Divalent ion competition reveals reorganization of an RNA ion atmosphere upon folding.

Although RNA interactions with K+ and Mg2+ have been studied extensively, much less is known about the third most abundant cation in bacterial cells, putrescine2+, and how RNA folding might be influenced by the three ions in combination. In a new approach, we have observed the competition between Mg2+ and putrescine2+ (in a background of K+) with native, partially unfolded and highly extended conformations of an adenine riboswitch aptamer. With the native state, putrescine2+ is a weak competitor when the ratio of the excess Mg2+ (which neutralizes phosphate charge) to RNA is very low, but becomes much more effective at replacing Mg2+ as the excess Mg2+ in the RNA ion atmosphere increases. Putrescine2+ is even more effective in competing Mg2+ from the extended conformation, independent of the Mg2+ excess. To account for these and other results, we propose that both ions closely approach the surface of RNA secondary structure, but the completely folded RNA tertiary structure develops small pockets of very negative electrostatic potential that are more accessible to the compact charge of Mg2+. The sensitivity of RNA folding to the combination of Mg2+ and putrescine2+ found in vivo depends on the architectures of both the unfolded and native conformations.

Comparison of interactions of diamine and Mg²âº with RNA tertiary structures: similar versus differential effects on the stabilities of diverse RNA folds.

Cations play a large role in stabilizing the native state of RNA in vivo. In addition to Mg²âº, putrescine²âº is an abundant divalent cation in bacterial cells, but its effect on the folding of RNA tertiary structure has not been widely explored. In this study, we look at how the stabilities of four structured RNAs, each with a different degree of dependence on K⁺ and Mg²âº, are affected by putrescine²âº relative to Mg²âº. Through the use of thermal melts, we observe that (i) at a given concentration, putrescine²âº is less effective than Mg²âº at stabilizing RNA, (ii) the stability imparted to RNA by various diamines is a function of charge density (average separation distance between charges) as well as the flexibility of the counterion, and (iii) when Mg²âº is already present in a buffer, further addition of putrescine²âº may either destabilize or stabilize RNA structure, depending on whether the native RNA does or does not chelate Mg²âº ion, respectively. At ion concentrations likely to be found in vivo, the effect of putrescine²âº on the free energy of folding of an RNA tertiary structure is probably quite small compared to that of Mg²âº, but the ability of mixed Mg²âº/putrescine²âº environments to (in effect) discriminate between different RNA architectures suggests that, in some cells, the evolution of functional RNA structures may have been influenced by the presence of putrescine²âº.

Folding of RNA tertiary structure: Linkages between backbone phosphates, ions, and water.

The functional forms of many RNAs have compact architectures. The placement of phosphates within such structures must be influenced not only by the strong electrostatic repulsion between phosphates, but also by networks of interactions between phosphates, water, and mobile ions. This review first explores what has been learned of the basic thermodynamic constraints on these arrangements from studies of hydration and ions in simple DNA molecules, and then gives an overview of what is known about ion and water interactions with RNA structures. A brief survey of RNA crystal structures identifies several interesting architectures in which closely spaced phosphates share hydration shells or phosphates are buried in environments that provide intramolecular hydrogen bonds or site-bound cations. Formation of these structures must require strong coupling between the uptake of ions and release of water.

Denaturation of RNA secondary and tertiary structure by urea: simple unfolded state models and free energy parameters account for measured m-values.

To investigate the mechanism by which urea destabilizes RNA structure, urea-induced unfolding of four different RNA secondary and tertiary structures was quantified in terms of an m-value, the rate at which the free energy of unfolding changes with urea molality. From literature data and our osmometric study of a backbone analogue, we derived average interaction potentials (per square angstrom of solvent accessible surface) between urea and three kinds of RNA surfaces: phosphate, ribose, and base. Estimates of the increases in solvent accessible surface areas upon RNA denaturation were based on a simple model of unfolded RNA as a combination of helical and single-strand segments. These estimates, combined with the three interaction potentials and a term to account for interactions of urea with released ions, yield calculated m-values that are in good agreement with experimental values (200 mm monovalent salt). Agreement was obtained only if single-stranded RNAs were modeled in a highly stacked, A-form conformation. The primary driving force for urea-induced denaturation is the strong interaction of urea with the large surface areas of bases that become exposed upon denaturation of either RNA secondary or tertiary structure, though interactions of urea with backbone and released ions may account for up to a third of the m-value. Urea m-values for all four RNAs are salt-dependent, which we attribute to an increased extension (or decreased charge density) of unfolded RNAs with an increased urea concentration. The sensitivity of the urea m-value to base surface exposure makes it a potentially useful probe of the conformations of RNA unfolded states.

