A thermodynamic framework for Mg2+ binding to RNA

Prediction of RNA pseudoknots using heuristic modeling with mapping and sequential folding

Predicting RNA secondary structure is often the first step to determining the structure of RNA. Prediction approaches have historically avoided searching for pseudoknots because of the extreme combinatorial and time complexity of the problem. Yet neglecting pseudoknots limits the utility of such approaches. Here, an algorithm utilizing structure mapping and thermodynamics is introduced for RNA pseudoknot prediction that finds the minimum free energy and identifies information about the flexibility of the RNA. The heuristic approach takes advantage of the 5′ to 3′ folding direction of many biological RNA molecules and is consistent with the hierarchical folding hypothesis and the contact order model. Mapping methods are used to build and analyze the folded structure for pseudoknots and to add important 3D structural considerations. The program can predict some well known pseudoknot structures correctly. The results of this study suggest that many functional RNA sequences are optimized for proper folding. They also suggest directions we can proceed in the future to achieve even better results.

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.

Ion atmosphere around nucleic acid

The poyion-ion preferential interaction coefficient Gamma describes the exclusion of coions and accumulations of counterions in the vicinity of a polyion in an aqueous solution. We give tight upper and lower bounds for Gamma when the polyion can be modeled by a cylinder of infinite length but of arbitrary charge density. This case can be used as a model for long strands of DNA or RNA in an aqueous solution containing univalent cations. The salt dependence of Gamma is predicted from low to intermediate and high salt concentrations. We also indicate how the bounds for the infinite polyion can be exploited to place bounds for polyions of length greater than a constant on the order of the inverse Debye screening length.

Solution structure of an rRNA substrate bound to the pseudouridylation pocket of a box H/ACA snoRNA

Base pairing between the RNA components of box H/ACA small nucleolar ribonucleoproteins (snoRNPs) and sequences in other eukaryotic RNAs target specific uridines for pseudouridylation. An RNA called HJ1 has been developed that interacts with the rRNA sequence targeted by the 5' pseudouridylation pocket of human U65 snoRNA the same way as intact U65 snoRNA. Sequences on both strands of the analog of the U65 snoRNP pseudouridylation pocket in HJ1 pair with its substrate sequence, and the resulting complex, called HJ3, is strongly stabilized by Mg(2+). The solution structure of HJ3 reveals an Omega-shaped RNA interaction motif that has not previously been described, which is likely to be common to all box H/ACA snoRNP-substrate complexes. The topology of the complex explains why the access of substrate sequences to snoRNPs is facile and how uridine selection may occur when these complexes form.

Internal versus terminal metalation of double-helical oligodeoxyribonucleotides

The formation of adducts between cis-[Pt(NH(3))(2)Cl(2)], Zn(II), and Mn(II) and double-stranded oligodeoxynucleotides was studied by 1D and 2D (1)H, (31)P, and (15)N NMR spectroscopy. For labile adducts involving Zn(II) and Mn(II), both (1)H chemical shifts (Zn(II)) and (1)H line-broadening effects (Mn(II)) showed that in the hexamer [d(GGCGCC)](2) I, the terminal G(1)-N7 is the exclusive binding site, while for the dodecamer [d(GGTACCGGTACC)](2) II, which contains both a terminal and internal GG pair, the preference for metal binding is the internal guanine G(7). Zn(II) binding to II was confirmed by natural-abundance 2D [(1)H,(15)N] HMBC NMR spectroscopy, which unambiguously showed that G(7)-N7 is the preferred binding site. The long duplex [d(GGTATATATACCGGTATATATACC)](2) III was expected to have a more pronounced accumulation of electrostatic potential towards the central part of the sequence (vs the terminal part) than does II. However, the Zn(II) titration of III showed no increase in coordination with the internal Gs (vs the terminal Gs), compared with what was observed for II. The reaction between the nonlabile metal complex cis-[PtCl(2)((15)NH(3))(2)] (cisplatin) and II showed a slight preference for the internal GG pair over the terminal GG pair. However, when the diaqua form of cisplatin cis-[Pt((15)NH(3))(2)(H(2)O)(2)] was reacted with II a more pronounced binding preference for the internal GG pair was observed.

The electrostatic characteristics of G.U wobble base pairs

G.U wobble base pairs are the most common and highly conserved non-Watson-Crick base pairs in RNA. Previous surface maps imply uniformly negative electrostatic potential at the major groove of G.U wobble base pairs embedded in RNA helices, suitable for entrapment of cationic ligands. In this work, we have used a Poisson-Boltzmann approach to gain a more detailed and accurate characterization of the electrostatic profile. We found that the major groove edge of an isolated G.U wobble displays distinctly enhanced negativity compared with standard GC or AU base pairs; however, in the context of different helical motifs, the electrostatic pattern varies. G.U wobbles with distinct widening have similar major groove electrostatic potentials to their canonical counterparts, whereas those with minimal widening exhibit significantly enhanced electronegativity, ranging from 0.8 to 2.5 kT/e, depending upon structural features. We propose that the negativity at the major groove of G.U wobble base pairs is determined by the combined effect of the base atoms and the sugar-phosphate backbone, which is impacted by stacking pattern and groove width as a result of base sequence. These findings are significant in that they provide predictive power with respect to which G.U sites in RNA are most likely to bind cationic ligands.

RNA helix stability in mixed Na+/Mg2+ solution

A recently developed tightly bound ion model can account for the correlation and fluctuation (i.e., different binding modes) of bound ions. However, the model cannot treat mixed ion solutions, which are physiologically relevant and biologically significant, and the model was based on B-DNA helices and thus cannot directly treat RNA helices. In the present study, we investigate the effects of ion correlation and fluctuation on the thermodynamic stability of finite length RNA helices immersed in a mixed solution of monovalent and divalent ions. Experimental comparisons demonstrate that the model gives improved predictions over the Poisson-Boltzmann theory, which has been found to underestimate the roles of multivalent ions such as Mg2+ in stabilizing DNA and RNA helices. The tightly bound ion model makes quantitative predictions on how the Na+-Mg2+ competition determines helix stability and its helix length-dependence. In addition, the model gives empirical formulas for the thermodynamic parameters as functions of Na+/Mg2+ concentrations and helix length. Such formulas can be quite useful for practical applications.

