Distinct contribution of electrostatics, initial conformational ensemble, and macromolecular stability in RNA folding

Optimized Magnesium Force Field Parameters for Biomolecular Simulations with Accurate Solvation, Ion-Binding, and Water-Exchange Properties

Magnesium ions play an essential role in many vital processes. To correctly describe their interactions in molecular dynamics simulations, an accurate parametrization is crucial. Despite the importance and considerable scientific effort, current force fields based on the commonly used 12-6 Lennard-Jones interaction potential fail to reproduce a variety of experimental solution properties. In particular, no parametrization exists so far that simultaneously reproduces the solvation free energy and the distance to the water oxygens in the first hydration shell. Moreover, current Mg2+ force fields significantly underestimate the rate of water exchange leading to unrealistically slow exchange kinetics. In order to make progress in the development of improved models, we systematically optimize the Mg2+ parameters in combination with the TIP3P water model in a much larger parameter space than previously done. The results show that a long-ranged interaction potential and modified Lorentz-Berthelot combination rules allow us to accurately reproduce multiple experimental properties including the solvation free energy, the distances to the oxygens of the first hydration shell, the hydration number, the activity coefficient derivative in MgCl2 solutions, the self-diffusion coefficient, and the binding affinity to the phosphate oxygen of RNA. Matching this broad range of thermodynamic properties, we present two sets of optimal parameters: MicroMg yields water exchange on the microsecond timescale in agreement with experiments. NanoMg yields water exchange on the nanosecond timescale facilitating the direct observation of ion-binding events. As shown for the example of the add A-riboswitch, the optimized parameters correctly reproduce the structure of specifically bound ions and permit the de novo prediction of Mg2+-binding sites in biomolecular simulations.

Genetic Variation in the Domain II, 3' Untranslated Region of Human and Mosquito Derived Dengue Virus Strains in Sri Lanka

Genetic variations in dengue virus (DENV) play a distinct role in epidemic emergence. The DENV 3′ UTR has become a recent interest in research. The objective of the study was to examine the genetic variation in the domain II, 3′ UTR region of human and mosquito-derived DENV. DENV-infected human sera were orally infected to laboratory reared Aedes aegypti mosquitoes. The domain II, 3′ UTR of each human- and mosquito-derived sample was amplified. The nucleotide sequence variation, phylogenetic and secondary structure analysis was carried out incorporating respective regions of so far recorded Sri Lankan and the reference genotype strains of the DENV3 and DENV1 serotypes. The human- and mosquito-derived domain II, 3′ UTR were identical in nucleotide sequences within the serotypes isolated, indicating the conserved nature of the region during host switch. The sequence analysis revealed distinct variations in study isolates compared to so far recorded Sri Lankan isolates. However, despite single nucleotide variations, the maintenance of structural integrity was evident in related strains within the serotypes in the secondary structure analysis. The phylogenetic analysis revealed distinct clade segregation of the study sequences from so far reported Sri Lankan isolates and illustrated the phylogenetic relations of the study sequences to the available global isolates of respective serotypes.

Assessing the Performance of the Nonbonded Mg2+ Models in a Two-Metal-Dependent Ribonuclease

Magnesium ions (Mg²⁺), abundant in living cells, are essential for biomolecular structure, dynamics, and function. The biological importance of Mg²⁺ has motivated continuous development and improvement of various Mg²⁺ models for molecular dynamics (MD) simulations during the last decades. There are four types of nonbonded Mg²⁺ models: the point charge models based on a 12-6 or 12-6-4 type Lennard-Jones (LJ) potential, and the multisite models based on a 12-6 or 12-6-4 LJ potential. Here, we systematically assessed the performance of these four types of nonbonded Mg²⁺ models (21 models in total) in terms of maintaining a challenging intermediate state configuration captured in the structure of a prototypical two-metal-ion RNase H complex with an RNA/DNA hybrid. Our data demonstrate that the 12-6-4 multisite models, which account for charge-induced dipole interactions, perform the best in reproducing all the unique coordination modes in this intermediate state and maintaining the correct carboxylate denticity. Our benchmark work provides a useful guideline for MD simulations and structural refinement of Mg²⁺-containing biomolecular systems.