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.

Diagnostic usefulness of graded exercise testing in pediatric supraventricular tachycardia.

BACKGROUND: Episodic symptoms, often reported during exertion, complicate the assessment of suspected supraventricular tachycardia (SVT). OBJECTIVE: To examine the diagnostic sensitivity of graded exercise testing in young patients with documented SVT or ventricular preexcitation. METHODS: A single-centre retrospective review identified 53 patients (5.1 to 17.5 years of age) with structurally normal hearts who had undergone 65 graded treadmill exercise tests in the setting of either documented SVT with normal resting electrocardiograms (n=30) or ventricular preexcitation (n=23). Twenty-five patients (13 pre-excited and 12 nonpreexcited) had exercise-related symptoms. SVT induction during exercise testing was assessed in relation to pre-excitation and the patient's history of exercise-induced symptoms. RESULTS: SVT was induced during six of the 65 exercise tests performed in three of 53 patients (overall sensitivity 5.7%). All three patients had a history of exercise- induced symptoms, and two had ventricular preexcitation. SVT was induced in 12% of patients with exercise- related symptoms. No other rhythm disturbances occurred during exercise testing. CONCLUSION: The diagnostic yield of graded exercise testing in patients with suspected SVT is limited, even among those with exercise related symptoms.

Molecular simulation studies of monovalent counterion-mediated interactions in a model RNA kissing loop.

A kissing loop is a highly stable complex formed by loop-loop base-pairing between two RNA hairpins. This common structural motif is utilized in a wide variety of RNA-mediated processes, including antisense recognition, substrate recognition in riboswitches, and viral replication. Recent work has shown that the Tar-Tar(*) complex, an archetypal kissing loop, can form without Mg(2+), so long as high concentrations of alkali chloride salts are present. Interestingly, the stability of the complex is found to decrease with increasing cation size. In this work, we used molecular simulations to develop a molecular-level understanding of the origins of the observed counterion specificity. The ionic atmosphere of the Tar-Tar(*) complex was examined in the presence of 800 mm (where m denotes molality) NaCl, KCl, or CsCl. We used spatial free-energy density profiles to analyze differences in counterion accumulation at different spatial extents from the RNA molecule. We found that the lowest free-energy levels, which are situated in the vicinity of the loop-loop interface, can accommodate roughly two counterions, irrespective of counterion type. However, as we moved into higher free-energy levels, which are farther from the loop-loop interface, we observed increased differences in the numbers of accumulated counterions, with this number being largest for Na(+) and smallest for Cs(+). We analyzed the source of these differences and were able to attribute these to two distinct features: The extent of partial dehydration varies based on cation type; the smaller the cation, the greater the degree of dehydration. While smaller ions bind their first-hydration-shell water molecules more tightly than larger ions, they are also able to shed these water molecules for stronger electrostatic interactions with the RNA molecule. Secondly, we observed a distinct asymmetry in the numbers of accumulated cations around each hairpin in the Tar-Tar(*) complex. We were able to ascribe this asymmetry to the presence of a guanine tract in the Tar hairpin, which facilitates partial dehydration of the counterions. However, the smaller ions compensate for this asymmetry by forming a belt around the loop-loop interface in intermediate free-energy levels. As a result, the degree of asymmetry in counterion accumulation around individual hairpins shows an inverse correlation with the experimentally observed cation specificity for the stability of Tar-Tar(*) (i.e., the smaller the asymmetry, the greater the experimentally observed stability). This in turn provides a plausible explanation for why the smaller cations help stabilize the Tar-Tar(*) complex better than the larger cations. These findings suggest that the specific sequence and structural features of the Tar-Tar(*) complex may be the source of the experimentally observed cation specificity in Tar-Tar(*) stability. Our results lead to testable predictions for how changes in sequence might alter the observed counterion specificity in kissing loop stability.

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.

Direct quantitation of Mg2+-RNA interactions by use of a fluorescent dye.

