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

Atomistic Simulations Reveal Crucial Role of Metal Ions for Ligand Binding in Guanidine-I Riboswitch

Riboswitches are structured ribonucleic acid (RNA) segments that act as specific sensors for small molecules in bacterial metabolism. Due to the flexible nature of these highly charged macromolecules, molecular dynamics simulations are instrumental to investigating the mechanistic details of their regulatory function. In the present study, the guanidine-I riboswitch serves as an example of how atomistic simulations can shed light on the effect of ions on the structure and dynamics of RNA and on ligand binding. Relying on two orthologous crystal structures from different bacterial species, it is demonstrated how the ion setup crucially determines whether the simulation yields meaningful insights into the conformational stability of the RNA, functionally relevant residues and RNA-ligand interactions. The ion setup in this context includes diffuse ions in solution and bound ions associated directly with the RNA, in particular a triad of 2 Mg2+ ions and a K+ ion in close proximity to the guanidinium binding site. A detailed investigation of the binding pocket reveals that the K+ from the ion triad plays a decisive role in stabilizing the ligand binding by stabilizing important localized interactions, which in turn contribute to the overall shape of the folded state of the RNA.

Disentangling contact and ensemble epistasis in a riboswitch

Mutations introduced into macromolecules often exhibit epistasis, where the effect of one mutation alters the effect of another. Knowing the mechanisms that lead to epistasis is important for understanding how macromolecules work and evolve, as well as for effective macromolecular engineering. Here, we investigate the interplay between "contact epistasis" (epistasis arising from physical interactions between mutated residues) and "ensemble epistasis" (epistasis that occurs when a mutation redistributes the conformational ensemble of a macromolecule, thus changing the effect of the second mutation). We argue that the two mechanisms can be distinguished in allosteric macromolecules by measuring epistasis at differing allosteric effector concentrations. Contact epistasis manifests as nonadditivity in the microscopic equilibrium constants describing the conformational ensemble. This epistatic effect is independent of allosteric effector concentration. Ensemble epistasis manifests as nonadditivity in thermodynamic observables-such as ligand binding-that are determined by the distribution of ensemble conformations. This epistatic effect strongly depends on allosteric effector concentration. Using this framework, we experimentally investigated the origins of epistasis in three pairwise mutant cycles introduced into the adenine riboswitch aptamer domain by measuring ligand binding as a function of allosteric effector concentration. We found evidence for both contact and ensemble epistasis in all cycles. Furthermore, we found that the two mechanisms of epistasis could interact with each other. For example, in one mutant cycle we observed 6 kcal/mol of contact epistasis in a microscopic equilibrium constant. In that same cycle, the maximum epistasis in ligand binding was only 1.5 kcal/mol: shifts in the ensemble masked the contribution of contact epistasis. Finally, our work yields simple heuristics for identifying contact and ensemble epistasis based on measurements of a biochemical observable as a function of allosteric effector concentration.

Potential effects of metal ion induced two-state allostery on the regulatory mechanism of add adenine riboswitch

Riboswitches normally regulate gene expression through structural changes in response to the specific binding of cellular metabolites or metal ions. Taking add adenine riboswitch as an example, we explore the influences of metal ions (especially for K⁺ and Mg²⁺ ions) on the structure and dynamics of riboswitch aptamer (with and without ligand) by using molecular dynamic (MD) simulations. Our results show that a two-state transition marked by the structural deformation at the connection of J12 and P1 (C_J12-P1) is not only related to the binding of cognate ligands, but also strongly coupled with the change of metal ion environments. Moreover, the deformation of the structure at C_J12-P1 can be transmitted to P1 directly connected to the expression platform in multiple ways, which will affect the structure and stability of P1 to varying degrees, and finally change the regulation state of this riboswitch.

Molecular dynamic simulations are employed to assess the influence of metal ions on riboswitch structure and dynamics, suggesting a conformational control of riboswitch aptamers by metal ions before ligand binding.

Measurement of the specific and non-specific binding energies of Mg2+ to RNA

Determining the non-specific and specific electrostatic contributions of magnesium binding to RNA is a challenging problem. We introduce a single-molecule method based on measuring the folding energy of a native RNA in magnesium and at its equivalent sodium concentration. The latter is defined so that the folding energy in sodium equals the non-specific electrostatic contribution in magnesium. The sodium equivalent can be estimated according to the empirical 100/1 rule (1 M NaCl is equivalent to 10 mM MgCl2), which is a good approximation for most RNAs. The method is applied to an RNA three-way junction (3WJ) that contains specific Mg2+ binding sites and misfolds into a double hairpin structure without binding sites. We mechanically pull the RNA with optical tweezers and use fluctuation theorems to determine the folding energies of the native and misfolded structures in magnesium (10 mM MgCl2) and at the equivalent sodium condition (1 M NaCl). While the free energies of the misfolded structure are equal in magnesium and sodium, they are not for the native structure, the difference being due to the specific binding energy of magnesium to the 3WJ, which equals ΔG≃ 10 kcal/mol. Besides stabilizing the 3WJ, Mg2+ also kinetically rescues it from the misfolded structure over timescales of tens of seconds in a force-dependent manner. The method should generally be applicable to determine the specific binding energies of divalent cations to other tertiary RNAs.

Diffuse Ions Coordinate Dynamics in a Ribonucleoprotein Assembly

Proper ionic concentrations are required for the functional dynamics of RNA and ribonucleoprotein (RNP) assemblies. While experimental and computational techniques have provided many insights into the properties of chelated ions, less is known about the energetic contributions of diffuse ions to large-scale conformational rearrangements. To address this, we present a model that is designed to quantify the influence of diffuse monovalent and divalent ions on the dynamics of biomolecular assemblies. This model employs all-atom (non-H) resolution and explicit ions, where effective potentials account for hydration effects. We first show that the model accurately predicts the number of excess Mg²⁺ ions for prototypical RNA systems, at a level comparable to modern coarse-grained models. We then apply the model to a complete ribosome and show how the balance between diffuse Mg²⁺ and K⁺ ions can control the dynamics of tRNA molecules during translation. The model predicts differential effects of diffuse ions on the free-energy barrier associated with tRNA entry and the energy of tRNA binding to the ribosome. Together, this analysis reveals the direct impact of diffuse ions on the dynamics of an RNP assembly.