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.

Visualizing the formation of an RNA folding intermediate through a fast highly modular secondary structure switch

Intermediates play important roles in RNA folding but can be difficult to characterize when short-lived or not significantly populated. By combining (15)N relaxation dispersion NMR with chemical probing, we visualized a fast (kex=k1+k-1≈423 s(-1)) secondary structural switch directed towards a low-populated (∼3%) partially folded intermediate in tertiary folding of the P5abc subdomain of the 'Tetrahymena' group I intron ribozyme. The secondary structure switch changes the base-pairing register across the P5c hairpin, creating a native-like structure, and occurs at rates of more than two orders of magnitude faster than tertiary folding. The switch occurs robustly in the absence of tertiary interactions, Mg(2+) or even when the hairpin is excised from the three-way junction. Fast, highly modular secondary structural switches may be quite common during RNA tertiary folding where they may help smoothen the folding landscape by allowing folding to proceed efficiently via additional pathways.

Force Field for Mg(2+), Mn(2+), Zn(2+), and Cd(2+) Ions That Have Balanced Interactions with Nucleic Acids

Divalent metal ions are of fundamental importance to the function and folding of nucleic acids. Divalent metal ion-nucleic acid interactions are complex in nature and include both territorial and site specific binding. Commonly employed nonbonded divalent ion models, however, are often parametrized against bulk ion properties and are subsequently utilized in biomolecular simulations without considering any data related to interactions at specific nucleic acid sites. Previously, we assessed the ability of 17 different nonbonded Mg(2+) ion models to reproduce different properties of Mg(2+) in aqueous solution including radial distribution functions, solvation free energies, water exchange rates, and translational diffusion coefficients. In the present work, we depart from the recently developed 12-6-4 potential models for divalent metal ions developed by Li and Merz and tune the pairwise parameters for Mg(2+), Mn(2+), Zn(2+), and Cd(2+) binding dimethyl phosphate, adenosine, and guanosine in order to reproduce experimental site specific binding free energies derived from potentiometric pH titration data. We further apply these parameters to investigate a metal ion migration previously proposed to occur during the catalytic reaction of the hammerhead ribozyme. The new parameters are shown to be accurate and balanced for nucleic acid binding in comparison with available experimental data and provide an important tool for molecular dynamics and free energy simulations of nucleic acids where these ions may exhibit different binding modes.

GARN: Sampling RNA 3D Structure Space with Game Theory and Knowledge-Based Scoring Strategies

Cellular processes involve large numbers of RNA molecules. The functions of these RNA molecules and their binding to molecular machines are highly dependent on their 3D structures. One of the key challenges in RNA structure prediction and modeling is predicting the spatial arrangement of the various structural elements of RNA. As RNA folding is generally hierarchical, methods involving coarse-grained models hold great promise for this purpose. We present here a novel coarse-grained method for sampling, based on game theory and knowledge-based potentials. This strategy, GARN (Game Algorithm for RNa sampling), is often much faster than previously described techniques and generates large sets of solutions closely resembling the native structure. GARN is thus a suitable starting point for the molecular modeling of large RNAs, particularly those with experimental constraints. GARN is available from: http://garn.lri.fr/.

Multiple conformations are a conserved and regulatory feature of the RB1 5' UTR

Folding to a well-defined conformation is essential for the function of structured ribonucleic acids (RNAs) like the ribosome and tRNA. Structured elements in the untranslated regions (UTRs) of specific messenger RNAs (mRNAs) are known to control expression. The importance of unstructured regions adopting multiple conformations, however, is still poorly understood. High-resolution SHAPE-directed Boltzmann suboptimal sampling of the Homo sapiens Retinoblastoma 1 (RB1) 5' UTR yields three distinct conformations compatible with the experimental data. Private single nucleotide variants (SNVs) identified in two patients with retinoblastoma each collapse the structural ensemble to a single but distinct well-defined conformation. The RB1 5' UTRs from Bos taurus (cow) and Trichechus manatus latirostris (manatee) are divergent in sequence from H. sapiens (human) yet maintain structural compatibility with high-probability base pairs. SHAPE chemical probing of the cow and manatee RB1 5' UTRs reveals that they also adopt multiple conformations. Luciferase reporter assays reveal that 5' UTR mutations alter RB1 expression. In a traditional model of disease, causative SNVs disrupt a key structural element in the RNA. For the subset of patients with heritable retinoblastoma-associated SNVs in the RB1 5' UTR, the absence of multiple structures is likely causative of the cancer. Our data therefore suggest that selective pressure will favor multiple conformations in eukaryotic UTRs to regulate expression.