Role of metal ions in the tetraloop-receptor complex as analyzed by NMR

Metal ions are critical for the proper folding of RNA, and the GAAA tetraloop-receptor is necessary for the optimal folding and function of many RNAs. We have used NMR to investigate the role of metal ions in the structure of the tetraloop-receptor in solution. The NMR data indicate native tertiary structure is formed under a wide range of ionic conditions. The lack of conformational adaptation in response to very different ionic conditions argues against a structural role for divalent ions. Nuclear Overhauser effects to cobalt hexammine and paramagnetic relaxation enhancement induced by manganese ions were used to determine the NMR structures of the tetraloop receptor in association with metal ions, providing the first atomic-level view of these interactions in the solution state. Five manganese and two cobalt hexammine ions could be localized to the RNA surface. The locations of the associated metal ions are similar, but not identical to, those of previously determined crystal structures. The sites of association are in general agreement with nonlinear Poisson-Boltzmann calculations of the electrostatic surface, emphasizing the general importance of diffusely associated ions in RNA tertiary structure.

Calculation of pKas in RNA: on the structural origins and functional roles of protonated nucleotides

pK(a) calculations based on the Poisson-Boltzmann equation have been widely used to study proteins and, more recently, DNA. However, much less attention has been paid to the calculation of pK(a) shifts in RNA. There is accumulating evidence that protonated nucleotides can stabilize RNA structure and participate in enzyme catalysis within ribozymes. Here, we calculate the pK(a) shifts of nucleotides in RNA structures using numerical solutions to the Poisson-Boltzmann equation. We find that significant shifts are predicted for several nucleotides in two catalytic RNAs, the hairpin ribozyme and the hepatitis delta virus ribozyme, and that the shifts are likely to be related to their functions. We explore how different structural environments shift the pK(a)s of nucleotides from their solution values. RNA structures appear to use two basic strategies to shift pK(a)s: (a) the formation of compact structural motifs with structurally-conserved, electrostatic interactions; and (b) the arrangement of the phosphodiester backbone to focus negative electrostatic potential in specific regions.

Electrostatic free energy landscapes for nucleic acid helix assembly

Metal ions are crucial for nucleic acid folding. From the free energy landscapes, we investigate the detailed mechanism for ion-induced collapse for a paradigm system: loop-tethered short DNA helices. We find that Na+ and Mg2+ play distinctive roles in helix-helix assembly. High [Na+] (>0.3 M) causes a reduced helix-helix electrostatic repulsion and a subsequent disordered packing of helices. In contrast, Mg2+ of concentration >1 mM is predicted to induce helix-helix attraction and results in a more compact and ordered helix-helix packing. Mg2+ is much more efficient in causing nucleic acid compaction. In addition, the free energy landscape shows that the tethering loops between the helices also play a significant role. A flexible loop, such as a neutral loop or a polynucleotide loop in high salt concentration, enhances the close approach of the helices in order to gain the loop entropy. On the other hand, a rigid loop, such as a polynucleotide loop in low salt concentration, tends to de-compact the helices. Therefore, a polynucleotide loop significantly enhances the sharpness of the ion-induced compaction transition. Moreover, we find that a larger number of helices in the system or a smaller radius of the divalent ions can cause a more abrupt compaction transition and a more compact state at high ion concentration, and the ion size effect becomes more pronounced as the number of helices is increased.

Mg2+-RNA interaction free energies and their relationship to the folding of RNA tertiary structures

Mg2+ ions are very effective at stabilizing tertiary structures in RNAs. In most cases, folding of an RNA is so strongly coupled to its interactions with Mg2+ that it is difficult to separate free energies of Mg2+-RNA interactions from the intrinsic free energy of RNA folding. To devise quantitative models accounting for this phenomenon of Mg2+-induced RNA folding, it is necessary to independently determine Mg2+-RNA interaction free energies for folded and unfolded RNA forms. In this work, the energetics of Mg2+-RNA interactions are derived from an assay that measures the effective concentration of Mg2+ in the presence of RNA. These measurements are used with other measures of RNA stability to develop an overall picture of the energetics of Mg2+-induced RNA folding. Two different RNAs are discussed, a pseudoknot and an rRNA fragment. Both RNAs interact strongly with Mg2+ when partially unfolded, but the two folded RNAs differ dramatically in their inherent stability in the absence of Mg2+ and in the free energy of their interactions with Mg2+. From these results, it appears that any comprehensive framework for understanding Mg2+-induced stabilization of RNA will have to (i) take into account the interactions of ions with the partially unfolded RNAs and (ii) identify factors responsible for the widely different strengths with which folded tertiary structures interact with Mg2+.

Electrostatic properties of cowpea chlorotic mottle virus and cucumber mosaic virus capsids

Electrostatic properties of cowpea chlorotic mottle virus (CCMV) and cucumber mosaic virus (CMV) were investigated using numerical solutions to the Poisson-Boltzmann equation. Experimentally, it has been shown that CCMV particles swell in the absence of divalent cations when the pH is raised from 5 to 7. CMV, although structurally homologous, does not undergo this transition. An analysis of the calculated electrostatic potential confirms that a strong electrostatic repulsion at the calcium-binding sites in the CCMV capsid is most likely the driving force for the capsid swelling process during the release of calcium. The binding interaction between the encapsulated genome material (RNA) inside of the capsid and the inner capsid shell is weakened during the swelling transition. This probably aids in the RNA release process, but it is unlikely that the RNA is released through capsid openings due to unfavorable electrostatic interaction between the RNA and capsid inner shell residues at these openings. Calculations of the calcium binding energies show that Ca(2+) can bind both to the native and swollen forms of the CCMV virion. Favorable binding to the swollen form suggests that Ca(2+) ions can induce the capsid contraction and stabilize the native form.

Electrostatic correlations and fluctuations for ion binding to a finite length polyelectrolyte

A statistical mechanical model is presented which explicitly accounts for the fluctuations, the electrostatic, and the excluded volume correlations for ions bound to a polyelectrolyte such as DNA. The method can be employed to treat a wide range of ionic conditions including multivalent ions. The microscopic framework of the theory permits the use of realistic finite length and grooved structural model for the polyelectrolyte and modeling of the finite size of the bound ions. Test against Monte Carlo simulations suggests that the theory can give accurate predictions for the ion distribution and the thermodynamic properties. For multivalent ions, the theory makes improved predictions as compared with the mean-field approach. Moreover, for long polyelectrolyte and dilute salt concentration, the theory predicts ion binding properties that agree with the counterion condensation theory.