Multifunctional Nanomachinery for Enhancement of Bone Healing

The visionary idea that RNA adopts nonbiological roles in today's nanomaterial world has been nothing short of phenomenal. These RNA molecules have ample chemical functionality and self-assemble to form distinct nanostructures in response to external stimuli. They may be combined with inorganic materials to produce nanomachines that carry cargo to a target site in a controlled manner and respond dynamically to environmental changes. Comparable to biological cells, programmed RNA nanomachines have the potential to replicate bone healing in vitro. Here, an RNA-biomineral nanomachine is developed, which accomplishes intrafibrillar and extrafibrillar mineralization of collagen scaffolds to mimic bone formation in vitro. Molecular dynamics simulation indicates that noncovalent hydrogen bonding provides the energy source that initiates self-assembly of these nanomachines. Incorporation of the RNA-biomineral nanomachines into collagen scaffolds in vivo creates an osteoinductive microenvironment within a bone defect that is conducive to rapid biomineralization and osteogenesis. Addition of RNA-degrading enzymes into RNA-biomineral nanomachines further creates a stop signal that inhibits unwarranted bone formation in tissues. The potential of RNA in building functional nanostructures has been underestimated in the past. The concept of RNA-biomineral nanomachines participating in physiological processes may transform the nanoscopic world of life science.

Chelated Magnesium Logic Gate Regulates Riboswitch Pseudoknot Formation

Magnesium plays a critical role in the structure, dynamics, and function of RNA. The precise microscopic effect of chelated magnesium on RNA structure is yet to be explored. Magnesium is known to act through its diffuse cloud around RNA, through the outer sphere (water-mediated), inner sphere, and often chelated ion-mediated interactions. A mechanism is proposed for the role of experimentally discovered site-specific chelated magnesium ions on the conformational dynamics of SAM-I riboswitch aptamers in bacteria. This mechanism is observed with atomistic simulations performed in a physiological mixed salt environment at a high temperature. The simulations were validated with phosphorothioate interference mapping experiments that help to identify crucial inner-sphere Mg²⁺ sites prescribing an appropriate initial distribution of inner- and outer-sphere magnesium ions to maintain a physiological ion concentration of monovalent and divalent salts. A concerted role of two chelated magnesium ions is newly discovered since the presence of both supports the formation of the pseudoknot. This constitutes a logical AND gate. The absence of any of these magnesium ions instigates the dissociation of long-range pseudoknot interaction exposing the inner core of the RNA. A base triple is the epicenter of the magnesium chelation effect. It allosterically controls RNA pseudoknot by bolstering the direct effect of magnesium chelation in protecting the functional fold of RNA to control ON and OFF transcription switching.

Structure folding of RNA kissing complexes in salt solutions: predicting 3D structure, stability, and folding pathway

RNA kissing complexes are essential for genomic RNA dimerization and regulation of gene expression, and their structures and stability are critical to their biological functions. In this work, we used our previously developed coarse-grained model with an implicit structure-based electrostatic potential to predict three-dimensional (3D) structures and stability of RNA kissing complexes in salt solutions. For extensive RNA kissing complexes, our model shows great reliability in predicting 3D structures from their sequences, and our additional predictions indicate that the model can capture the dependence of 3D structures of RNA kissing complexes on monovalent/divalent ion concentrations. Moreover, the comparisons with extensive experimental data show that the model can make reliable predictions on the stability for various RNA kissing complexes over wide ranges of monovalent/divalent ion concentrations. Notably, for RNA kissing complexes, our further analyses show the important contribution of coaxial stacking to the 3D structures and stronger stability than the corresponding kissing-interface duplexes at high salts. Furthermore, our comprehensive analyses for RNA kissing complexes reveal that the thermally folding pathway for a complex sequence is mainly determined by the relative stability of two possible folded states of kissing complex and extended duplex, which can be significantly modulated by its sequence.

Theory and simulations for RNA folding in mixtures of monovalent and divalent cations

RNA molecules cannot fold in the absence of counterions. Experiments are typically performed in the presence of monovalent and divalent cations. How to treat the impact of a solution containing a mixture of both ion types on RNA folding has remained a challenging problem for decades. By exploiting the large concentration difference between divalent and monovalent ions used in experiments, we develop a theory based on the reference interaction site model (RISM), which allows us to treat divalent cations explicitly while keeping the implicit screening effect due to monovalent ions. Our theory captures both the inner shell and outer shell coordination of divalent cations to phosphate groups, which we demonstrate is crucial for an accurate calculation of RNA folding thermodynamics. The RISM theory for ion-phosphate interactions when combined with simulations based on a transferable coarse-grained model allows us to predict accurately the folding of several RNA molecules in a mixture containing monovalent and divalent ions. The calculated folding free energies and ion-preferential coefficients for RNA molecules (pseudoknots, a fragment of the rRNA, and the aptamer domain of the adenine riboswitch) are in excellent agreement with experiments over a wide range of monovalent and divalent ion concentrations. Because the theory is general, it can be readily used to investigate ion and sequence effects on DNA properties.

Predicting Monovalent Ion Correlation Effects in Nucleic Acids

Ion correlation and fluctuation can play a potentially significant role in metal ion-nucleic acid interactions. Previous studies have focused on the effects for multivalent cations. However, the correlation and fluctuation effects can be important also for monovalent cations around the nucleic acid surface. Here, we report a model, gMCTBI, that can explicitly treat discrete distributions of both monovalent and multivalent cations and can account for the correlation and fluctuation effects for the cations in the solution. The gMCTBI model enables investigation of the global ion binding properties as well as the detailed discrete distributions of the bound ions. Accounting for the ion correlation effect for monovalent ions can lead to more accurate predictions, especially in a mixed monovalent and multivalent salt solution, for the number and location of the bound ions. Furthermore, although the monovalent ion-mediated correlation does not show a significant effect on the number of bound ions, the correlation may enhance the accumulation of monovalent ions near the nucleic acid surface and hence affect the ion distribution. The study further reveals novel ion correlation-induced effects in the competition between the different cations around nucleic acids.

