Quantifying the thermodynamic consequences of cation (M2+, M+) accumulation and anion (X-) exclusion in mixed salt solutions of polyanionic DNA usingMonte Carlo and Poisson-Boltzmann calculations of ion-polyion preferentialinteraction coefficients

Quantitative interpretations of the large Coulombic effects of changes in c ation concentrations on processes involving polyanionic DNA require accurat e theoretical descriptions of the thermodynamic consequences of cation-DNA interactions. In the present study, the thermodynamic consequences of accum ulation of divalent and/or univalent cations in the vicinity of polyionic d ouble-stranded DNA and of exclusion of univalent co-ions are characterized by ion-polyion preferential interaction coefficients Gamma(i) (i = 2+, +, o r -). These are calculated using integrals of ion distributions generated f rom either canonical Monte Carlo (CMC) simulations or numerical solutions o f the cylindrical Poisson-Boltzmann (PB) equation, for the same minimally p arameterized cylindrical cell model over experimentally relevant ranges and ratios of the uni- and/or divalent cations. For solutions containing both types of cations, trends in Gamma(i)(MC) and in Gamma(i)(PB) With changes i n the absolute and relative values of the divalent and univalent cation con centrations are examined and compared with trends calculated for solutions containing only one type of cation. Differences between Gamma(i)(MC) and Ga mma(i)(PB) are quantified and related to differences between MC and PB pred ictions of the extents of local cation accumulation within 3 Angstrom of th e polyion surface. Discrepancies between Gamma(2+)(MC) and Gamma(2+)(PB), a nd between Gamma-(MC) and Gamma-(PB), are significant whether or not unival ent cations are present, but the difference Delta Gamma(2+) = Gamma(2+)(MC) - Gamma(2+)(PB) is relatively insensitive to changes in the concentration of salt (excess 1:1). Therefore, PB calculations may provide a satisfactory alternative to more computationally demanding MC simulations as a basis fo r analyzing the salt-concentration dependences of Gamma(2+) and of the clos ely related measurable thermodynamic properties that reflect the importance of Coulombic interactions.