Ion-mediated nucleic acid helix-helix interactions

Salt ions are essential for the folding of nucleic acids. We use the tightly bound ion (TBI) model, which can account for the correlations and fluctuations for the ions bound to the nucleic acids, to investigate the electrostatic free-energy landscape for two parallel nucleic acid helices in the solution of added salt. The theory is based on realistic atomic structures of the helices. In monovalent salt, the helices are predicted to repel each other. For divalent salt, while the mean-field Poisson-Boltzmann theory predicts only the repulsion, the TBI theory predicts an effective attraction between the helices. The helices are predicted to be stabilized at an interhelix distance approximately 26-36 A, and the strength of the attractive force can reach -0.37 k(B)T/bp for helix length in the range of 9-12 bp. Both the stable helix-helix distance and the strength of the attraction are strongly dependent on the salt concentration and ion size. With the increase of the salt concentration, the helix-helix attraction becomes stronger and the most stable helix-helix separation distance becomes smaller. For divalent ions, at very high ion concentration, further addition of ions leads to the weakening of the attraction. Smaller ion size causes stronger helix-helix attraction and stabilizes the helices at a shorter distance. In addition, the TBI model shows that a decrease in the solvent dielectric constant would enhance the ion-mediated attraction. The theoretical findings from the TBI theory agree with the experimental measurements on the osmotic pressure of DNA array as well as the results from the computer simulations.

Forced-unfolding and force-quench refolding of RNA hairpins

Nanomanipulation of individual RNA molecules, using laser optical tweezers, has made it possible to infer the major features of their energy landscape. Time-dependent mechanical unfolding trajectories, measured at a constant stretching force (f(S)) of simple RNA structures (hairpins and three-helix junctions) sandwiched between RNA/DNA hybrid handles show that they unfold in a reversible all-or-none manner. To provide a molecular interpretation of the experiments we use a general coarse-grained off-lattice Gō-like model, in which each nucleotide is represented using three interaction sites. Using the coarse-grained model we have explored forced-unfolding of RNA hairpin as a function of f(S) and the loading rate (r(f)). The simulations and theoretical analysis have been done both with and without the handles that are explicitly modeled by semiflexible polymer chains. The mechanisms and timescales for denaturation by temperature jump and mechanical unfolding are vastly different. The directed perturbation of the native state by f(S) results in a sequential unfolding of the hairpin starting from their ends, whereas thermal denaturation occurs stochastically. From the dependence of the unfolding rates on r(f) and f(S) we show that the position of the unfolding transition state is not a constant but moves dramatically as either r(f) or f(S) is changed. The transition-state movements are interpreted by adopting the Hammond postulate for forced-unfolding. Forced-unfolding simulations of RNA, with handles attached to the two ends, show that the value of the unfolding force increases (especially at high pulling speeds) as the length of the handles increases. The pathways for refolding of RNA from stretched initial conformation, upon quenching f(S) to the quench force f(Q), are highly heterogeneous. The refolding times, upon force-quench, are at least an order-of-magnitude greater than those obtained by temperature-quench. The long f(Q)-dependent refolding times starting from fully stretched states are analyzed using a model that accounts for the microscopic steps in the rate-limiting step, which involves the trans to gauche transitions of the dihedral angles in the GAAA tetraloop. The simulations with explicit molecular model for the handles show that the dynamics of force-quench refolding is strongly dependent on the interplay of their contour length and persistence length and the RNA persistence length. Using the generality of our results, we also make a number of precise experimentally testable predictions.

Molego-based definition of the architecture and specificity of metal-binding sites

Decomposing proteins into "molegos," building blocks that are conserved in sequence and 3D-structure, can identify functional elements. To demonstrate the specificity of the decomposition method, the PCPMer program suite was used to numerically define physical chemical property motifs corresponding to the molegos that make up the metal-containing active sites of three distinct enzyme families, from the dimetallic phosphatases, DNase 1 related nucleases/phosphatases, and dioxygenases. All three superfamilies bind metal ions in a beta-strand core region but differ in the number and type of ions needed for activity. The motifs were then used to automatically identify proteins in the ASTRAL40 database that contained similar motifs. The proteins with the highest PCPMer score in the database were primarily metal-binding enzymes that were related in function to those in the alignment used to generate the PCPMer motif lists. The proteins that contained motifs similar to the dioxygenases differed from those found with PCP-motifs for phosphatases and nucleases. Relatively few metal-binding enzymes were detected when the search was done with PCP-motifs defined for interleukin-1 related proteins, which have a beta-strand core but do not bind metal ions. While the box architecture was constant in each superfamily, the specificity for the metal ion preferred for enzymatic activity is determined by the pattern of carbonyl, hydroxyl or imadazole groups in key positions in the molegos. These results have implications for the design of metal-binding enzymes, and illustrate the ability of the PCPMer approach to distinguish, at the sequence level, structural and functional elements.

Nucleic acid helix stability: effects of salt concentration, cation valence and size, and chain length

Metal ions play crucial roles in thermal stability and folding kinetics of nucleic acids. For ions (especially multivalent ions) in the close vicinity of nucleic acid surface, interion correlations and ion-binding mode fluctuations may be important. Poisson-Boltzmann theory ignores these effects whereas the recently developed tightly bound ion (TBI) theory explicitly accounts for these effects. Extensive experimental data demonstrate that the TBI theory gives improved predictions for multivalent ions (e.g., Mg2+) than the Poisson-Boltzmann theory. In this study, we use the TBI theory to investigate how the metal ions affect the folding stability of B-DNA helices. We quantitatively evaluate the effects of ion concentration, ion size and valence, and helix length on the helix stability. Moreover, we derive practically useful analytical formulas for the thermodynamic parameters as functions of finite helix length, ion type, and ion concentration. We find that the helix stability is additive for high ion concentration and long helix and nonadditive for low ion concentration and short helix. All these results are tested against and supported by extensive experimental data.