Comparison of structural, thermodynamic, kinetic and mass transport properties of Mg(2+) ion models commonly used in biomolecular simulations

The prevalence of Mg(2+) ions in biology and their essential role in nucleic acid structure and function has motivated the development of various Mg(2+) ion models for use in molecular simulations. Currently, the most widely used models in biomolecular simulations represent a nonbonded metal ion as an ion-centered point charge surrounded by a nonelectrostatic pairwise potential that takes into account dispersion interactions and exchange effects that give rise to the ion's excluded volume. One strategy toward developing improved models for biomolecular simulations is to first identify a Mg(2+) model that is consistent with the simulation force fields that closely reproduces a range of properties in aqueous solution, and then, in a second step, balance the ion-water and ion-solute interactions by tuning parameters in a pairwise fashion where necessary. The present work addresses the first step in which we compare 17 different nonbonded single-site Mg(2+) ion models with respect to their ability to simultaneously reproduce structural, thermodynamic, kinetic and mass transport properties in aqueous solution. None of the models based on a 12-6 nonelectrostatic nonbonded potential was able to reproduce the experimental radial distribution function, solvation free energy, exchange barrier and diffusion constant. The models based on a 12-6-4 potential offered improvement, and one model in particular, in conjunction with the SPC/E water model, performed exceptionally well for all properties. The results reported here establish useful benchmark calculations for Mg(2+) ion models that provide insight into the origin of the behavior in aqueous solution, and may aid in the development of next-generation models that target specific binding sites in biomolecules.

Molecular crowding overcomes the destabilizing effects of mutations in a bacterial ribozyme

The native structure of the Azoarcus group I ribozyme is stabilized by the cooperative formation of tertiary interactions between double helical domains. Thus, even single mutations that break this network of tertiary interactions reduce ribozyme activity in physiological Mg(2+) concentrations. Here, we report that molecular crowding comparable to that in the cell compensates for destabilizing mutations in the Azoarcus ribozyme. Small angle X-ray scattering, native polyacrylamide gel electrophoresis and activity assays were used to compare folding free energies in dilute and crowded solutions containing 18% PEG1000. Crowder molecules allowed the wild-type and mutant ribozymes to fold at similarly low Mg(2+) concentrations and stabilized the active structure of the mutant ribozymes under physiological conditions. This compensation helps explains why ribozyme mutations are often less deleterious in the cell than in the test tube. Nevertheless, crowding did not rescue the high fraction of folded but less active structures formed by double and triple mutants. We conclude that crowding broadens the fitness landscape by stabilizing compact RNA structures without improving the specificity of self-assembly.

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.

Insights into RNA structure and function from genome-wide studies

A comprehensive understanding of RNA structure will provide fundamental insights into the cellular function of both coding and non-coding RNAs. Although many RNA structures have been analysed by traditional biophysical and biochemical methods, the low-throughput nature of these approaches has prevented investigation of the vast majority of cellular transcripts. Triggered by advances in sequencing technology, genome-wide approaches for probing the transcriptome are beginning to reveal how RNA structure affects each step of protein expression and RNA stability. In this Review, we discuss the emerging relationships between RNA structure and the regulation of gene expression.

