Dependence of RNA Tertiary Structural Stability on Mg2+ Concentration: Interpretation of the Hill Equation and Coefficient

The Mg2+-induced folding of RNA tertiary Structures is readily observed via titrations of RNA with MgCl2. Such titrations are commonly analyzed using a site binding formalism that includes a parameter, the Hill coefficient n, which is sometimes deemed the number of Mg2+ tons bound by the native RNA at specific sites. However, the long-range nature of electrostatic interactions allows ions some distance from the RNA to stabilize an RNA structure. A complete description of all interactions taking place between Mg2+ and an RNA uses a preferential Interaction coefficient, Gamma(2+), which represents the excess Mg2+ neutralizing the RNA charge. The difference between Gamma(2+) for the native mid unfolded RNA Forms (Delta Gamma(2+)) is the number of Mg2+ tons taken up by an RNA upon folding. Here we determine the conditions Under which the Hill coefficient n call be equated to file ion Uptake Delta Gamma(2+) and find that two approximations arc necessary: (i) the Mg2+ activity coefficient is independent of concentration during a titration, and (ii) the dependence Delta Gamma(2-)riboswitch were designed to test these approximations. Inclusion of a 30-fold excess of KCl over MgCl2 was Sufficient to maintain a constant Mg2+ activity coefficient. We also observed that Mg2+ Uptake by the RNA varied from near zero to similar to 2.6 as the Mg2+ concentration increases over an similar to 100-fold range. It is possible to determine Delta Gamma(2+) from Mg2+-RNA titrations, but the Values are only applicable to a limited range of solution conditions.