Dynamics and metal ion binding in the U6 RNA intramolecular stem-loop as analyzed by NMR

The U6 RNA intramolecular stem-loop (ISL) is a conserved component of the spliceosome, and contains an essential metal ion binding site centered between a protonated adenine, A79, and U80. Correlated with protonation of A79, U80 undergoes a base-flipping conformational change accompanied by significant helical movement. We have investigated the dynamics of the U6 ISL by analyzing the power dependence of 13C NMR relaxation rates in the rotating frame. The data provide evidence that the conformational transition is centered around an exchange lifetime of 84 micros. The U80 nucleotide displays low internal mobility on the picosecond time-scale at pH 7.0 but high internal mobility at pH 6.0, in agreement with the global transition resulting in the base of U80 adopting a looped-out conformation with increased dynamic disorder. A kinetic analysis suggests that the conformational change, rather than adenine protonation, is the rate-limiting step in the pathway of the conformational transition. Two nucleotides, U70 and U80, were found from chemical shift perturbation mapping to interact with the magnesium ion, with apparent K(d) values in the micromolar to millimolar range. These nucleotides also displayed metal ion-induced elevation of R1 rates, which can be explained by a model that assumes dynamic metal ion coordination concomitant with an induced higher shielding anisotropy for the base 13C nuclei. Addition of Mg2+ shifts the conformational equilibrium toward the high-pH (base-stacked) structure, accompanied by a significant drop in the apparent pK(a) of A79.

Coevolution of protein and RNA structures within a highly conserved ribosomal domain

The X-ray crystal structure of a ribosomal L11-rRNA complex with chloroplast-like mutations in both protein and rRNA is presented. The global structure is almost identical to that of the wild-type (bacterial) complex, with only a small movement of the protein alpha helix away from the surface of the RNA required to accommodate the altered protein residue. In contrast, the specific hydrogen bonding pattern of the mutated residues is substantially different, and now includes a direct interaction between the protein side chain and an RNA base edge and a water-mediated contact. Comparison of the two structures allows the observations of sequence variation and relative affinities of wild-type and mutant complexes to be clearly rationalized, but reinforces the concept that there is no single simple code for protein-RNA recognition.

Determining the Mg2+ stoichiometry for folding an RNA metal ion core

The folding and catalytic function of RNA molecules depend on their interactions with divalent metal ions, such as magnesium. As with every molecular process, the most basic knowledge required for understanding the close relationship of an RNA with its metal ions is the stoichiometry of the interaction. Unfortunately, inventories of the numbers of divalent ions associated with unfolded and folded RNA states have been unattainable. A common approach has been to interpret Hill coefficients fit to folding equilibria as the number of metal ions bound upon folding. However, this approach is vitiated by the presence of diffusely associated divalent ions in a dynamic ion atmosphere and by the likelihood of multiple transitions along a folding pathway. We demonstrate that the use of molar concentrations of background monovalent salt can alleviate these complications. These simplifying solution conditions allow a precise determination of the stoichiometry of the magnesium ions involved in folding the metal ion core of the P4-P6 domain of the Tetrahymena group I ribozyme. Hill analysis of hydroxyl radical footprinting data suggests that the P4-P6 RNA core folds cooperatively upon the association of two metal ions. This unexpectedly small stoichiometry is strongly supported by counting magnesium ions associated with the P4-P6 RNA via fluorescence titration and atomic emission spectroscopy. By pinpointing the metal ion stoichiometry, these measurements provide a critical but previously missing step in the thermodynamic dissection of the coupling between metal ion binding and RNA folding.

Ions and RNA Folding

The problem of how ions influence the folding of RNA into specific tertiary structures is being addressed from both thermodynamic (by how much do different salts affect the free energy change of folding) and structural (how are ions arranged on or near an RNA and what kinds of environments do they occupy) points of view. The challenge is to link these different approaches in a theoretical framework that relates the energetics of ion-RNA interactions to the spatial distribution of ions. This review distinguishes three different kinds of ion environments that differ in the extent of direct ion-RNA contacts and the degree to which the ion hydration is perturbed, and summarizes the current understanding of the way each environment relates to the overall energetics of RNA folding.

Substrate discrimination in RNase P RNA-mediated cleavage: importance of the structural environment of the RNase P cleavage site

Like the translational elongation factor EF-Tu, RNase P interacts with a large number of substrates where RNase P with its RNA subunit generates tRNAs with matured 5' termini by cleaving tRNA precursors immediately 5' of the residue at +1, i.e. at the position that corresponds to the first residue in tRNA. Most tRNAs carry a G+1C+72 base pair at the end of the aminoacyl acceptor-stem whereas in tRNA(Gln) G+1C+72 is replaced with U+1A+72. Here, we investigated RNase P RNA-mediated cleavage as a function of having G+1C+72 versus U+1A+72 in various substrate backgrounds, two full-size tRNA precursors (pre-tRNA(Gln) and pre-tRNA(Tyr)Su3) and a model RNA hairpin substrate (pATSer). Our data showed that replacement of G+1C+72 with U+1A+72 influenced ground state binding, cleavage efficiency under multiple and single turnover conditions in a substrate-dependent manner. Interestingly, we observed differences both in ground state binding and rate of cleavage comparing two full-size tRNA precursors, pre-tRNA(Gln) and pre-tRNA(Tyr)Su3. These findings provide evidence for substrate discrimination in RNase P RNA-mediated cleavage both at the level of binding, as previously observed for EF-Tu, as well as at the catalytic step. In our experiments where we used model substrate derivatives further indicated the importance of the +1/+72 base pair in substrate discrimination by RNase P RNA. Finally, we provide evidence that the structural architecture influences Mg2+ binding, most likely in its vicinity.

Calculation of the binding free energy for magnesium-RNA interactions

The nature of the interaction between nucleic acids and divalent ions in solution is complex. It includes long-range electrostatic and short-range nonelectrostatic forces. Water molecules can be in an inner coordination shell that intervenes between the ion and its binding site. This work describes a method for calculating the binding free energy and applies it to a specific Mg-RNA system in the presence of monovalent salt. The approach combines high-level ab initio theory with Poisson-Boltzmann calculations and provides an accurate description of all terms of the binding free energy for magnesium ions located at the RNA surface (including nonelectrostatic interactions). Some alternative macroscopic approaches are also discussed.