Mapping the kinetic barriers of a Large RNA molecule's folding landscape

The folding of linear polymers into discrete three-dimensional structures is often required for biological function. The formation of long-lived intermediates is a hallmark of the folding of large RNA molecules due to the ruggedness of their energy landscapes. The precise thermodynamic nature of the barriers (whether enthalpic or entropic) that leads to intermediate formation is still poorly characterized in large structured RNA molecules. A classic approach to analyzing kinetic barriers are temperature dependent studies analyzed with Eyring's transition state theory. We applied Eyring's theory to time-resolved hydroxyl radical (•OH) footprinting kinetics progress curves collected at eight temperature from 21.5 °C to 51 °C to characterize the thermodynamic nature of folding intermediate formation for the Mg(2+)-mediated folding of the Tetrahymena thermophila group I ribozyme. A common kinetic model configuration describes this RNA folding reaction over the entire temperature range studied consisting of primary (fast) transitions to misfolded intermediates followed by much slower secondary transitions, consistent with previous studies. Eyring analysis reveals that the primary transitions are moderate in magnitude and primarily enthalpic in nature. In contrast, the secondary transitions are daunting in magnitude and entropic in nature. The entropic character of the secondary transitions is consistent with structural rearrangement of the intermediate species to the final folded form. This segregation of kinetic control reveals distinctly different molecular mechanisms during the two stages of RNA folding and documents the importance of entropic barriers to defining rugged RNA folding landscapes.

Exploring the electrostatic energy landscape for tetraloop-receptor docking

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.

Evolutionary evidence for alternative structure in RNA sequence co-variation

Sequence conservation and co-variation of base pairs are hallmarks of structured RNAs. For certain RNAs (e.g. riboswitches), a single sequence must adopt at least two alternative secondary structures to effectively regulate the message. If alternative secondary structures are important to the function of an RNA, we expect to observe evolutionary co-variation supporting multiple conformations. We set out to characterize the evolutionary co-variation supporting alternative conformations in riboswitches to determine the extent to which alternative secondary structures are conserved. We found strong co-variation support for the terminator, P1, and anti-terminator stems in the purine riboswitch by extending alignments to include terminator sequences. When we performed Boltzmann suboptimal sampling on purine riboswitch sequences with terminators we found that these sequences appear to have evolved to favor specific alternative conformations. We extended our analysis of co-variation to classic alignments of group I/II introns, tRNA, and other classes of riboswitches. In a majority of these RNAs, we found evolutionary evidence for alternative conformations that are compatible with the Boltzmann suboptimal ensemble. Our analyses suggest that alternative conformations are selected for and thus likely play functional roles in even the most structured of RNAs.

RNA (Ribonucleic Acid) is a messenger of genetic information, master regulator, and catalyst in the cell. To carry out its function, RNA can fold into complex three-dimensional structures. Certain classes of RNAs, called riboswitches, adopt at least two alternative structures to act as a switch. We set out to detect the evolutionary signal for alternative structures in riboswitches as we hypothesize that these RNA sequences must have evolved to allow both conformations. We find that indeed such signals exist when we compare the sequences of riboswitches from multiple species. When we extend this analysis to other RNA regulators in the cell that are not thought of as switches, we detect equivalent evolutionary support for alternative structures. Viewed through the lens of evolutionary structure conservation RNA sequences appear to have adapted to adopt multiple conformations.

The long-range P3 helix of the Tetrahymena ribozyme is disrupted during folding between the native and misfolded conformations

RNAs are prone to misfolding, but how misfolded structures are formed and resolved remains incompletely understood. The Tetrahymena group I intron ribozyme folds in vitro to a long-lived misfolded conformation (M) that includes extensive native structure but is proposed to differ in topology from the native state (N). A leading model predicts that exchange of the topologies requires unwinding of the long-range, core helix P3, despite the presence of P3 in both conformations. To test this model, we constructed 16 mutations to strengthen or weaken P3. Catalytic activity and in-line probing showed that nearly all of the mutants form the M state before folding to N. The P3-weakening mutations accelerated refolding from M (3- to 30-fold) and the P3-strengthening mutations slowed refolding (6- to 1400-fold), suggesting that P3 indeed unwinds transiently. Upon depletion of Mg(2+), the mutations had analogous effects on unfolding from N to intermediates that subsequently fold to M. The magnitudes for the P3-weakening mutations were larger than in refolding from M, and small-angle X-ray scattering showed that the ribozyme expands rapidly to intermediates from which P3 is disrupted subsequently. These results are consistent with previous results indicating unfolding of native peripheral structure during refolding from M, which probably permits rearrangement of the core. Together, our results demonstrate that exchange of the native and misfolded conformations requires loss of a core helix in addition to peripheral structure. Further, the results strongly suggest that misfolding arises from a topological error within the ribozyme core, and a specific topology is proposed.

