Dependence of RNA tertiary structural stability on Mg2+ concentration: Interpretation of the hill equation and coefficient

Abstract

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+ ions 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, ΓT2+, which represents the "excess" Mg2+ neutralizing the RNA charge. The difference between Γ2+ for the native and unfolded RNA forms (ΔΓT2+) is the number of Mg2+ ions "taken up" by an RNA upon folding. Here we determine the conditions under which the Hill coefficient n can be equated to the ion uptake ΔΓ2+ and find that two approximations are necessary: (i) the Mg2+ activity coefficient is independent of concentration during a titration, and (ii) the dependence of ΔΔΓT2+ on Mg2+ concentration is weak. Titration experiments with a Mg2+-binding dye and an adenine-binding 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 ∼ 2.6 as the Mg2+ concentration increases over an ∼ 100-fold range. It is possible to determine ΔΓT2+ from Mg2+-RNA titrations, but the values are only applicable to a limited range of solution conditions. © 2010 American Chemical Society.