The ionic composition of a solution strongly influences the folding of an RNA into its native structure; of particular importance, the stabilities of RNA tertiary structures are sharply dependent on the concentration of Mg2+. Most measurements of the extent of Mg2+ interaction with an RNA have relied on equilibrium dialysis or indirect measurements. Here we describe an approach, based on titrations in the presence of a fluorescent indicator dye, that accurately measures the excess Mg2+ ion neutralizing the charge of an RNA (the interaction or Donnan coefficient, Gamma2+) and the total free energy of Mg2+-RNA interactions (DeltaG(RNA-2+)). Automated data collection with computer-controlled titrators enables the collection of much larger data sets in a short time, compared to equilibrium dialysis. Gamma2+ and DeltaG(RNA-2+) are thermodynamically rigorous quantities that are directly comparable with the results of theoretical calculations and simulations. In the event that RNA folding is coupled to the addition of MgCl2, the method directly monitors the uptake of Mg2+ associated with the folding transition.

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.

RNA folding: thermodynamic and molecular descriptions of the roles of ions.

The stability of a compact RNA tertiary structure is exquisitely sensitive to the concentrations and types of ions that are present. This review discusses the progress that has been made in developing a quantitative understanding of the thermodynamic parameters and molecular detail that underlie this sensitivity, including the nature of the ion atmosphere, the occurrence of specific ion binding sites, and the importance of the ensemble of partially unfolded states from which folding to the native structure occurs.

Specific interactions of the L10(L12)4 ribosomal protein complex with mRNA, rRNA, and L11.

Large ribosomal subunit proteins L10 and L12 form a pentameric protein complex, L10(L12) 4, that is intimately involved in the ribosome elongation cycle. Its contacts with rRNA or other ribosomal proteins have been only partially resolved by crystallography. In Escherichia coli, L10 and L12 are encoded from a single operon for which L10(L12) 4 is a translational repressor that recognizes a secondary structure in the mRNA leader. In this study, L10(L12) 4 was expressed from the moderate thermophile Bacillus stearothermophilus to quantitatively compare strategies for binding of the complex to mRNA and ribosome targets. The minimal mRNA recognition structure is widely distributed among bacteria and has the potential to form a kink-turn structure similar to one identified in the rRNA as part of the L10(L12) 4 binding site. Mutations in equivalent positions between the two sequences have similar effects on L10(L12) 4-RNA binding affinity and identify the kink-turn motif and a loop AA sequence as important recognition elements. In contrast to the larger rRNA structure, the mRNA apparently positions the kink-turn motif and loop for protein recognition without the benefit of Mg (2+)-dependent tertiary structure. The mRNA and rRNA fragments bind L10(L12) 4 with similar affinity ( approximately 10 (8) M (-1)), but fluorescence binding studies show that a nearby protein in the ribosome, L11, enhances L10(L12) 4 binding approximately 100-fold. Thus, mRNA and ribosome targets use similar RNA features, held in different structural contexts, to recognize L10(L12) 4, and the ribosome ensures the saturation of its L10(L12) 4 binding site by means of an additional protein-protein interaction.

Importance of partially unfolded conformations for Mg(2+)-induced folding of RNA tertiary structure: structural models and free energies of Mg2+ interactions.

RNA molecules in monovalent salt solutions generally adopt a set of partially folded conformations containing only secondary structure, the intermediate or I state. Addition of Mg2+ strongly stabilizes the native tertiary structure (N state) relative to the I state. In this paper, a combination of experimental and computational approaches is used to estimate the free energy of the interaction of Mg2+ with partially folded I state RNAs and to consider the possibility that Mg2+ favors "compaction" of the I state to a set of conformations with a higher average charge density. A sequence variant with a drastically destabilized tertiary structure was used as a mimic of I state RNA; as measured by small-angle X-ray scattering, it adopted a progressively more compact conformation over a wide Mg2+ concentration range. Average free energies of the interaction of Mg2+ with the I state mimic were obtained by a fluorescence titration method. To interpret these experimental data further, we generated molecular models of the I state and used them in calculations with the nonlinear Poisson-Boltzmann equation to estimate the change in Mg2+-RNA interaction free energy as the average I state dimensions decrease from expanded to compact. The same models were also used to reproduce quantitatively the experimental difference in excess Mg2+ between N and I states. On the basis of these experiments and calculations, I state compaction appears to enhance Mg2+-I state interaction free energies by 10-20%, but this enhancement is at most 5% of the overall Mg2+-associated stabilization free energy for this rRNA fragment.

Effects of osmolytes on RNA secondary and tertiary structure stabilities and RNA-Mg2+ interactions.