Understanding the role of three-dimensional topology in determining the folding intermediates of group I introns

Many RNA molecules exert their biological function only after folding to unique three-dimensional structures. For long, noncoding RNA molecules, the complexity of finding the native topology can be a major impediment to correct folding to the biologically active structure. An RNA molecule may fold to a near-native structure but not be able to continue to the correct structure due to a topological barrier such as crossed strands or incorrectly stacked helices. Achieving the native conformation thus requires unfolding and refolding, resulting in a long-lived intermediate. We investigate the role of topology in the folding of two phylogenetically related catalytic group I introns, the Twort and Azoarcus group I ribozymes. The kinetic models describing the Mg(2+)-mediated folding of these ribozymes were previously determined by time-resolved hydroxyl (∙OH) radical footprinting. Two intermediates formed by parallel intermediates were resolved for each RNA. These data and analytical ultracentrifugation compaction analyses are used herein to constrain coarse-grained models of these folding intermediates as we investigate the role of nonnative topology in dictating the lifetime of the intermediates. Starting from an ensemble of unfolded conformations, we folded the RNA molecules by progressively adding native constraints to subdomains of the RNA defined by the ∙OH time-progress curves to simulate folding through the different kinetic pathways. We find that nonnative topologies (arrangement of helices) occur frequently in the folding simulations despite using only native constraints to drive the reaction, and that the initial conformation, rather than the folding pathway, is the major determinant of whether the RNA adopts nonnative topology during folding. From these analyses we conclude that biases in the initial conformation likely determine the relative flux through parallel RNA folding pathways.

DelPhi Web Server: A comprehensive online suite for electrostatic calculations of biological macromolecules and their complexes

Here we report a web server, the DelPhi web server, which utilizes DelPhi program to calculate electrostatic energies and the corresponding electrostatic potential and ionic distributions, and dielectric map. The server provides extra services to fix structural defects, as missing atoms in the structural file and allows for generation of missing hydrogen atoms. The hydrogen placement and the corresponding DelPhi calculations can be done with user selected force field parameters being either Charmm22, Amber98 or OPLS. Upon completion of the calculations, the user is given option to download fixed and protonated structural file, together with the parameter and Delphi output files for further analysis. Utilizing Jmol viewer, the user can see the corresponding structural file, to manipulate it and to change the presentation. In addition, if the potential map is requested to be calculated, the potential can be mapped onto the molecule surface. The DelPhi web server is available from http://compbio.clemson.edu/delphi_webserver.

Toward a molecular understanding of RNA remodeling by DEAD-box proteins

DEAD-box proteins are superfamily 2 helicases that function in all aspects of RNA metabolism. They employ ATP binding and hydrolysis to generate tight, yet regulated RNA binding, which is used to unwind short RNA helices non-processively and promote structural transitions of RNA and RNA-protein substrates. In the last few years, substantial progress has been made toward a detailed, quantitative understanding of the structural and biochemical properties of DEAD-box proteins. Concurrently, progress has been made toward a physical understanding of the RNA rearrangements and folding steps that are accelerated by DEAD-box proteins in model systems. Here, we review the recent progress on both of these fronts, focusing on the mitochondrial DEAD-box proteins Mss116 and CYT-19 and their mechanisms in promoting the splicing of group I and group II introns.

