The interpretation of Mg2+ binding isotherms for nucleic acids using Poisson-Boltzmann theory

Magnesium ions play a crucial role in the structural integrity and biological activity of nucleic acids. Experimental thermodynamic descriptions of Mg2+ interactions with nucleic acids in solution have generally relied on the analyses of binding polynomials to estimate the energetic contributions of diffuse and site-bound ions. However, since ion binding is dominated by long-range electrostatic forces, such models provide only a phenomenological description of the experimental Mg2+ binding data and provide little insight into the actual mechanism of the binding equilibria. Here, we present a rigorous theoretical framework based on the non-linear Poisson-Boltzmann (NLPB) equation for understanding diffuse ion interactions that can be used to interpret experimental Mg2+ binding isotherms. As intuitively expected, in the NLPB model binding is simply the total accumulation of the ion around the nucleic acid. Comparing the experimental data to the calculated curves shows that the NLPB equation provides a remarkably accurate description of Mg2+ binding to linear polynucleotides like DNA and poly(A.U) without any fitted parameters. In particular, the NLPB model explains two general features of magnesium binding; the strong dependence on univalent salt concentration, and its substantial anticooperativity. Each of these effects can be explained by changes in the Mg2+ distribution around the polyion under different solution conditions. In order to more fully understand these different aspects of magnesium binding, the free energy of Mg2+ binding, Delta G(Mg), is calculated and partitioned into several salt-dependent contributions: the change in the electrostatic interaction free energy of the charges, Delta Delta G(E.D) (including Mg2+-phosphate, Mg2+-Mg2+, Mg2+-Na+ Na+-Na+, Na+-phosphate interactions, and similar contributions for Cl-) and the cratic free energies of (re)organizing the MgCl2 and NaCl atmospheres, Delta G(org)(Mg) and Delta Delta G(org)(Na), respectively. For the systems studied here, Delta G(Mg) is strongly influenced by entropic free energy changes in the distributions of both NaCl and MgCl2, Delta G(org)(Mg) and Delta Delta G(org)(Na). From this analysis, we also raise the possibility that colons added with the magnesium salt might play an important role in the overall stability of nucleic acids under some conditions. (C) 1999 Academic Press.