Quantitative Studies of an RNA Duplex Electrostatics by Ion Counting

RNAs are one of the most charged polyelectrolytes in nature, and understanding their electrostatics is fundamental to their structure and biological functions. An effective way to characterize the electrostatic field generated by nucleic acids is to quantify interactions between nucleic acids and ions that surround the molecules. These ions form a loosely associated cloud referred to as an ion atmosphere. Although theoretical and computational studies can describe the ion atmosphere around RNAs, benchmarks are needed to guide the development of these approaches, and experiments to date that read out RNA-ion interactions are limited. Here, we present ion counting studies to quantify the number of ions surrounding well-defined model systems of RNA and DNA duplexes. We observe that the RNA duplex attracts more cations and expels fewer anions compared to the DNA duplex, and the RNA duplex interacts significantly stronger with the divalent cation Mg²⁺, despite their identical total charge. These experimental results suggest that the RNA duplex generates a stronger electrostatic field than DNA, as is predicted based on the structural differences between their helices. Theoretical calculations using a nonlinear Poisson-Boltzmann equation give excellent agreement with experiments for monovalent ions but underestimate Mg²⁺-DNA and Mg²⁺-RNA interactions by 20%. These studies provide needed stringent benchmarks to use against other all-atom theoretical models of RNA-ion interactions, interactions that likely must be accurately accounted for in structural, dynamic, and energetic terms to confidently model RNA structure, interactions, and function.

Unraveling RNA dynamical behavior of TPP riboswitches: a comparison between Escherichia coli and Arabidopsis thaliana

Riboswitches are RNA sensors that affect post-transcriptional processes through their ability to bind to small molecules. Thiamine pyrophosphate (TPP) riboswitch class is the most widespread riboswitch occurring in all three domains of life. Even though it controls different genes involved in the synthesis or transport of thiamine and its phosphorylated derivatives in bacteria, archaea, fungi, and plants, the TPP aptamer has a conserved structure. In this study, we aimed at understanding differences in the structural dynamics of TPP riboswitches from Escherichia coli and Arabidopsis thaliana, based on their crystallographic structures (TPPsw^ec and TPPsw^at, respectively) and dynamics in aqueous solution, both in apo and holo states. A combination of Molecular Dynamics Simulations and Network Analysis empowered to find out slight differences in the dynamical behavior of TPP riboswitches, although relevant for their dynamics in bacteria and plants species. Our results suggest that distinct interactions in the microenvironment surrounding nucleotide U36 of TPPsw^ec (and U35 in TPPsw^at) are related to different responses to TPP. The network analysis showed that minor structural differences in the aptamer enable enhanced intramolecular communication in the presence of TPP in TPPsw^ec, but not in TPPsw^at. TPP riboswitches of plants present subtler and slower regulation mechanisms than bacteria do.

Single-Molecule FRET Kinetics of the Mn2+ Riboswitch: Evidence for Allosteric Mg2+ Control of "Induced-Fit" vs "Conformational Selection" Folding Pathways

Gene expression in bacteria is often regulated dynamically by conformational changes in a riboswitch upon ligand binding, a detailed understanding of which is very much in its infancy. For example, the manganese riboswitch is a widespread RNA motif that conformationally responds in regulating bacterial gene expression to micromolar levels of its eponymous ligand, Mn²⁺, but the mechanistic pathways are poorly understood. In this work, we quantitatively explore the dynamic folding behavior of the manganese riboswitch by single-molecule fluorescence resonance energy transfer spectroscopy as a function of cation/ligand conditions. From the detailed analysis of the kinetics, the Mn²⁺ is shown to fold the riboswitch by a "bind-then-fold" (i.e., "induced-fit", IF) mechanism, whereby the ligand binds first and then promotes folding. On the other hand, the data also clearly reveal the presence of a folded yet ligand-free structure predominating due to the addition of physiological Mg²⁺ to a nonselective metal ion binding site. Of particular kinetic interest, such a Mg²⁺ "prefolded" conformation of the riboswitch is shown to exhibit a significantly increased affinity for Mn²⁺ and further stabilization by subsequent binding of the ligand, thereby promoting efficient riboswitch folding by a "fold-then-bind" (i.e., "conformational selection", CS) mechanism. Our results not only demonstrate Mg²⁺-controlled switching between IF and CS riboswitch folding pathways but also suggest a novel heterotropic allosteric control in the manganese riboswitch activity co-regulated by Mg²⁺ binding.

Predicting RNA-Metal Ion Binding with Ion Dehydration Effects

Metal ions play essential roles in nucleic acids folding and stability. The interaction between metal ions and nucleic acids can be highly complicated because of the interplay between various effects such as ion correlation, fluctuation, and dehydration. These effects may be particularly important for multivalent ions such as Mg²⁺ ions. Previous efforts to model ion correlation and fluctuation effects led to the development of the Monte Carlo tightly bound ion model. Here, by incorporating ion hydration/dehydration effects into the Monte Carlo tightly bound ion model, we develop a, to our knowledge, new approach to predict ion binding. The new model enables predictions for not only the number of bound ions but also the three-dimensional spatial distribution of the bound ions. Furthermore, the new model reveals several intriguing features for the bound ions such as the mutual enhancement/inhibition in ion binding between the fully hydrated (diffuse) ions, the outer-shell dehydrated ions, and the inner-shell dehydrated ions and novel features for the monovalent-divalent ion interplay due to the hydration effect.

Effects of Preferential Counterion Interactions on the Specificity of RNA Folding

The real-time search for native RNA structure is essential for the operation of regulatory RNAs. We previously reported that a fraction of the Azoarcus ribozyme achieves a compact structure in less than a millisecond. To scrutinize the forces that drive initial folding steps, we used time-resolved SAXS to compare the folding dynamics of this ribozyme in thermodynamically isostable concentrations of different counterions. The results show that the size of the fast-folding population increases with the number of available counterions and correlates with the flexibility of initial RNA structures. Within 1 ms of folding, Mg²⁺ exhibits a smaller preferential interaction coefficient per charge, ΔΓ₊/ Z, than Na⁺ or [Co(NH₃)₆]³⁺. The lower ΔΓ₊/ Z corresponds to a smaller yield of folded RNA, although Mg²⁺ stabilizes native RNA more efficiently than other ions at equilibrium. These results suggest that strong Mg²⁺-RNA interactions impede the search for globally native structure during early folding stages.

