Salt-dependent folding energy landscape of RNA three-way junction.
ABSTRACT: RNAs are highly negatively charged chain molecules. Metal ions play a crucial role in RNA folding stability and conformational changes. In this work, we employ the recently developed tightly bound ion (TBI) model, which accounts for the correlation between ions and the fluctuation of ion distributions, to investigate the ion-dependent free energy landscape for the three-way RNA junction in a 16S rRNA domain. The predicted electrostatic free energy landscape suggests that 1), ion-mediated electrostatic interactions cause an ensemble of unfolded conformations narrowly populated around the maximally extended structure; and 2), Mg(2+) ion-induced correlation effects help bring the helices to the folded state. Nonelectrostatic interactions, such as noncanonical interactions within the junctions and between junctions and helix stems, might further limit the conformational diversity of the unfolded state, resulting in a more ordered unfolded state than the one predicted from the electrostatic effect. Moreover, the folded state is predominantly stabilized by the coaxial stacking force. The TBI-predicted folding stability agrees well with the experimental measurements for the different Na(+) and Mg(2+) ion concentrations. For Mg(2+) solutions, the TBI model, which accounts for the Mg(2+) ion correlation effect, gives more improved predictions than the Poisson-Boltzmann theory, which tends to underestimate the role of Mg(2+) in stabilizing the folded structure. Detailed control tests indicate that the dominant ion correlation effect comes from the charge-charge Coulombic correlation rather than the size (excluded volume) correlation between the ions. Furthermore, the model gives quantitative predictions for the ion size effect in the folding energy landscape and folding cooperativity.
Project description:<h4>Background</h4>Metal ions play a critical role in the stabilization of RNA structures. Therefore, accurate prediction of the ion effects in RNA folding can have a far-reaching impact on our understanding of RNA structure and function. Multivalent ions, especially Mg²?, are essential for RNA tertiary structure formation. These ions can possibly become strongly correlated in the close vicinity of RNA surface. Most of the currently available software packages, which have widespread success in predicting ion effects in biomolecular systems, however, do not explicitly account for the ion correlation effect. Therefore, it is important to develop a software package/web server for the prediction of ion electrostatics in RNA folding by including ion correlation effects.<h4>Results</h4>The TBI web server http://rna.physics.missouri.edu/tbi_index.html provides predictions for the total electrostatic free energy, the different free energy components, and the mean number and the most probable distributions of the bound ions. A novel feature of the TBI server is its ability to account for ion correlation and ion distribution fluctuation effects.<h4>Conclusions</h4>By accounting for the ion correlation and fluctuation effects, the TBI server is a unique online tool for computing ion-mediated electrostatic properties for given RNA structures. The results can provide important data for in-depth analysis for ion effects in RNA folding including the ion-dependence of folding stability, ion uptake in the folding process, and the interplay between the different energetic components.
Project description:RNA folding is enabled by interactions between the nucleic acid and its ion atmosphere, the mobile sheath of aqueous ions that surrounds and stabilizes it. Understanding the ion atmosphere requires the interplay of experiment and theory. However, even an apparently simple experiment to probe the ion atmosphere, measuring the dependence of DNA duplex stability upon ion concentration and identity, suffers from substantial complexity, because the unfolded ensemble contains many conformational states that are difficult to treat accurately with theory. To minimize this limitation, we measured the unfolding equilibrium of a DNA hairpin using a single-molecule optical trapping assay, in which the unfolded state is constrained to a limited set of elongated conformations. The unfolding free energy increased linearly with the logarithm of monovalent cation concentration for several cations, such that smaller cations tended to favor the folded state. Mg(2+) stabilized the hairpin much more effectively at low concentrations than did any of the monovalent cations. Poisson-Boltzmann theory captured trends in hairpin stability measured for the monovalent cation titrations with reasonable accuracy, but failed to do so for the Mg(2+) titrations. This finding is consistent with previous work, suggesting that Poisson-Boltzmann and other mean-field theories fail for higher valency cations where ion-ion correlation effects may become significant. The high-resolution data herein, because of the straightforward nature of both the folded and the unfolded states, should serve as benchmarks for the development of more accurate electrostatic theories that will be needed for a more quantitative and predictive understanding of nucleic acid folding.
