the electrostatic binding free energy vs log[Mn+]. The curvature for DAPI-DNA binding in mixed salts reflects the fact that divalent counterions interact with bound or free DNA molecules more strongly than monovalent counterions. However, the valence dependence of the electrostatic interaction between cations and negatively charged macromolecules is not solely responsible for the observed curvature. Rather anions, which can interact quite strongly with highly charged DNA-binding proteins, make a significant contribution to the observed salt effects. Our results support previous findings that treatments based on counterion condensation concepts break down for protein-DNA interactions; specifically, it is necessary to describe molecular structures in atomic detail if a realistic description of salt effects is to be obtained.