Application of the Poisson Boltzmann polyelectrolyte model for analysis of equilibria between single-, double-, and triple-stranded polynucleotides in the presence of K(+), Na(+), and Mg(2+) ions.

The Poisson Boltzmann (PB) cell model of polyelectrolyte solution has been used for numerical calculations of the change in electrostatic free energy, DeltaG(el), for transformations between different structural forms (tri-, double-, and single-stranded) of the polyribonucleotides poly(rA).poly(rU)2, poly(rA).poly(rU), poly(rA), and poly(rU). In particular, the dependence on monovalent salt concentration, MCl (M = Na or K) in the absence and in the presence of MgCl(2) has been calculated. The results were obtained for conditions relevant to available experimental values of structural transition ("melting") temperatures (T(m)) and other thermodynamic quantities. Using the experimental T(m) values and theoretical electrostatic DeltaG(el), DeltaH(el), and DeltaS(el) functions, non-electrostatic contributions to the corresponding thermodynamic parameters of the poly(rA)/poly(rU) melting transitions were determined in MCl solutions in the absence of Mg(2+). Qualitative and to a large extent quantitative reproduction of the experimental calorimetry enthalpy, entropy and heat capacity values was found from the results of the PB theory. Furthermore, dependencies of T(m) on MCl concentration in the presence of MgCl(2) for the poly(rA)/poly(rU) transitions were also calculated. Compared to a model considering Mg(2+) as a fully-hydrated ion, much better agreement between experimental and PB theory was achieved by assuming the ion size of Mg(2+) to be given by that of a bare non-hydrated ion smaller than that of hydrated Na(+) or K(+). In agreement with data of experimental studies reported in literature, this result indicates that magnesium(II) can bind to RNA as a bare ion in a way that is different from that of DNA. Generally, we can conclude that the PB polyelectrolyte theory can provide an adequate description of thermally induced structural transitions in polydeoxy- and polyribonucleotides in different salt solutions in spite of the rather simplified model treating the solvent as dielectric continuum, the polyion as a uniformly charged cylinder, and the mobile ions as hard spheres in the absence of excluded volume effects.