Modeling Structure, Stability, and Flexibility of Double-Stranded RNAs in Salt Solutions

Double-stranded (ds) RNAs play essential roles in many processes of cell metabolism. The knowledge of three-dimensional (3D) structure, stability, and flexibility of dsRNAs in salt solutions is important for understanding their biological functions. In this work, we further developed our previously proposed coarse-grained model to predict 3D structure, stability, and flexibility for dsRNAs in monovalent and divalent ion solutions through involving an implicit structure-based electrostatic potential. The model can make reliable predictions for 3D structures of extensive dsRNAs with/without bulge/internal loops from their sequences, and the involvement of the structure-based electrostatic potential and corresponding ion condition can improve the predictions for 3D structures of dsRNAs in ion solutions. Furthermore, the model can make good predictions for thermal stability for extensive dsRNAs over the wide range of monovalent/divalent ion concentrations, and our analyses show that the thermally unfolding pathway of dsRNA is generally dependent on its length as well as its sequence. In addition, the model was employed to examine the salt-dependent flexibility of a dsRNA helix, and the calculated salt-dependent persistence lengths are in good accordance with experiments.

Predicting 3D structure and stability of RNA pseudoknots in monovalent and divalent ion solutions

RNA pseudoknots are a kind of minimal RNA tertiary structural motifs, and their three-dimensional (3D) structures and stability play essential roles in a variety of biological functions. Therefore, to predict 3D structures and stability of RNA pseudoknots is essential for understanding their functions. In the work, we employed our previously developed coarse-grained model with implicit salt to make extensive predictions and comprehensive analyses on the 3D structures and stability for RNA pseudoknots in monovalent/divalent ion solutions. The comparisons with available experimental data show that our model can successfully predict the 3D structures of RNA pseudoknots from their sequences, and can also make reliable predictions for the stability of RNA pseudoknots with different lengths and sequences over a wide range of monovalent/divalent ion concentrations. Furthermore, we made comprehensive analyses on the unfolding pathway for various RNA pseudoknots in ion solutions. Our analyses for extensive pseudokonts and the wide range of monovalent/divalent ion concentrations verify that the unfolding pathway of RNA pseudoknots is mainly dependent on the relative stability of unfolded intermediate states, and show that the unfolding pathway of RNA pseudoknots can be significantly modulated by their sequences and solution ion conditions.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

Incorporation of isotopic, fluorescent, and heavy-atom-modified nucleotides into RNAs by position-selective labeling of RNA

Site-specific incorporation of labeled nucleotides is an extremely useful synthetic tool for many structural studies (e.g., NMR, electron paramagnetic resonance (EPR), fluorescence resonance energy transfer (FRET), and X-ray crystallography) of RNA. However, specific-position-labeled RNAs >60 nt are not commercially available on a milligram scale. Position-selective labeling of RNA (PLOR) has been applied to prepare large RNAs labeled at desired positions, and all the required reagents are commercially available. Here, we present a step-by-step protocol for the solid-liquid hybrid phase method PLOR to synthesize 71-nt RNA samples with three different modification applications, containing (i) a ¹³C¹⁵N-labeled segment; (ii) discrete residues modified with Cy3, Cy5, or biotin; or (iii) two iodo-U residues. The flexible procedure enables a wide range of downstream biophysical analyses using precisely localized functionalized nucleotides. All three RNAs were obtained in <2 d, excluding time for preparing reagents and optimizing experimental conditions. With optimization, the protocol can be applied to other RNAs with various labeling schemes, such as ligation of segmentally labeled fragments.

Consequences of Mg2+ binding on the geometry and stability of RNA base pairs

Quantum chemical calculations reveal the role of magnesium in stabilizing the geometries of intrinsically unstable RNA base pairs.

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.

Predicting Ion Effects in an RNA Conformational Equilibrium

We develop a partial charge-based tightly bound ion (PCTBI) model for the ion effects in RNA folding. On the basis of the Monte Carlo tightly bound ion (MCTBI) approach, the model can account for ion fluctuation and correlation effects, and can predict the ion distribution around the RNA. Furthermore, unlike the previous coarse-grained RNA charge models, where negative charges are placed on the phosphates only, the current new model considers the detailed all-atom partial charge distribution on the RNA. Thus, the model not only keeps the advantage of the MCTBI model, but also has the potential to provide important detailed information unattainable by the previous MCTBI models. For example, the model predicts the reduction in ion binding upon protein binding and ion-induced conformational switches. For hepatitis C virus genomic RNA, the model predicts a Mg²⁺-induced stabilization of a kissing motif for a cis-acting regulatory element in the genomic RNA. Extensive theory-experiment comparisons support the reliability of the theoretical predictions. Therefore, the model may serve as a robust starting point for further development of an accurate method for ion effects in an RNA conformational equilibrium and RNA-cofactor interactions.

MCTBI: a web server for predicting metal ion effects in RNA structures

Metal ions play critical roles in RNA structure and function. However, web servers and software packages for predicting ion effects in RNA structures are notably scarce. Furthermore, the existing web servers and software packages mainly neglect ion correlation and fluctuation effects, which are potentially important for RNAs. We here report a new web server, the MCTBI server (http://rna.physics.missouri.edu/MCTBI), for the prediction of ion effects for RNA structures. This server is based on the recently developed MCTBI, a model that can account for ion correlation and fluctuation effects for nucleic acid structures and can provide improved predictions for the effects of metal ions, especially for multivalent ions such as Mg²⁺ effects, as shown by extensive theory-experiment test results. The MCTBI web server predicts metal ion binding fractions, the most probable bound ion distribution, the electrostatic free energy of the system, and the free energy components. The results provide mechanistic insights into the role of metal ions in RNA structure formation and folding stability, which is important for understanding RNA functions and the rational design of RNA structures.

Theory and Modeling of RNA Structure and Interactions with Metal Ions and Small Molecules

In addition to continuous rapid progress in RNA structure determination, probing, and biophysical studies, the past decade has seen remarkable advances in the development of a new generation of RNA folding theories and models. In this article, we review RNA structure prediction models and models for ion-RNA and ligand-RNA interactions. These new models are becoming increasingly important for a mechanistic understanding of RNA function and quantitative design of RNA nanotechnology. We focus on new methods for physics-based, knowledge-based, and experimental data-directed modeling for RNA structures and explore the new theories for the predictions of metal ion and ligand binding sites and metal ion-dependent RNA stabilities. The integration of these new methods with theories about the cellular environment effects in RNA folding, such as molecular crowding and cotranscriptional kinetic effects, may ultimately lead to an all-encompassing RNA folding model.