Evaluating our ability to predict the structural disruption of RNA by SNPs

The structure of RiboNucleic Acid (RNA) has the potential to be altered by a Single Nucleotide Polymorphism (SNP). Disease-associated SNPs mapping to non-coding regions of the genome that are transcribed into RiboNucleic Acid (RNA) can potentially affect cellular regulation (and cause disease) by altering the structure of the transcript. We performed a large-scale meta-analysis of Selective 2'-Hydroxyl Acylation analyzed by Primer Extension (SHAPE) data, which probes the structure of RNA. We found that several single point mutations exist that significantly disrupt RNA secondary structure in the five transcripts we analyzed. Thus, every RNA that is transcribed has the potential to be a “RiboSNitch;” where a SNP causes a large conformational change that alters regulatory function. Predicting the SNPs that will have the largest effect on RNA structure remains a contemporary computational challenge. We therefore benchmarked the most popular RNA structure prediction algorithms for their ability to identify mutations that maximally affect structure. We also evaluated metrics for rank ordering the extent of the structural change. Although no single algorithm/metric combination dramatically outperformed the others, small differences in AUC (Area Under the Curve) values reveal that certain approaches do provide better agreement with experiment. The experimental data we analyzed nonetheless show that multiple single point mutations exist in all RNA transcripts that significantly disrupt structure in agreement with the predictions.

DelPhi: a comprehensive suite for DelPhi software and associated resources

Background

Accurate modeling of electrostatic potential and corresponding energies becomes increasingly important for understanding properties of biological macromolecules and their complexes. However, this is not an easy task due to the irregular shape of biological entities and the presence of water and mobile ions.

Results

Here we report a comprehensive suite for the well-known Poisson-Boltzmann solver, DelPhi, enriched with additional features to facilitate DelPhi usage. The suite allows for easy download of both DelPhi executable files and source code along with a makefile for local installations. The users can obtain the DelPhi manual and parameter files required for the corresponding investigation. Non-experienced researchers can download examples containing all necessary data to carry out DelPhi runs on a set of selected examples illustrating various DelPhi features and demonstrating DelPhi’s accuracy against analytical solutions.

Conclusions

DelPhi suite offers not only the DelPhi executable and sources files, examples and parameter files, but also provides links to third party developed resources either utilizing DelPhi or providing plugins for DelPhi. In addition, the users and developers are offered a forum to share ideas, resolve issues, report bugs and seek help with respect to the DelPhi package. The resource is available free of charge for academic users from URL: http://compbio.clemson.edu/DelPhi.php.

Statistical mechanical modeling of RNA folding: from free energy landscape to tertiary structural prediction

In spite of the success of computational methods for predicting RNA secondary structure, the problem of predicting RNA tertiary structure folding remains. Low-resolution structural models show promise as they allow for rigorous statistical mechanical computation for the conformational entropies, free energies, and the coarse-grained structures of tertiary folds. Molecular dynamics refinement of coarse-grained structures leads to all-atom 3D structures. Modeling based on statistical mechanics principles also has the unique advantage of predicting the full free energy landscape, including local minima and the global free energy minimum. The energy landscapes combined with the 3D structures form the basis for quantitative predictions of RNA functions. In this chapter, we present an overview of statistical mechanical models for RNA folding and then focus on a recently developed RNA statistical mechanical model -- the Vfold model. The main emphasis is placed on the physics underpinning the models, the computational strategies, and the connections to RNA biology.

RNA catalysis as a probe for chaperone activity of DEAD-box helicases

DEAD-box proteins are vitally important to cellular processes and make up the largest class of helicases. Many DEAD-box proteins function as RNA chaperones by accelerating structural transitions of RNA, which can result in the resolution of misfolded conformers or conversion between functional structures. While the biological importance of chaperone proteins is clear, their mechanisms are incompletely understood. Here, we illustrate how the catalytic activity of certain RNAs can be used to measure RNA chaperone activity. By measuring the amount of substrate converted to product, the fraction of catalytically active molecules is measured over time, providing a quantitative measure of the formation or loss of native RNA. The assays are described with references to group I and group II introns and their ribozyme derivatives, and examples are included that illustrate potential complications and indicate how catalytic activity measurements can be combined with physical approaches to gain insights into the mechanisms of DEAD-box proteins as RNA chaperones.

