Dependence of RNA tertiary structural stability on Mg2+ concentration: interpretation of the Hill equation and coefficient.
The Mg(2+)-induced folding of RNA tertiary structures is readily observed via titrations of RNA with MgCl(2). 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 Mg(2+) 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 Mg(2+) and an RNA uses a preferential interaction coefficient, Gamma(2+), which represents the "excess" Mg(2+) neutralizing the RNA charge. The difference between Gamma(2+) for the native and unfolded RNA forms (DeltaGamma(2+)) is the number of Mg(2+) 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 DeltaGamma(2+) and find that two approximations are necessary: (i) the Mg(2+) activity coefficient is independent of concentration during a titration, and (ii) the dependence of DeltaGamma(2+) on Mg(2+) concentration is weak. Titration experiments with a Mg(2+)-binding dye and an adenine-binding riboswitch were designed to test these approximations. Inclusion of a 30-fold excess of KCl over MgCl(2) was sufficient to maintain a constant Mg(2+) activity coefficient. We also observed that Mg(2+) uptake by the RNA varied from near zero to approximately 2.6 as the Mg(2+) concentration increases over an approximately 100-fold range. It is possible to determine DeltaGamma(2+) from Mg(2+)-RNA titrations, but the values are only applicable to a limited range of solution conditions.
Leipply
Desirae
D
Program in Molecular Biophysics and Department of Biophysics, Johns Hopkins University, Baltimore, Maryland 21218, USA.
Draper
David E
DE
D001483:Base Sequence; D001665:Binding Sites; D002413:Cations, Divalent / Q000737:chemistry / Q000378:metabolism; D002712:Chlorides / Q000737:chemistry / Q000378:metabolism; D004734:Energy Metabolism; D008024:Ligands; D008274:Magnesium / Q000737:chemistry* / Q000378:metabolism; D015636:Magnesium Chloride / Q000737:chemistry / Q000378:metabolism; D008969:Molecular Sequence Data; D009690:Nucleic Acid Conformation; D020871:RNA Stability; D055672:Static Electricity; D013816:Thermodynamics; D017186:Titrimetry
D002413:Cations, Divalent; D002712:Chlorides; D008024:Ligands; D015636:Magnesium Chloride; D008274:Magnesium