Approach to the unfolding and folding dynamics of add A-riboswitch upon adenine dissociation using a coarse-grained elastic network model

Riboswitches are noncoding mRNA segments that can regulate the gene expression via altering their structures in response to specific metabolite binding. We proposed a coarse-grained Gaussian network model (GNM) to examine the unfolding and folding dynamics of adenosine deaminase (add) A-riboswitch upon the adenine dissociation, in which the RNA is modeled by a nucleotide chain with interaction networks formed by connecting adjoining atomic contacts. It was shown that the adenine binding is critical to the folding of the add A-riboswitch while the removal of the ligand can result in drastic increase of the thermodynamic fluctuations especially in the junction regions between helix domains. Under the assumption that the native contacts with the highest thermodynamic fluctuations break first, the iterative GNM simulations showed that the unfolding process of the adenine-free add A-riboswitch starts with the denature of the terminal helix stem, followed by the loops and junctions involving ligand binding pocket, and then the central helix domains. Despite the simplified coarse-grained modeling, the unfolding dynamics and pathways are shown in close agreement with the results from atomic-level MD simulations and the NMR and single-molecule force spectroscopy experiments. Overall, the study demonstrates a new avenue to investigate the binding and folding dynamics of add A-riboswitch molecule which can be readily extended for other RNA molecules.

Types and concentrations of metal ions affect local structure and dynamics of RNA

The roles that metal ions play in the structure and dynamics of RNA molecules are long-standing problems that have been studied extensively but are still not well understood. Here we show that metal ions have distributions around RNA molecules that strongly depend on the types and concentrations of the metal ions and also the electrostatic surface of the molecule. In particular, the ion distributions may not balance all the local electronegativity of the molecule. These ion distributions do not only greatly affect local structures but also lead to different local dynamics of RNA. We studied the effects of different ion solutions on the structure and dynamics of RNA by taking the preQ_{1} riboswitch aptamer domain as an illustrative example and using molecular dynamics simulations. Since the local structures and dynamics of RNAs are important to their functions, our results also indicate that the selection of proper ion conditions is necessary to model them correctly, in contrast to the use of diverse ion solutions in current molecular dynamics simulations.

Predicting 3D Structure, Flexibility, and Stability of RNA Hairpins in Monovalent and Divalent Ion Solutions

A full understanding of RNA-mediated biology would require the knowledge of three-dimensional (3D) structures, structural flexibility, and stability of RNAs. To predict RNA 3D structures and stability, we have previously proposed a three-bead coarse-grained predictive model with implicit salt/solvent potentials. In this study, we further develop the model by improving the implicit-salt electrostatic potential and including a sequence-dependent coaxial stacking potential to enable the model to simulate RNA 3D structure folding in divalent/monovalent ion solutions. The model presented here can predict 3D structures of RNA hairpins with bulges/internal loops (<77 nucleotides) from their sequences at the corresponding experimental ion conditions with an overall improved accuracy compared to the experimental data; the model also makes reliable predictions for the flexibility of RNA hairpins with bulge loops of different lengths at several divalent/monovalent ion conditions. In addition, the model successfully predicts the stability of RNA hairpins with various loops/stems in divalent/monovalent ion solutions.

Does Cation Size Affect Occupancy and Electrostatic Screening of the Nucleic Acid Ion Atmosphere?

Electrostatics are central to all aspects of nucleic acid behavior, including their folding, condensation, and binding to other molecules, and the energetics of these processes are profoundly influenced by the ion atmosphere that surrounds nucleic acids. Given the highly complex and dynamic nature of the ion atmosphere, understanding its properties and effects will require synergy between computational modeling and experiment. Prior computational models and experiments suggest that cation occupancy in the ion atmosphere depends on the size of the cation. However, the computational models have not been independently tested, and the experimentally observed effects were small. Here, we evaluate a computational model of ion size effects by experimentally testing a blind prediction made from that model, and we present additional experimental results that extend our understanding of the ion atmosphere. Giambasu et al. developed and implemented a three-dimensional reference interaction site (3D-RISM) model for monovalent cations surrounding DNA and RNA helices, and this model predicts that Na(+) would outcompete Cs(+) by 1.8-2.1-fold; i.e., with Cs(+) in 2-fold excess of Na(+) the ion atmosphere would contain an equal number of each cation (Nucleic Acids Res. 2015, 43, 8405). However, our ion counting experiments indicate that there is no significant preference for Na(+) over Cs(+). There is an ∼25% preferential occupancy of Li(+) over larger cations in the ion atmosphere but, counter to general expectations from existing models, no size dependence for the other alkali metal ions. Further, we followed the folding of the P4-P6 RNA and showed that differences in folding with different alkali metal ions observed at high concentration arise from cation-anion interactions and not cation size effects. Overall, our results provide a critical test of a computational prediction, fundamental information about ion atmosphere properties, and parameters that will aid in the development of next-generation nucleic acid computational models.

Predicting Molecular Crowding Effects in Ion-RNA Interactions

We develop a new statistical mechanical model to predict the molecular crowding effects in ion-RNA interactions. By considering discrete distributions of the crowders, the model can treat the main crowder-induced effects, such as the competition with ions for RNA binding, changes of electrostatic interaction due to crowder-induced changes in the dielectric environment, and changes in the nonpolar hydration state of the crowder-RNA system. To enhance the computational efficiency, we sample the crowder distribution using a hybrid approach: For crowders in the close vicinity of RNA surface, we sample their discrete distributions; for crowders in the bulk solvent away from the RNA surface, we use a continuous mean-field distribution for the crowders. Moreover, using the tightly bound ion (TBI) model, we account for ion fluctuation and correlation effects in the calculation for ion-RNA interactions. Applications of the model to a variety of simple RNA structures such as RNA helices show a crowder-induced increase in free energy and decrease in ion binding. Such crowding effects tend to contribute to the destabilization of RNA structure. Further analysis indicates that these effects are associated with the crowder-ion competition in RNA binding and the effective decrease in the dielectric constant. This simple ion effect model may serve as a useful framework for modeling more realistic crowders with larger, more complex RNA structures.