The Azoarcus group I intron ribozyme misfolds and is accelerated for refolding by ATP-dependent RNA chaperone proteins

Structured RNAs traverse complex energy landscapes that include valleys representing misfolded intermediates. In Neurospora crassa and Saccharomyces cerevisiae, efficient splicing of mitochondrial group I and II introns requires the DEAD box proteins CYT-19 and Mss116p, respectively, which promote folding transitions and function as general RNA chaperones. To test the generality of RNA misfolding and the activities of DEAD box proteins in vitro, here we measure native folding of a small group I intron ribozyme from the bacterium Azoarcus by monitoring its catalytic activity. To develop this assay, we first measure cleavage of an oligonucleotide substrate by the prefolded ribozyme. Substrate cleavage is rate-limited by binding and is readily reversible, with an internal equilibrium near unity, such that the amount of product observed is less than the amount of native ribozyme. We use this assay to show that approximately half of the ribozyme folds readily to the native state, whereas the other half forms an intermediate that transitions slowly to the native state. This folding transition is accelerated by urea and increased temperature and slowed by increased Mg(2+) concentration, suggesting that the intermediate is misfolded and must undergo transient unfolding during refolding to the native state. CYT-19 and Mss116p accelerate refolding in an ATP-dependent manner, presumably by disrupting structure in the intermediate. These results highlight the tendency of RNAs to misfold, underscore the roles of CYT-19 and Mss116p as general RNA chaperones, and identify a refolding transition for further dissection of the roles of DEAD box proteins in RNA folding.

RNA molecules with conserved catalytic cores but variable peripheries fold along unique energetically optimized pathways

Functional and kinetic constraints must be efficiently balanced during the folding process of all biopolymers. To understand how homologous RNA molecules with different global architectures fold into a common core structure we determined, under identical conditions, the folding mechanisms of three phylogenetically divergent group I intron ribozymes. These ribozymes share a conserved functional core defined by topologically equivalent tertiary motifs but differ in their primary sequence, size, and structural complexity. Time-resolved hydroxyl radical probing of the backbone solvent accessible surface and catalytic activity measurements integrated with structural-kinetic modeling reveal that each ribozyme adopts a unique strategy to attain the conserved functional fold. The folding rates are not dictated by the size or the overall structural complexity, but rather by the strength of the constituent tertiary motifs which, in turn, govern the structure, stability, and lifetime of the folding intermediates. A fundamental general principle of RNA folding emerges from this study: The dominant folding flux always proceeds through an optimally structured kinetic intermediate that has sufficient stability to act as a nucleating scaffold while retaining enough conformational freedom to avoid kinetic trapping. Our results also suggest a potential role of naturally selected peripheral A-minor interactions in balancing RNA structural stability with folding efficiency.

Sharing and archiving nucleic acid structure mapping data

Nucleic acids are particularly amenable to structural characterization using chemical and enzymatic probes. Each individual structure mapping experiment reveals specific information about the structure and/or dynamics of the nucleic acid. Currently, there is no simple approach for making these data publically available in a standardized format. We therefore developed a standard for reporting the results of single nucleotide resolution nucleic acid structure mapping experiments, or SNRNASMs. We propose a schema for sharing nucleic acid chemical probing data that uses generic public servers for storing, retrieving, and searching the data. We have also developed a consistent nomenclature (ontology) within the Ontology of Biomedical Investigations (OBI), which provides unique identifiers (termed persistent URLs, or PURLs) for classifying the data. Links to standardized data sets shared using our proposed format along with a tutorial and links to templates can be found at http://snrnasm.bio.unc.edu.

Importance of diffuse metal ion binding to RNA

RNAs are highly charged polyanionic molecules. RNA structure and function are strongly correlated with the ionic condition of the solution. The primary focus of this article is on the role of diffusive ions in RNA folding. Due to the long-range nature of electrostatic interactions, the diffuse ions can contribute significantly to RNA structural stability and folding kinetics. We present an overview of the experimental findings as well as the theoretical developments on the diffuse ion effects in RNA folding. This review places heavy emphasis on the effect of magnesium ions. Magnesium ions play a highly efficient role in stabilizing RNA tertiary structures and promoting tertiary structural folding. The highly efficient role goes beyond the mean-field effect such as the ionic strength. In addition to the effects of specific ion binding and ion dehydration, ion-ion correlation for the diffuse ions can contribute to the efficient role of the multivalent ions such as the magnesium ions in RNA folding.