Project description:Accurate quantification of the ionic contribution to RNA folding stability could greatly enhance our ability to understand and predict RNA functions. Recently, motivated by the potential importance of ion correlation and fluctuation in RNA folding, we developed the tightly bound ion (TBI) model. Extensive experimental tests showed that the TBI model can lead to better treatment of multivalent ions than the Poisson-Boltzmann equation. In this study, we use the model to quantify the contribution of salt (Na(+) and Mg(2+)) to the RNA tertiary structure folding free energy. Folding of the RNA tertiary structure often involves intermediates. We focus on the folding transition from an intermediate state to the native state, and compute the electrostatic folding free energy of the RNA. Based on systematic calculations for a variety of RNA molecules, we derive a set of formulas for the electrostatic free energy for tertiary structural folding as a function of the sequence length and compactness of the RNA and the Na(+) and Mg(2+) concentrations. Extensive comparisons with experimental data suggest that our model and the extracted empirical formulas are quite reliable.
Project description:To form secondary structure, nucleic acids (NAs) must overcome electrostatic strand-strand repulsion, which is moderated by the surrounding atmosphere of screening ions. The free energy of NA folding therefore depends on the interactions of this ion atmosphere with both the folded and unfolded states. We quantify such interactions using the preferential ion interaction coefficient or ion excess: the number of ions present near the NA in excess of the bulk concentration. The ion excess of the folded, double-helical state has been extensively studied; however, much less is known about the salt-dependent ion excess of the unfolded, single-stranded state. We measure this quantity using three complementary approaches: a direct approach of Donnan equilibrium dialysis read out by atomic emission spectroscopy and two indirect approaches involving either single-molecule force spectroscopy or existing thermal denaturation data. The results of these three approaches, each involving an independent experimental technique, are in good agreement. Even though the single-stranded NAs are flexible polymers that are expected to adopt random-coil configurations, we find that their ion atmosphere is quantitatively described by rod-like models that neglect large-scale conformational freedom, an effect that we explain in terms of the competition between the relevant structural and electrostatic length scales.
Project description:Electrostatic forces, acting between helices and modulated by the presence of the ion atmosphere, are key determinants in the energetic balance that governs RNA folding. Previous studies have employed Poisson-Boltzmann (PB) theory to compute the energetic contribution of these forces in RNA folding. However, the complex interaction of these electrostatic forces with RNA features such as tertiary contact formation, specific ion-binding, and complex interhelical junctions present in prior studies precluded a rigorous evaluation of PB theory, especially in physiologically important Mg(2+) solutions. To critically assess PB theory, we developed a model system that isolates these electrostatic forces. The model system, composed of two DNA duplexes tethered by a polyethylene glycol junction, is an analog for the unfolded state of canonical helix-junction-helix motifs found in virtually all structured RNAs. This model system lacks the complicating features that have precluded a critical assessment of PB in prior studies, ensuring that interhelical electrostatic forces dominate the behavior of the system. The system's simplicity allows PB predictions to be directly compared with small-angle X-ray scattering experiments over a range of monovalent and divalent ion concentrations. These comparisons indicate that PB is a reasonable description of the underlying electrostatic energies for monovalent ions, but large deviations are observed for divalent ions. The validation of PB for monovalent solutions allows analysis of the change in the conformational ensemble of this simple motif as salt concentration is changed. Addition of ions allows the motif to sample more compact microstates, increasing its conformational entropy. The increase of conformational entropy presents an additional barrier to folding by stabilizing the unfolded state. Neglecting this effect will adversely impact the accuracy of folding analyses and models.