Monte Carlo Tightly Bound Ion Model: Predicting Ion-Binding Properties of RNA with Ion Correlations and Fluctuations

Experiments have suggested that ion correlation and fluctuation effects can be potentially important for multivalent ions in RNA folding. However, most existing computational methods for the ion electrostatics in RNA folding tend to ignore these effects. The previously reported tightly bound ion (TBI) model can treat ion correlation and fluctuation but its applicability to biologically important RNAs is severely limited by the low computational efficiency. Here, on the basis of Monte Carlo sampling for the many-body ion distribution, we develop a new computational model, the Monte Carlo tightly bound ion (MCTBI) model, for ion-binding properties around an RNA. Because of an enhanced sampling algorithm for ion distribution, the model leads to a significant improvement in computational efficiency. For example, for a 160-nt RNA, the model causes a more than 10-fold increase in the computational efficiency, and the improvement in computational efficiency is more pronounced for larger systems. Furthermore, unlike the earlier model that describes ion distribution using the number of bound ions around each nucleotide, the current MCTBI model is based on the three-dimensional coordinates of the ions. The higher efficiency of the model allows us to treat the ion effects for medium to large RNA molecules, RNA-ligand complexes, and RNA-protein complexes. This new model together with proper RNA conformational sampling and the energetics model may serve as a starting point for further development for the ion effects in RNA folding and conformational changes and for large nucleic acid systems.

Applications of PLOR in labeling large RNAs at specific sites

Incorporation of modified or labeled nucleotides at specific sites in RNAs is critical for gaining insights into the structure and function of RNAs. Preparation of site-specifically labeled large RNAs in amounts suitable for structural or functional studies is extremely difficult using current methodologies. The position-selective labeling of RNA, PLOR, is a recently developed method that makes such syntheses possible. PLOR allows incorporation of various probes, including (2)D/(13)C/(15)N-isotopic labels, Cy3/Cy5/Alexa488/Alexa555 fluorescent dyes, biotin and other chemical groups, into specific positions in long RNAs. Here, we describe in detail the use of PLOR to label RNAs at specific segment(s) or discrete sites.

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.

Generalized Manning Condensation Model Captures the RNA Ion Atmosphere

RNA is highly sensitive to the ionic environment and typically requires Mg(2+) to form compact structures. There is a need for models capable of describing the ion atmosphere surrounding RNA with quantitative accuracy. We present a model of RNA electrostatics and apply it within coarse-grained molecular dynamics simulation. The model treats Mg(2+) ions explicitly to account for ion-ion correlations neglected by mean-field theories. Since mean-field theories capture KCl well, it is treated implicitly by a generalized Manning counterion condensation model. The model extends Manning condensation to deal with arbitrary RNA conformations, nonlimiting KCl concentrations, and the ion inaccessible volume of RNA. The model is tested against experimental measurements of the excess Mg(2+) associated with the RNA, Γ(2+), because Γ(2+) is directly related to the Mg(2+)-RNA interaction free energy. The excellent agreement with experiment demonstrates that the model captures the ionic dependence of the RNA free energy landscape.

Synthesis and applications of RNAs with position-selective labelling and mosaic composition

Knowledge of the structure and dynamics of RNA molecules is critical to understanding their many biological functions. Furthermore, synthetic RNAs have applications as therapeutics and molecular sensors. Both research and technological applications of RNA would be dramatically enhanced by methods that enable incorporation of modified or labelled nucleotides into specifically designated positions or regions of RNA. However, the synthesis of tens of milligrams of such RNAs using existing methods has been impossible. Here we develop a hybrid solid-liquid phase transcription method and automated robotic platform for the synthesis of RNAs with position-selective labelling. We demonstrate its use by successfully preparing various isotope- or fluorescently labelled versions of the 71-nucleotide aptamer domain of an adenine riboswitch for nuclear magnetic resonance spectroscopy or single-molecule Förster resonance energy transfer, respectively. Those RNAs include molecules that were selectively isotope-labelled in specific loops, linkers, a helix, several discrete positions, or a single internal position, as well as RNA molecules that were fluorescently labelled in and near kissing loops. These selectively labelled RNAs have the same fold as those transcribed using conventional methods, but they greatly simplify the interpretation of NMR spectra. The single-position isotope- and fluorescently labelled RNA samples reveal multiple conformational states of the adenine riboswitch. Lastly, we describe a robotic platform and the operation that automates this technology. Our selective labelling method may be useful for studying RNA structure and dynamics and for making RNA sensors for a variety of applications including cell-biological studies, substance detection, and disease diagnostics.

Kissing loop interaction in adenine riboswitch: insights from umbrella sampling simulations

INTRODUCTION

Riboswitches are cis-acting regulatory RNA elements prevalently located in the leader sequences of bacterial mRNA. An adenine sensing riboswitch cis-regulates adeninosine deaminase gene (add) in Vibrio vulnificus. The structural mechanism regulating its conformational changes upon ligand binding mostly remains to be elucidated. In this open framework it has been suggested that the ligand stabilizes the interaction of the distal "kissing loop" complex. Using accurate full-atom molecular dynamics with explicit solvent in combination with enhanced sampling techniques and advanced analysis methods it could be possible to provide a more detailed perspective on the formation of these tertiary contacts.

METHODS

In this work, we used umbrella sampling simulations to study the thermodynamics of the kissing loop complex in the presence and in the absence of the cognate ligand. We enforced the breaking/formation of the loop-loop interaction restraining the distance between the two loops. We also assessed the convergence of the results by using two alternative initialization protocols. A structural analysis was performed using a novel approach to analyze base contacts.

RESULTS

Contacts between the two loops were progressively lost when larger inter-loop distances were enforced. Inter-loop Watson-Crick contacts survived at larger separation when compared with non-canonical pairing and stacking interactions. Intra-loop stacking contacts remained formed upon loop undocking. Our simulations qualitatively indicated that the ligand could stabilize the kissing loop complex. We also compared with previously published simulation studies.

DISCUSSION AND CONCLUSIONS

Kissing complex stabilization given by the ligand was compatible with available experimental data. However, the dependence of its value on the initialization protocol of the umbrella sampling simulations posed some questions on the quantitative interpretation of the results and called for better converged enhanced sampling simulations.

Multiple conformational states of riboswitches fine-tune gene regulation

Riboswitches are structured regions of mRNAs that modulate gene expression in response to specific binding of low molecular-weight ligands. They function by induced transitions between different functional conformations. The standard model assumed that the two functional states, the ligand-bound and ligand-free state, populated only two stable conformations. Recent discoveries of multiple conformations for the apo-state and holo-state of riboswitches challenge this model. Moreover, it becomes evident that detected conformational heterogeneity--mostly in the apo-state--provides sensitivity to multiple environmental inputs for riboswitch-based gene-regulation.