Mechanical unfolding of RNA hairpins

Mechanical unfolding trajectories, generated by applying constant force in optical-tweezer experiments, show that RNA hairpins and the P5abc subdomain of the group I intron unfold reversibly. We use coarse-grained Go-like models for RNA hairpins to explore forced unfolding over a broad range of temperatures. A number of predictions that are amenable to experimental tests are made. At the critical force, the hairpin jumps between folded and unfolded conformations without populating any discernible intermediates. The phase diagram in the force-temperature (f, T) plane shows that the hairpin unfolds by an all-or-none process. The cooperativity of the unfolding transition increases dramatically at low temperatures. Free energy of stability, obtained from time averages of mechanical unfolding trajectories, coincides with ensemble averages, which establishes ergodicity. The hopping time between the native basin of attraction (NBA) and the unfolded basin increases dramatically along the phase boundary. Thermal unfolding is stochastic, whereas mechanical unfolding occurs in "quantized steps" with great variations in the step lengths. Refolding times, upon force quench, from stretched states to the NBA are at least an order of magnitude greater than folding times by temperature quench. Upon force quench from stretched states, the NBA is reached in at least three stages. In the initial stages, the mean end-to-end distance decreases nearly continuously, and there is a sudden transition to the NBA only in the last stage. Because of the generality of the results, we propose that similar behavior should be observed in force quench refolding of proteins.

Recognition of the spliceosomal branch site RNA helix on the basis of surface and electrostatic features

We have investigated electrostatic and surface features of an essential region of the catalytic core of the spliceosome, the eukaryotic precursor messenger (pre-m)RNA splicing apparatus. The nucleophile for the first of two splicing reactions is the 2′-hydroxyl (OH) of the ribose of a specific adenosine within the intron. During assembly of the spliceosome's catalytic core, this adenosine is positioned by pairing with a short region of the U2 small nuclear (sn)RNA to form the pre-mRNA branch site helix. The solution structure of the spliceosomal pre-mRNA branch site [Newby,M.I. and Greenbaum,N.L. (2002) Nature Struct. Biol., 9, 958–965] showed that a phylogenetically conserved pseudouridine (ψ) residue in the segment of U2 snRNA that pairs with the intron induces a markedly different structure compared with that of its unmodified counterpart. In order to achieve a more detailed understanding of the factors that contribute to recognition of the spliceosome's branch site helix and activation of the nucleophile for the first step of pre-mRNA splicing, we have calculated surface areas and electrostatic potentials of ψ-modified and unmodified branch site duplexes. There was no significant difference between the total accessible area or ratio of total polar:nonpolar groups between modified and unmodified duplexes. However, there was substantially greater exposure of nonpolar area of the adenine base, and less exposure of the 2′-OH, in the ψ-modified structure. Electrostatic potentials computed using a hybrid boundary element and finite difference nonlinear Poisson–Boltzmann approach [Boschitsch, A.H. and Fenley, M.O. (2004) J. Comput. Chem., 25, 935–955] revealed a region of exceptionally negative potential in the major groove surrounding the 2′-OH of the branch site adenosine. These surface and electrostatic features may contribute to the overall recognition of the pre-mRNA branch site region by other components of the splicing reaction.

Electrostatic correlations and fluctuations for ion binding to a finite length polyelectrolyte

A statistical mechanical model is presented which explicitly accounts for the fluctuations, the electrostatic, and the excluded volume correlations for ions bound to a polyelectrolyte such as DNA. The method can be employed to treat a wide range of ionic conditions including multivalent ions. The microscopic framework of the theory permits the use of realistic finite length and grooved structural model for the polyelectrolyte and modeling of the finite size of the bound ions. Test against Monte Carlo simulations suggests that the theory can give accurate predictions for the ion distribution and the thermodynamic properties. For multivalent ions, the theory makes improved predictions as compared with the mean-field approach. Moreover, for long polyelectrolyte and dilute salt concentration, the theory predicts ion binding properties that agree with the counterion condensation theory.

Ionic interactions between PRNA and P protein in Bacillus subtilis RNase P characterized using a magnetocapture-based assay

Ribonuclease P (RNase P) is a ribonucleoprotein complex that catalyzes the cleavage of the 5' end of precursor tRNA. To characterize the interface between the Bacillus subtilis RNA (PRNA) and protein (P protein) components, the intraholoenzyme KD is determined as a function of ionic strength using a magnetocapture-based assay. Three distinct phases are evident. At low ionic strength, the affinity of PRNA for P protein is enhanced as the ionic strength increases mainly due to stabilization of the PRNA structure by cations. Lithium substitution in lieu of potassium enhances the affinity at low ionic strength, whereas the addition of ATP, known to stabilize the structure of P protein, does not affect the affinity. At high ionic strength, the observed affinity decreases as the ionic strength increases, consistent with disruption of ionic interactions. These data indicate that three to four ions are released on formation of holoenzyme, reflecting the number of ion pairs that occur between the P protein and PRNA. At moderate ionic strength, the two effects balance so that the apparent KD is not dependent on the ionic strength. The KD between the catalytic domain (C domain) and P protein has a similar triphasic dependence on ionic strength. Furthermore, the intraholoenzyme KD is identical to or tighter than that of full-length PRNA, demonstrating that the P protein binds solely to the C domain. Finally, pre-tRNAasp (but not tRNAasp) stabilizes the PRNA*P protein complex, as predicted by the direct interaction between the P protein and pre-tRNA leader.

Evidence for U-tail stabilization of gRNA/mRNA interactions in kinetoplastid RNA editing

The most dramatic example of RNA editing is found in the mitochondria of trypanosomes. In these organisms, U-insertions/deletions can create mRNAs that are twice as large as the gene that encodes them. Guide RNAs (gRNAs) that are complementary to short stretches of the mature message direct the precise placements of the U residues. The binding of gRNA to mRNA is a fundamental step in RNA editing and understanding the relative importance of the elements that confer affinity and specificity on this interaction is critical to our understanding of the editing process. In this study, we have analyzed the relative binding affinities of two different gRNA/mRNA pairs. The affinity of gA6-14 for its message (ATPase 6) is high, with an apparent K(D) in the 5-10 nM range. In contrast, gCYb-558 has a low affinity for its cognate mRNA. Deletion of the gRNA U-tail caused a significant reduction in the binding affinity for only the gCYb-558 pair, and was observed only under physiological magnesium conditions. These results indicate that the U-tail contribution can differ substantially between the different gRNA/mRNA pairs. In addition, our results suggest that the efficiency of gRNA/mRNA interaction is highly dependent on thermodynamic parameters determined by the local sequences and their adopted structures surrounding the anchor-binding site.

