Evidence for a thermodynamically distinct Mg2+ ion associated with formation of an RNA tertiary structure.

A folding strategy adopted by some RNAs is to chelate cations in pockets or cavities, where the ions neutralize charge from solvent-inaccessible phosphate. Although such buried Mg(2+)-RNA chelates could be responsible for a significant fraction of the Mg(2+)-dependent stabilization free energy of some RNA tertiary structures, direct measurements have not been feasible because of the difficulty of finding conditions under which the free energy of Mg(2+) chelation is uncoupled from RNA folding and from unfavorable interactions with Mg(2+) ions in other environments. In a 58mer rRNA fragment, we have used a high-affinity thermophilic ribosomal protein to trap the RNA in a structure nearly identical to native; Mg(2+)- and protein-stabilized structures differ in the solvent exposure of a single nucleotide located at the chelation site. Under these conditions, titration of a high affinity chelation site takes place in a micromolar range of Mg(2+) concentration, and is partially resolved from the accumulation of Mg(2+) in the ion atmosphere. From these experiments, we estimate the total and site-specific Mg(2+)-RNA interaction free energies over the range of accessed Mg(2+) concentrations. At 0.1 mM Mg(2+) and 60 mM K(+), specific site binding contributes ∼-3 kcal/mol of the total Mg(2+) interaction free energy of ∼-13 kcal/mol from all sources; at higher Mg(2+) concentrations the site-binding contribution becomes a smaller proportion of the total (-4.5 vs -33 kcal/mol). Under approximately physiological ionic conditions, the specific binding site will be saturated but will provide only a fraction of the total free energy of Mg(2+)-RNA interactions.

Effects of Mg2+ on the free energy landscape for folding a purine riboswitch RNA.

There are potentially several ways Mg2+ might promote formation of an RNA tertiary structure: by causing a general "collapse" of the unfolded ensemble to more compact conformations, by favoring a reorganization of structure within a domain to a form with specific tertiary contacts, and by enhancing cooperative linkages between different sets of tertiary contacts. To distinguish these different modes of action, we have studied Mg2+ interactions with the adenine riboswitch, in which a set of tertiary interactions that forms around a purine-binding pocket is thermodynamically linked to the tertiary "docking" of two hairpin loops in another part of the molecule. Each of four RNA forms with different extents of tertiary structure were characterized by small-angle X-ray scattering. The free energy of interconversion between different conformations in the absence of Mg2+ and the free energy of Mg2+ interaction with each form have been estimated, yielding a complete picture of the folding energy landscape as a function of Mg2+ concentration. At 1 mM Mg2+ (50 mM K+), the overall free energy of stabilization by Mg2+ is large, -9.8 kcal/mol, and about equally divided between its effect on RNA collapse to a partially folded structure and on organization of the binding pocket. A strong cooperative linkage between the two sets of tertiary contacts is intrinsic to the RNA. This quantitation of the effects of Mg2+ on an RNA with two distinct sets of tertiary interactions suggests ways that Mg2+ may work to stabilize larger and more complex RNA structures.

The osmolyte TMAO stabilizes native RNA tertiary structures in the absence of Mg2+: evidence for a large barrier to folding from phosphate dehydration.

The stabilization of RNA tertiary structures by ions is well known, but the neutral osmolyte trimethylamine oxide (TMAO) can also effectively stabilize RNA tertiary structure. To begin to understand the physical basis for the effects of TMAO on RNA, we have quantitated the TMAO-induced stabilization of five RNAs with known structures. So-called m values, the increment in unfolding free energy per molal of osmolyte at constant KCl activity, are ∼0 for a hairpin secondary structure and between 0.70 and 1.85 kcal mol(-1)m(-1) for four RNA tertiary structures (30-86 nt). Further analysis of two RNAs by small-angle X-ray scattering and hydroxyl radical probing shows that TMAO reduces the radius of gyration of the unfolded ensemble to the same endpoint as seen in titration with Mg(2+) and that the structures stabilized by TMAO and Mg(2+) are indistinguishable. Remarkably, TMAO induces the native conformation of a Mg(2+) ion chelation site formed in part by a buried phosphate, even though Mg(2+) is absent. TMAO interacts weakly, if at all, with KCl, ruling out the possibility that TMAO stabilizes RNA indirectly by increasing salt activity. TMAO is, however, strongly excluded from the vicinity of dimethylphosphate (unfavorable interaction free energy, +211 cal mol(-1)m(-1) for the potassium salt), an ion that mimics the RNA backbone phosphate. We suggest that formation of RNA tertiary structure is accompanied by substantial phosphate dehydration (loss of 66-173 water molecules in the RNA structures studied) and that TMAO works principally by reducing the energetic penalty associated with this dehydration. The strong parallels we find between the effects of TMAO and Mg(2+) suggest that RNA sequence is more important than specific ion interactions in specifying the native structure.

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.

The influence of monovalent cation size on the stability of RNA tertiary structures.

Many RNA tertiary structures are stable in the presence of monovalent ions alone. To evaluate the degree to which ions at or near the surfaces of such RNAs contribute to stability, the salt-dependent stability of a variety of RNA structures was measured with each of the five group I cations. The stability of hairpin secondary structures and a pseudoknot tertiary structure are insensitive to the ion identity, but the tertiary structures of two other RNAs, an adenine riboswitch and a kissing loop complex, become more stable by 2-3 kcal/mol as ion size decreases. This "default" trend is attributed to the ability of smaller ions to approach the RNA surface more closely. The degree of cation accumulation around the kissing loop complex was also inversely proportional to ion radius, perhaps because of the presence of sterically restricted pockets that can be accessed only by smaller ions. An RNA containing the tetraloop-receptor motif shows a strong (up to approximately 3 kcal/mol) preference for Na(+) or K(+) over other group I ions, consistent with the chelation of K(+) by this motif in some crystal structures. This RNA reverts to the default dependence on ion size when a base forming part of the chelation site is mutated. Lastly, an RNA aptamer for cobinamide, which was originally selected in the presence of high concentrations of LiCl, binds ligand more strongly in the presence of Li(+) than other monovalent ions. On the basis of these trends in RNA stability with group I ion size, it is argued that two features of RNA tertiary structures may promote strong interactions with ions at or near the RNA surface: negative charge densities that are higher than that in secondary structures, and the occasional presence of chelation sites, which are electronegative pockets that selectively bind ions of an optimum size.

Ion-RNA interactions thermodynamic analysis of the effects of mono- and divalent ions on RNA conformational equilibria.

RNA secondary and tertiary structures are strongly stabilized by added salts, and a quantitative thermodynamic analysis of the relevant ion-RNA interactions is an important aspect of the RNA folding problem. Because of long-range electrostatic forces, an RNA perturbs the distribution of both cations and anions throughout a large volume. Binding formalisms that require a distinction between "bound" and "free" ions become problematic in such situations. A more fundamental thermodynamic framework is developed here, based on preferential interaction coefficients; linkage equations derived from this framework provide a model-free description of the "uptake" or "release" of cations and anions that accompany an RNA conformational transition. Formulas appropriate for analyzing the dependence of RNA stability on either mono- or divalent salt concentration are presented and their application to experimental data is illustrated. Two example datasets are analyzed with respect to the monovalent salt dependence of tertiary structure formation in different RNAs, and three different experimental methods for quantitating the "uptake" of Mg(2+) ions are applied to the folding of a riboswitch RNA. Advantages and limitations of each method are discussed.