The purine riboswitch as a model system for exploring RNA biology and chemistry

Over the past decade the purine riboswitch, and in particular its nucleobase-binding aptamer domain, has emerged as an important model system for exploring various aspects of RNA structure and function. Its relatively small size, structural simplicity and readily observable activity enable application of a wide variety of experimental approaches towards the study of this RNA. These analyses have yielded important insights into small molecule recognition, co-transcriptional folding and secondary structural switching, and conformational dynamics that serve as a paradigm for other RNAs. In this article, the current state of understanding of the purine riboswitch family and how this growing knowledge base is starting to be exploited in the creation of novel RNA devices are examined. This article is part of a Special Issue entitled: Riboswitches.

Dynamics of riboswitches: Molecular simulations

Riboswitch RNAs play key roles in bacterial metabolism and represent a promising new class of antibiotic targets for treatment of infectious disease. While many studies of riboswitches have been performed, the exact mechanism of riboswitch operation is still not fully understood at the atomistic level of detail. Molecular dynamics simulations are useful for interpreting existing experimental data and producing predictions for new experiments. Here, a wide range of computational studies on riboswitches is reviewed. By elucidating the key principles of riboswitch operation, computation may aid in the effort to design more specific antibiotics with affinities greater than those of the native ligand. Such a detailed understanding may be required to improve efficacy and reduce side effects. These studies are laying the groundwork for understanding the action mechanism of new compounds that inhibit riboswitch activity. Future directions such as magnesium effects, large-scale conformational changes, expression platforms and co-transcriptional folding are also discussed. This article is part of a Special Issue entitled: Riboswitches.

RNA self-assembly and RNA nanotechnology

CONSPECTUS: Nanotechnology's central goal involves the direct control of matter at the molecular nanometer scale to build nanofactories, nanomachines, and other devices for potential applications including electronics, alternative fuels, and medicine. In this regard, the nascent use of nucleic acids as a material to coordinate the precise arrangements of specific molecules marked an important milestone in the relatively recent history of nanotechnology. While DNA served as the pioneer building material in nucleic acid nanotechnology, RNA continues to emerge as viable alternative material with its own distinct advantages for nanoconstruction. Several complementary assembly strategies have been used to build a diverse set of RNA nanostructures having unique structural attributes and the ability to self-assemble in a highly programmable and controlled manner. Of the different strategies, the architectonics approach uniquely endeavors to understand integrated structural RNA architectures through the arrangement of their characteristic structural building blocks. Viewed through this lens, it becomes apparent that nature routinely uses thermodynamically stable, recurrent modular motifs from natural RNA molecules to generate unique and more complex programmable structures. With the design principles found in natural structures, a number of synthetic RNAs have been constructed. The synthetic nanostructures constructed to date have provided, in addition to affording essential insights into RNA design, important platforms to characterize and validate the structural self-folding and assembly properties of RNA modules or building blocks. Furthermore, RNA nanoparticles have shown great promise for applications in nanomedicine and RNA-based therapeutics. Nevertheless, the synthetic RNA architectures achieved thus far consist largely of static, rigid particles that are still far from matching the structural and functional complexity of natural responsive structural elements such as the ribosome, large ribozymes, and riboswitches. Thus, the next step in synthetic RNA design will involve new ways to implement these same types of dynamic and responsive architectures into nanostructures functioning as real nanomachines in and outside the cell. RNA nanotechnology will likely garner broader utility and influence with a greater focus on the interplay between thermodynamic and kinetic influences on RNA self-assembly and using natural RNAs as guiding principles.

Fluorescence tools to investigate riboswitch structural dynamics

Riboswitches are novel regulatory elements that respond to cellular metabolites to control gene expression. They are constituted of highly conserved domains that have evolved to recognize specific metabolites. Such domains, so-called aptamers, are folded into intricate structures to enable metabolite recognition. Over the years, the development of ensemble and single-molecule fluorescence techniques has allowed to probe most of the mechanistic aspects of aptamer folding and ligand binding. In this review, we summarize the current fluorescence toolkit available to study riboswitch structural dynamics. We fist describe those methods based on fluorescent nucleotide analogues, mostly 2-aminopurine (2AP), to investigate short-range conformational changes, including some key steady-state and time-resolved examples that exemplify the versatility of fluorescent analogues as structural probes. The study of long-range structural changes by Förster resonance energy transfer (FRET) is mostly discussed in the context of single-molecule studies, including some recent developments based on the combination of single-molecule FRET techniques with controlled chemical denaturation methods. This article is part of a Special Issue entitled: Riboswitches.

Reduced model captures Mg(2+)-RNA interaction free energy of riboswitches

The stability of RNA tertiary structures depends heavily on Mg(2+). The Mg(2+)-RNA interaction free energy that stabilizes an RNA structure can be computed experimentally through fluorescence-based assays that measure Γ2+, the number of excess Mg(2+) associated with an RNA molecule. Previous explicit-solvent simulations predict that the majority of excess Mg(2+) ions interact closely and strongly with the RNA, unlike monovalent ions such as K(+), suggesting that an explicit treatment of Mg(2+) is important for capturing RNA dynamics. Here we present a reduced model that accurately reproduces the thermodynamics of Mg(2+)-RNA interactions. This model is able to characterize long-timescale RNA dynamics coupled to Mg(2+) through the explicit representation of Mg(2+) ions. KCl is described by Debye-Hückel screening and a Manning condensation parameter, which represents condensed K(+) and models its competition with condensed Mg(2+). The model contains one fitted parameter, the number of condensed K(+) ions in the absence of Mg(2+). Values of Γ2+ computed from molecular dynamics simulations using the model show excellent agreement with both experimental data on the adenine riboswitch and previous explicit-solvent simulations of the SAM-I riboswitch. This agreement confirms the thermodynamic accuracy of the model via the direct relation of Γ2+ to the Mg(2+)-RNA interaction free energy, and provides further support for the predictions from explicit-solvent calculations. This reduced model will be useful for future studies of the interplay between Mg(2+) and RNA dynamics.