Project description:Our 13C- and 1H-chemical exchange saturation transfer (CEST) experiments previously revealed a dynamic exchange between partially closed and open conformations of the SAM-II riboswitch in the absence of ligand. Here, all-atom structure-based molecular simulations, with the electrostatic effects of Manning counter-ion condensation and explicit magnesium ions are employed to calculate the folding free energy landscape of the SAM-II riboswitch. We use this analysis to predict that magnesium ions remodel the landscape, shifting the equilibrium away from the extended, partially unfolded state towards a compact, pre-organized conformation that resembles the ligand-bound state. Our CEST and SAXS experiments, at different magnesium ion concentrations, quantitatively confirm our simulation results, demonstrating that magnesium ions induce collapse and pre-organization. Agreement between theory and experiment bolsters microscopic interpretation of our simulations, which shows that triplex formation between helix P2b and loop L1 is highly sensitive to magnesium and plays a key role in pre-organization. Pre-organization of the SAM-II riboswitch allows rapid detection of ligand with high selectivity, which is important for biological function.
Project description:The recently developed Tightly Bound Ion (TBI) model offers improved predictions for ion effect in nucleic acid systems by accounting for ion correlation and fluctuation effects. However, further application of the model to larger systems is limited by the low computational efficiency of the model. Here, we develop a new computational efficient TBI model using free energy landscape-guided sampling method. The method leads to drastic reduction in the computer time by a factor of 50 for RNAs of 50-100 nucleotides long. The improvement in the computational efficiency would be more significant for larger structures. To test the new method, we apply the model to predict the free energies and the number of bound ions for a series of RNA folding systems. The validity of this new model is supported by the nearly exact agreement with the results from the original TBI model and the agreement with the experimental data. The method may pave the way for further applications of the TBI model to treat a broad range of biologically significant systems such as tetraloop-receptor and riboswitches.
Project description: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.
Project description:It has long been appreciated that Mg(2+) is essential for the stabilization of RNA tertiary structure. However, the problem of quantitative prediction for the ion effect in tertiary structure folding remains. By using the virtual bond RNA folding model (Vfold) to generate RNA conformations and the newly improved tightly bound ion model (TBI) to treat ion-RNA interactions, we investigate Mg(2+)-facilitated tetraloop-receptor docking. For the specific construct of the tetraloop-receptor system, the theoretical analysis shows that the Mg(2+)-induced stabilizing force for the docked state is predominantly entropic and the major contribution comes from the entropy of the diffusive ions. Furthermore, our results show that Mg(2+) ions promote tetraloop-receptor docking mainly through the entropy of the diffusive ions. The theoretical prediction agrees with experimental analysis. The method developed in this paper, which combines the theory for the (Mg(2+)) ion effects in RNA folding and RNA conformational sampling, may provide a useful framework for studying the ion effect in the folding of more complex RNA structures.
Project description:Ion-mediated electrostatic interactions play an important role in RNA folding stability. For a RNA in a solution with higher Mg(2+) ion concentration, more counterions in the solution can bind to the RNA, causing a strong many-body coupling between the bound ions. The many-body effect can change the effective potential of mean force between the tightly bound ions. This effect tends to dampen ion binding and lower RNA folding stability. Neglecting the many-body effect leads to a systematic error (over-estimation) of RNA folding stability at high Mg(2+) ion concentrations. Using the tightly bound ion model combined with a conformational ensemble model, we investigate the influence of the many-body effect on the ion-dependent RNA folding stability. Comparisons with the experimental data indicate that including the many-body effect led to much improved predictions for RNA folding stability at high Mg(2+) ion concentrations. The results suggest that the many-body effect can be important for RNA folding in high concentrations of multivalent ions. Further investigation showed that the many-body effect can influence the spatial distribution of the tightly bound ions and the effect is more pronounced for compact RNA structures and structures prone to the formation of local clustering of ions.