A guide to ions and RNA structure

RNA folding into stable tertiary structures is remarkably sensitive to the concentrations and types of cations present; an understanding of the physical basis of ion-RNA interactions is therefore a prerequisite for a quantitative accounting of RNA stability. This article summarizes the energetic factors that must be considered when ions interact with two different RNA environments. "Diffuse ions" accumulate near the RNA because of the RNA electrostatic field and remain largely hydrated. A "chelated" ion directly contacts a specific location on the RNA surface and is held in place by electrostatic forces. Energetic costs of ion chelation include displacement of some of the waters of hydration by the RNA surface and repulsion of diffuse ions. Methods are discussed for computing both the free energy of the set of diffuse ions associated with an RNA and the binding free energies of individual chelated ions. Such calculations quantitatively account for the effects of Mg(2+) on RNA stability where experimental data are available. An important conclusion is that diffuse ions are a major factor in the stabilization of RNA tertiary structures.

Site-resolved stabilization of a DNA triple helix by magnesium ions

Proton exchange and NMR spectroscopy have been used to define the effects of Mg2+ ions upon the stability of individual base pairs in the intramolecular parallel triple helix formed by the DNA oligonucleotide d(GAAGAGGTTTTTCCTCTTCTTTTTCTTCTCC). The rates of exchange of individual Watson-Crick and Hoogsteen imino protons in the DNA triple helix were measured in the absence and in the presence of Mg2+ ions. The results reveal that Mg2+ lowers the exchange rates of most imino protons in the structure by stabilizing the corresponding base pairs in their native closed conformation. Comparison of the DNA triple helix containing Na+ counterions to the same helix containing Mg2+ counterions shows that these stabilizing effects result, in large part, from Mg2+ ions closely associated with the DNA. Moreover, the effects are site-specific and depend on the number and location of protonated cytosines relative to the observed base. These findings provide new insights into the molecular roles of C+*GC triads in determining the stability of DNA triple-helical structures.

Cations as hydrogen bond donors: a view of electrostatic interactions in DNA

Cations are bound to nucleic acids in a solvated state. High-resolution X-ray diffraction studies of oligonucleotides provide a detailed view of Mg2+, and occasionally other ions bound to DNA. In a survey of several such structures, certain general observations emerge. First, cations bind preferentially to the guanine base in the major groove or to phosphate group oxygen atoms. Second, cations interact with DNA most frequently via water molecules in their primary solvation shell, direct ion-DNA contacts being only rarely observed. Thus, the solvated ions should be viewed as hydrogen bond donors in addition to point charges. Finally, ion interaction sites are readily exchangeable: The same site may be occupied by any ion, including spermine, as well as by a water molecule.

Mg2+-induced triplex formation of an equimolar mixture of poly(rA) and poly(rU)

Magnesium ions strongly influence the structure and biochemical activity of RNA. The interaction of Mg2+ with an equimolar mixture of poly(rA) and poly(rU) has been investigated by UV spectroscopy, isothermal titration calorimetry, ultrasound velocimetry and densimetry. Measurements in dilute aqueous solutions at 20 degrees C revealed two differ ent processes: (i) Mg2+ binding to unfolded poly(rA)*poly(rU) up to [Mg2+]/[phosphate] = 0.25; and (ii) poly(rA)*2poly(rU) triplex formation at [Mg2+]/[phosphate] between 0.25 and 0.5. The enthalpies of these two different processes are favorable and similar to each other, approximately -1.6 kcal x mol(-1) of base pairs. Volume and compressibility effects of the first process are positive, 8 cm3 x mol(-1) and 24 x 10(-4) cm3 x mol(-1) x bar(-1), respectively, and correspond to the release of water molecules from the hydration shells of Mg2+ and the polynucleotides. The triplex formation is also accompanied by a positive change in compressibility, 14 x 10(-4) cm3 x mol(-1) x bar(-1), but only a small change in volume, 1 cm3 x mol(-1). A phase diagram has been constructed from the melting experiments of poly(rA)*poly(rU) at a constant K+ concentration, 140 mM, and various amounts of Mg2+. Three discrete regions were observed, corresponding to single-, double- and triple-stranded complexes. The phase boundary corresponding to the transition between double and triple helical conformations lies near physiological salt concentrations and temperature.

Microenvironment analysis and identification of magnesium binding sites in RNA

Interactions with magnesium (Mg2+) ions are essential for RNA folding and function. The locations and function of bound Mg2+ ions are difficult to characterize both experimentally and computationally. In particular, the P456 domain of the Tetrahymena thermophila group I intron, and a 58 nt 23s rRNA from Escherichia coli have been important systems for studying the role of Mg2+ binding in RNA, but characteristics of all the binding sites remain unclear. We therefore investigated the Mg2+ binding capabilities of these RNA systems using a computational approach to identify and further characterize their Mg2+ binding sites. The approach is based on the FEATURE algorithm, reported previously for microenvironment analysis of protein functional sites. We have determined novel physicochemical descriptions of site-bound and diffusely bound Mg2+ ions in RNA that are useful for prediction. Electrostatic calculations using the Non-Linear Poisson Boltzmann (NLPB) equation provided further evidence for the locations of site-bound ions. We confirmed the locations of experimentally determined sites and further differentiated between classes of ion binding. We also identified potentially important, high scoring sites in the group I intron that are not currently annotated as Mg2+ binding sites. We note their potential function and believe they deserve experimental follow-up.

