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

Magnesium ions play a crucial role in the structural integrity and biologic al activity of nucleic acids. Experimental thermodynamic descriptions of Mg 2+ 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 lo ng-range electrostatic forces, such models provide only a phenomenological description of the experimental Mg2+ binding data and provide little insigh t into the actual mechanism of the binding equilibria. Here, we present a r igorous theoretical framework based on the non-linear Poisson-Boltzmann (NL PB) 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 f itted parameters. In particular, the NLPB model explains two general featur es of magnesium binding; the strong dependence on univalent salt concentrat ion, and its substantial anticooperativity. Each of these effects can be ex plained by changes in the Mg2+ distribution around the polyion under differ ent 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: t he change in the electrostatic interaction free energy of the charges, Delt a Delta G(E.D) (including Mg2+-phosphate, Mg2+-Mg2+, Mg2+-Na+ Na+-Na+, Na+- phosphate interactions, and similar contributions for Cl-) and the cratic f ree 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(o rg)(Na). From this analysis, we also raise the possibility that colons adde d with the magnesium salt might play an important role in the overall stabi lity of nucleic acids under some conditions. (C) 1999 Academic Press.