Osmolytes are small organic molecules accumulated by cells in response to osmotic stress. Although their effects on protein stability have been studied, there has been no systematic documentation of their influence on RNA. Here, the effects of nine osmolytes on the secondary and tertiary structure stabilities of six RNA structures of differing complexity and stability have been surveyed. Using thermal melting analysis, m-values (change in DeltaG degrees of RNA folding per molal concentration of osmolyte) have been measured. All the osmolytes destabilize RNA secondary structure, although to different extents, probably because they favor solubilization of base surfaces. Osmolyte effects on tertiary structure, however, can be either stabilizing or destabilizing. We hypothesize that the stabilizing osmolytes have unfavorable interactions with the RNA backbone, which becomes less accessible to solvent in most tertiary structures. Finally, it was found that as a larger fraction of the negative charge of an RNA tertiary structure is neutralized by hydrated Mg(2+), the RNA becomes less responsive to stabilizing osmolytes and may even be destabilized. The natural selection of osmolytes as protective agents must have been influenced by their effects on the stabilities of functional RNA structures, though in general, the effects of osmolytes on RNA and protein stabilities do not parallel each other. Our results also suggest that some osmolytes can be useful tools for studying intrinsically unstable RNA folds and assessing the mechanisms of Mg(2+)-induced RNA stabilization.

The structure of free L11 and functional dynamics of L11 in free, L11-rRNA(58 nt) binary and L11-rRNA(58 nt)-thiostrepton ternary complexes.

The L11 binding site is one of the most important functional sites in the ribosome. The N-terminal domain of L11 has been implicated as a "reversible switch" in facilitating the coordinated movements associated with EF-G-driven GTP hydrolysis. The reversible switch mechanism has been hypothesized to require conformational flexibility involving re-orientation and re-positioning of the two L11 domains, and warrants a close examination of the structure and dynamics of L11. Here we report the solution structure of free L11, and relaxation studies of free L11, L11 complexed to its 58 nt RNA recognition site, and L11 in a ternary complex with the RNA and thiostrepton antibiotic. The binding site of thiostrepton on L11 was also defined by analysis of structural and dynamics data and chemical shift mapping. The conclusions of this work are as follows: first, the binding of L11 to RNA leads to sizable conformation changes in the regions flanking the linker and in the hinge area that links a beta-sheet and a 3(10)-helix-turn-helix element in the N terminus. Concurrently, the change in the relative orientation may lead to re-positioning of the N terminus, as implied by a decrease of radius of gyration from 18.5 A to 16.2 A. Second, the regions, which undergo large conformation changes, exhibit motions on milliseconds-microseconds or nanoseconds-picoseconds time scales. Third, binding of thiostrepton results in more rigid conformations near the linker (Thr71) and near its putative binding site (Leu12). Lastly, conformational changes in the putative thiostrepton binding site are implicated by the re-emergence of cross-correlation peaks in the spectrum of the ternary complex, which were missing in that of the binary complex. Our combined analysis of both the chemical shift perturbation and dynamics data clearly indicates that thiostrepton binds to a pocket involving residues in the 3(10)-helix in L11.

Tertiary structure of an RNA pseudoknot is stabilized by "diffuse" Mg2+ ions.

The aim of this study is to obtain a comprehensive experimental and theoretical description of the contributions of Mg2+ ions to the free energy of folding a pseudoknot RNA tertiary structure. A fluorescence method for measuring the effective concentration of Mg2+ in the presence of an RNA was used to study Mg2+-RNA interactions with both folded and partially unfolded forms of an RNA pseudoknot. These data established the excess number of Mg2+ ions accumulated by the folded or partially unfolded RNAs as a function of bulk Mg2+ concentration, from which free energies of Mg2+-RNA interactions were derived. Complementary thermal melting experiments were also used to obtain RNA-folding free energies. These experimental data were compared with the results of calculations based on the nonlinear Poisson-Boltzmann equation, which describes the interaction of "diffuse" (fully hydrated) Mg2+ ions with the different RNA forms. Good agreement between the calculations and experimental data suggests that essentially all of the Mg2+-induced stabilization of the native pseudoknot structure arises from the stronger interaction of diffuse ions with the folded tertiary structure compared to that with a partially unfolded state. It is unlikely that the stability of the RNA depends on dehydrated ions bound to specific sets of RNA ligands in the folded state. The data also suggest that the Mg2+-dependent free energy of folding is sensitive to factors that influence the ensemble of RNA conformations present in the partially unfolded state.