Electrostatic interactions in a peptide--RNA complex

Parallel experimental measurements and theoretical calculations have been used to investigate the energetics of electrostatic interactions in the complex formed between a 22 residue, alpha-helical peptide from the N protein of phage lambda and its cognate 19 nucleotide box B RNA hairpin. Salt-dependent free energies were measured for both peptide folding from coil to helix and peptide binding to RNA, and from these the salt-dependence of binding pre-folded, helical peptide to RNA was determined ( partial differential (DeltaG degrees (dock))/ partial differential log[KCl]=5.98(+/-0.21)kcal/mol). (A folding transition taking place in the RNA hairpin loop was shown to have a negligible dependence on salt concentration.) The non-linear Poisson-Boltzmann equation was used to calculate the same salt dependence of the binding free energy as 5.87(+/-0.22)kcal/mol, in excellent agreement with the measured value. Close agreement between experimental measurements and calculations was also obtained for two variant peptides in which either a basic or acidic residue was replaced with an uncharged residue, and for an RNA variant with a deletion of a single loop nucleotide. The calculations suggest that the strength of electrostatic interactions between a peptide residue and RNA varies considerably with environment, but that all 12 positive and negative N peptide charges contribute significantly to the electrostatic free energy of RNA binding, even at distances up to 11A from backbone phosphate groups. Calculations also show that the net release of ions that accompanies complex formation originates from rearrangements of both peptide and RNA ion atmospheres, and includes accumulation of ions in some regions of the complex as well as displacement of cations and anions from the ion atmospheres of the RNA and peptide, respectively.

Binding of Mg2+ to single-stranded polynucleotides: hydration and optical studies

The binding of Mg(2+) to single-stranded ribo- and deoxy-polynucleotides, poly(rA), poly(rU), poly(dA) and poly(dT), has been investigated in dilute aqueous solutions at pH 7.5 and 20 degrees C. A combination of ultrasound velocimetry, density, UV and CD spectroscopy have been employed to study hydration and spectral effects of Mg(2+) binding to the polynucleotides. Volume and compressibility effects of Mg(2+) binding to random-coiled poly(rU) and poly(dT) correspond to two coordination bonds probably between the adjacent phosphate groups. The same parameters for poly(rA)+Mg(2+) correspond to an inner-sphere complex with three-four direct contacts. However, almost no hydration effects are arising in binding to its deoxy analog, poly(dA), indicating mostly a delocalized binding mode. In agreement with hydration studies, optical investigations revealed almost no influence of Mg(2+) on poly(dA) properties, while it stabilizes and aggregates poly(rA) single-helix. The evidence presented here indicates that Mg(2+) are able to bind specifically to single-stranded polynucleotides, and recognize their composition and backbone conformation.

RNA folding: models and perspectives

Intrinsic events during RNA folding include conformational search and metal ion binding. Several experimentally testable models have been proposed to explain how large ribozymes accomplish folding. Future challenges include the validation of these models, and the correlation of experimental results and theoretical simulations.

A thermodynamic framework for the magnesium-dependent folding of RNA

The goal of this review is to present a unified picture of the relationship between ion binding and RNA folding based on recent theoretical and computational advances. In particular, we present a model describing how the association of magnesium ions is coupled to the tertiary structure folding of several well-characterized RNA molecules. This model is developed in terms of the nonlinear Poisson-Boltzmann (NLPB) equation, which provides a rigorous electrostatic description of the interaction between Mg(2+) and specific RNA structures. In our description, most of the ions surrounding an RNA behave as a thermally fluctuating ensemble distributed according to a Boltzmann weighted average of the mean electrostatic potential around the RNA. In some cases, however, individual ions near the RNA may shed some of their surrounding waters to optimize their Coulombic interactions with the negatively charged ligands on the RNA. These chelated ions are energetically distinct from the surrounding ensemble and must be treated explicitly. This model is used to explore several different RNA systems that interact differently with Mg(2+). In each case, the NLPB equation accurately describes the stoichiometric and energetic linkage between Mg(2+) binding and RNA folding without requiring any fitted parameters in the calculation. Based on this model, we present a physical description of how Mg(2+) binds and stabilizes specific RNA structures to promote the folding reaction.

The bulge region of HIV-1 TAR RNA binds metal ions in solution

Binding of Mg2+, Ca2+ and Co(NH3)6(3+) ions to the HIV-1 TAR RNA in solution was analysed by 19F NMR spectroscopy, metal ion-induced RNA cleavages and Brownian dynamics (BD) simulations. Chemically synthesised 29mer oligoribonucleotides of the TAR sequence labelled with 5-fluorouridine (FU) were used for 19F NMR-monitored metal ion titration. The chemical shift changes of fluorine resonances FU-23, FU-25 and FU-40 upon titration with Mg2+ and Ca2+ ions indicated specific, although weak, binding at the bulge region with the dissociation constants (K(d)) of 0.9 +/- 0.6 and 2.7 +/- 1.7 mM, respectively. Argininamide, inducing largest (19)F chemical shifts changes at FU-23, was used as a reference ligand (K(d) = 0.3 +/- 0.1 mM). In the Pb2+-induced TAR RNA cleavage experiment, strong and selective cleavage of the C24-U25 phosphodiester bond was observed, while Mg2+ and Ca2+ induced cuts at all 3-nt residues of the bulge. The inhibition of Pb2+-specific TAR cleavage by di- and trivalent metal ions revealed a binding specificity [in the order Co(NH3)6(3+) > Mg2+ > Ca2+] at the bulge site. A BD simulation search of potential magnesium ion sites within the NMR structure of HIV-1 TAR RNA was conducted on a set of 20 conformers (PDB code 1ANR). For most cases, the bulge region was targeted by magnesium cations.

A compact RNA tertiary structure contains a buried backbone-K+ complex

The structure of a 58 nucleotide ribosomal RNA fragment buries several phosphate groups of a hairpin loop within a large tertiary core. During refinement of an X-ray crystal structure containing this RNA, a potassium ion was found to be contacted by six oxygen atoms from the buried phosphate groups; the ion is contained completely within the solvent-accessible surface of the RNA. The electrostatic potential at the ion chelation site is unusually large, and more than compensates for the substantial energetic penalties associated with partial dehydration of the ion and displacement of delocalized ions. The very large predicted binding free energy, approximately -30 kcal/mol, implies that the site must be occupied for the RNA to fold. These findings agree with previous studies of the ion-dependent folding of tertiary structure in this RNA, which concluded that a monovalent ion was bound in a partially dehydrated environment where Mg2+ could not easily compete for binding. By compensating the unfavorable free energy of buried phosphate groups with a chelated ion, the RNA is able to create a larger and more complex tertiary fold than would be possible otherwise.