Insights into ligand binding to PreQ1 Riboswitch Aptamer from molecular dynamics simulations

Riboswitches play roles in transcriptional or translational regulation through specific ligand binding of their aptamer domains. Although a number of ligand-bound aptamer complex structures have been solved, it is important to know ligand-free conformations of the aptamers in order to understand the mechanism of specific binding by ligands. In this paper, preQ₁ riboswitch aptamer domain from Bacillus subtilis is studied by overall 1.5 μs all-atom molecular dynamics simulations We found that the ligand-free aptamer has a stable state with a folded P1-L3 and open binding pocket. The latter forms a cytosine-rich pool in which the nucleotide C19 oscillates between close and open positions, making it a potential conformation for preQ₁ entrance. The dynamic picture further suggests that the specific recognition of preQ₁ by the aptamer domain is not only facilitated by the key nucleotide C19 but also aided and enhanced by other cytosines around the binding pocket. These results should help to understand the details of preQ₁ binding.

The cellular environment stabilizes adenine riboswitch RNA structure

There are large differences between the intracellular environment and the conditions widely used to study RNA structure and function in vitro. To assess the effects of the crowded cellular environment on RNA, we examined the structure and ligand binding function of the adenine riboswitch aptamer domain in healthy, growing Escherichia coli cells at single-nucleotide resolution on the minute time scale using SHAPE (selective 2'-hydroxyl acylation analyzed by primer extension). The ligand-bound aptamer structure is essentially the same in cells and in buffer at 1 mM Mg(2+), the approximate Mg(2+) concentration we measured in cells. In contrast, the in-cell conformation of the ligand-free aptamer is much more similar to the fully folded ligand-bound state. Even adding high Mg(2+) concentrations to the buffer used for in vitro analyses did not yield the conformation observed for the free aptamer in cells. The cellular environment thus stabilizes the aptamer significantly more than does Mg(2+) alone. Our results show that the intracellular environment has a large effect on RNA structure that ultimately favors highly organized conformations.

Ligand-induced stabilization of the aptamer terminal helix in the add adenine riboswitch

Riboswitches are structured mRNA elements that modulate gene expression. They undergo conformational changes triggered by highly specific interactions with sensed metabolites. Among the structural rearrangements engaged by riboswitches, the forming and melting of the aptamer terminal helix, the so-called P1 stem, is essential for genetic control. The structural mechanisms by which this conformational change is modulated upon ligand binding mostly remain to be elucidated. Here, we used pulling molecular dynamics simulations to study the thermodynamics of the P1 stem in the add adenine riboswitch. The P1 ligand-dependent stabilization was quantified in terms of free energy and compared with thermodynamic data. This comparison suggests a model for the aptamer folding in which direct P1-ligand interactions play a minor role on the conformational switch when compared with those related to the ligand-induced aptamer preorganization.

Single-molecule chemical denaturation of riboswitches

To date, single-molecule RNA science has been developed almost exclusively around the effect of metal ions as folding promoters and stabilizers of the RNA structure. Here, we introduce a novel strategy that combines single-molecule Förster resonance energy transfer (FRET) and chemical denaturation to observe and manipulate RNA dynamics. We demonstrate that the competing interplay between metal ions and denaturant agents provides a platform to extract information that otherwise will remain hidden with current methods. Using the adenine-sensing riboswitch aptamer as a model, we provide strong evidence for a rate-limiting folding step of the aptamer domain being modulated through ligand binding, a feature that is important for regulation of the controlled gene. In the absence of ligand, the rate-determining step is dominated by the formation of long-range key tertiary contacts between peripheral stem-loop elements. In contrast, when the adenine ligand interacts with partially folded messenger RNAs, the aptamer requires specifically bound Mg²⁺ ions, as those observed in the crystal structure, to progress further towards the native form. Moreover, despite that the ligand-free and ligand-bound states are indistinguishable by FRET, their different stability against urea-induced denaturation allowed us to discriminate them, even when they coexist within a single FRET trajectory; a feature not accessible by existing methods.

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.

Biomolecular electrostatics and solvation: a computational perspective

An understanding of molecular interactions is essential for insight into biological systems at the molecular scale. Among the various components of molecular interactions, electrostatics are of special importance because of their long-range nature and their influence on polar or charged molecules, including water, aqueous ions, proteins, nucleic acids, carbohydrates, and membrane lipids. In particular, robust models of electrostatic interactions are essential for understanding the solvation properties of biomolecules and the effects of solvation upon biomolecular folding, binding, enzyme catalysis, and dynamics. Electrostatics, therefore, are of central importance to understanding biomolecular structure and modeling interactions within and among biological molecules. This review discusses the solvation of biomolecules with a computational biophysics view toward describing the phenomenon. While our main focus lies on the computational aspect of the models, we provide an overview of the basic elements of biomolecular solvation (e.g. solvent structure, polarization, ion binding, and non-polar behavior) in order to provide a background to understand the different types of solvation models.

Magnesium fluctuations modulate RNA dynamics in the SAM-I riboswitch

Experiments demonstrate that Mg(2+) is crucial for structure and function of RNA systems, yet the detailed molecular mechanism of Mg(2+) action on RNA is not well understood. We investigate the interplay between RNA and Mg(2+) at atomic resolution through ten 2-μs explicit solvent molecular dynamics simulations of the SAM-I riboswitch with varying ion concentrations. The structure, including three stemloops, is very stable on this time scale. Simulations reveal that outer-sphere coordinated Mg(2+) ions fluctuate on the same time scale as the RNA, and that their dynamics couple. Locally, Mg(2+) association affects RNA conformation through tertiary bridging interactions; globally, increasing Mg(2+) concentration slows RNA fluctuations. Outer-sphere Mg(2+) ions responsible for these effects account for 80% of Mg(2+) in our simulations. These ions are transiently bound to the RNA, maintaining interactions, but shuttled from site to site. Outer-sphere Mg(2+) are separated from the RNA by a single hydration shell, occupying a thin layer 3-5 Å from the RNA. Distribution functions reveal that outer-sphere Mg(2+) are positioned by electronegative atoms, hydration layers, and a preference for the major groove. Diffusion analysis suggests transient outer-sphere Mg(2+) dynamics are glassy. Since outer-sphere Mg(2+) ions account for most of the Mg(2+) in our simulations, these ions may change the paradigm of Mg(2+)-RNA interactions. Rather than a few inner-sphere ions anchoring the RNA structure surrounded by a continuum of diffuse ions, we observe a layer of outer-sphere coordinated Mg(2+) that is transiently bound but strongly coupled to the RNA.