Metal ion binding and the folding of the hairpin ribozyme

The hairpin ribozyme comprises two formally unpaired loops carried on two arms of a four-way helical RNA junction. Addition of divalent metal ions brings about a conformational transition into an antiparallel structure in which there is an intimate association between the loops to generate the active form of the ribozyme. In this study, we have used fluorescence resonance energy transfer to analyze the global folding of the complete ribozyme, and the simple four-way junction derived from it, over a wide concentration range of divalent and monovalent metal ions. The simple junction undergoes an ion-induced rotation into an antiparallel form. In the presence of a constant background concentration of sodium ions, the magnesium-ion-induced transition is characterized by noncooperative binding with a Hill coefficient n = 1. By contrast, the magnesium-ion-induced folding of the complete ribozyme is more complex, involving two distinct binding phases. The first phase occurs in the micromolar range, and involves the cooperative binding of at least three magnesium ions. This can also be achieved by high concentrations of sodium ions, and is therefore likely to be due to diffuse binding of cations at the junction and the interface of the loop-loop interaction. The second phase occurs in the millimolar range, and can only be induced by divalent metal ions. This transition occurs in response to the noncooperative, site-specific binding of magnesium ions. We observe a good correlation between the extent of ion-induced folding and cleavage activity.

59Co solid-state NMR as a new probe for elucidating metal binding in polynucleotides

Although magnesium fulfills several essential biochemical roles, direct studies on this ion are complicated by its unfavorable spectroscopic characteristics. This contribution explores the possibility of monitoring magnesium-nucleic acid binding via a combination of [Co(NH3)6]3+ as surrogate for [Mg(H2O)6]2+, and of high-resolution solid-state 59Co NMR as a spectroscopic probe. Such strategy quenches fast cationic exchanges between bound and free states, while exploiting the superior NMR properties of the 59Co spin. Experiments on relatively small amounts of tRNA can then discern resonances corresponding to different metal binding environments. These characterizations were assisted by studies on model compounds and by multinuclear 31P-59Co recoupling experiments.

The linkage between magnesium binding and RNA folding

Understanding the linkage between Mg(2+) binding and RNA folding requires a proper theoretical model describing the energetics of Mg(2+) binding to the folded and unfolded states of RNA. Our current understanding of Mg(2+) binding to these different RNA states derives from empirical thermodynamic models that depend on a number of unjustified assumptions. We present a rigorous theoretical model describing the linkage between RNA folding and magnesium ion binding. In this model, based on the non-linear Poisson-Boltzmann (NLPB) equation, the stabilization of RNA by Mg(2+) arises from two distinct binding modes, diffuse binding and site binding. Diffusely bound Mg(2+) are described as an ensemble of hydrated ions that are attracted to the negative charge of the RNA. Site-bound Mg(2+) are partially desolvated ions that are attracted to electronegative pockets on the RNA surface. We explore two systems, yeast tRNA(Phe) and a 58-nucleotide rRNA fragment, with different Mg(2+) binding properties. The NLPB equation accurately describes both the stoichiometric and energetic linkage between Mg(2+) binding and RNA folding for both of these systems without requiring any fitted parameters in the calculation. Moreover, the NLPB model presents a well-defined physical description of how Mg(2+) binding helps fold an RNA. For both of the molecules studied here, the relevant unfolded state is a disordered intermediate state (I) that contains stable helical secondary structure without any tertiary contacts. Diffusely bound Mg(2+) interact with these secondary structure elements to stabilize the I state. The secondary structural elements of the I state fold into a compact, native tertiary structure (the N state). Diffuse binding plays a dominant role in stabilizing the N state for both RNAs studied. However, for the rRNA fragment, site-binding to a location with extraordinarily high electrostatic potential is also coupled to folding. Our results suggest that much experimental data measuring the linkage between Mg(2+) binding and RNA folding must be reinterpreted.

Metal ions and flexibility in a viral RNA pseudoknot at atomic resolution

Many pathogenic viruses use programmed -1 ribosomal frameshifting to regulate translation of their structural and enzymatic proteins from polycistronic mRNAs. Frameshifting is commonly stimulated by a pseudoknot located downstream from a slippery sequence, the latter positioned at the ribosomal A and P sites. We report here the structures of two crystal forms of the frameshifting RNA pseudoknot from beet western yellow virus at resolutions of 1.25 and 2.85 A. Because of the very high resolution of 1.25 A, ten mono- and divalent metal ions per asymmetric unit could be identified, giving insight into potential roles of metal ions in stabilizing the pseudoknot. A magnesium ion located at the junction of the two pseudoknot stems appears to play a crucial role in stabilizing the structure. Because the two crystal forms exhibit mostly unrelated packing interactions and local crystallographic disorder in the high-resolution form was resolvable, the two structures offer the most detailed view yet of the conformational preference and flexibility of an RNA pseudoknot.

DNA-cation interactions: quo vadis?

The interactions between double helical DNA and cations, specifically mono- and divalent metal ions, have recently received increased attention. Molecular dynamics simulations, solution NMR, and X-ray crystallography have all shed light on the coordination of ions in the major and minor grooves of DNA. Metal ion interactions may play key roles in the control of DNA conformation and topology, but despite progress in locating the ions and determining their precise binding modes, it remains difficult to figure out just how important ions really are. What have we learned and what remains to be done?

Water counting: quantitating the hydration level of paramagnetic metal ions bound to nucleotides and nucleic acids

Binding of divalent metal ions plays a key role in the structure and function of ribozymes and other RNAs. In turn, the energetics and kinetics of the specific binding process are dominated by the balance between the cost of dehydrating the aqueous ion and the energy gained from inner-sphere interactions with the macromolecule. In this work, we introduce the use of the pulsed EPR technique of 2H Electron Spin-Echo Envelope Modulation (ESEEM) to determine the hydration level of Mn2+ ions bound to nucleotides and nucleic acids. Mn2+ is an excellent structural and functional mimic for Mg2+, the most common divalent ion of physiological interest. Comparison of data in D2O and H2O, with aqueous Mn2+ as a reference standard, allows a robust and precise determination of the number of bound water molecules, and therefore the number of RNA-derived ligands. Examples of applications to the mononucleotide models MnGMP and MnATP, as well as to the paradigmatic RNA system tRNAPhe, are shown.