Roles of DEAD-box proteins in RNA and RNP Folding

RNAs and RNA-protein complexes (RNPs) traverse rugged energy landscapes as they fold to their native structures, and many continue to undergo conformational rearrangements as they function. Due to the inherent stability of local RNA structure, proteins are required to assist with RNA conformational transitions during initial folding and in exchange between functional structures. DEAD-box proteins are superfamily 2 RNA helicases that are ubiquitously involved in RNA-mediated processes. Some of these proteins use an ATP-dependent cycle of conformational changes to disrupt RNA structure nonprocessively, accelerating structural transitions of RNAs and RNPs in a manner that bears a strong resemblance to the activities of certain groups of protein chaperones. This review summarizes recent work using model substrates and tractable self-splicing intron RNAs, which has given new insights into how DEAD-box proteins promote RNA folding steps and conformational transitions, and it summarizes recent progress in identifying sites and mechanisms of DEAD-box protein activity within more complex cellular targets.

Taming free energy landscapes with RNA chaperones

Many non-coding RNAs fold into complex three-dimensional structures, yet the self-assembly of RNA structure is hampered by mispairing, weak tertiary interactions, electrostatic barriers, and the frequent requirement that the 5' and 3' ends of the transcript interact. This rugged free energy landscape for RNA folding means that some RNA molecules in a population rapidly form their native structure, while many others become kinetically trapped in misfolded conformations. Transient binding of RNA chaperone proteins destabilize misfolded intermediates and lower the transition states between conformations, producing a smoother landscape that increases the rate of folding and the probability that a molecule will find the native structure. DEAD-box proteins couple the chemical potential of ATP hydrolysis with repetitive cycles of RNA binding and release, expanding the range of conditions under which they can refold RNA structures.

Multiple unfolding events during native folding of the Tetrahymena group I ribozyme

Despite the ubiquitous nature of misfolded intermediates in RNA folding, little is known about their physical properties or the folding transitions that allow them to continue folding productively. Folding of the Tetrahymena group I ribozyme includes sequential accumulation of two intermediates, termed I(trap) and misfolded (M). Here, we probe the structure and folding transition of I(trap) and compare them to those of M. Hydroxyl radical and dimethyl sulfate footprinting show that both I(trap) and M are extensively structured and crudely resemble the native RNA. However, regions of the core P3-P8 domain are more exposed to solvent in I(trap) than in M. I(trap) rearranges to continue folding nearly 1000-fold faster than M, and urea accelerates folding of I(trap) much less than M. Thus, the rate-limiting transition from I(trap) requires a smaller increase in exposed surface. Mutations that disrupt peripheral tertiary contacts give large and nearly uniform increases in re-folding of M, whereas the same mutations give at most modest increases in folding from I(trap). Intriguingly, mutations within the peripheral element P5abc give 5- to 10-fold accelerations in escape from I(trap), whereas ablation of P13, which lies on the opposite surface in the native structure, near the P3-P8 domain, has no effect. Thus, the unfolding required from I(trap) appears to be local, whereas the unfolding of M appears to be global. Further, the modest effects from several mutations suggest that there are multiple pathways for escape from I(trap) and that escape is aided by loosening nearby native structural constraints, presumably to facilitate local movements of nucleotides or segments that have not formed native contacts. Overall, these and prior results suggest a model in which the global architecture and peripheral interactions of the RNA are achieved relatively early in folding. Multiple folding and re-folding events occur on the predominant pathway to the native state, with increasing native core interactions and cooperativity as folding progresses.

Compact intermediates in RNA folding

Large noncoding RNAs fold into their biologically functional structures via compact yet disordered intermediates, which couple the stable secondary structure of the RNA with the emerging tertiary fold. The specificity of the collapse transition, which coincides with the assembly of helical domains, depends on RNA sequence and counterions. It determines the specificity of the folding pathways and the magnitude of the free energy barriers to the ensuing search for the native conformation. By coupling helix assembly with nascent tertiary interactions, compact folding intermediates in RNA also play a crucial role in ligand binding and RNA-protein recognition.

Advances in RNA structure analysis by chemical probing

RNA is arguably the most versatile biological macromolecule because of its ability both to encode and to manipulate genetic information. The diverse roles of RNA depend on its ability to fold back on itself to form biologically functional structures that bind small molecule and large protein ligands, to change conformation, and to affect the cellular regulatory state. These features of RNA biology can be structurally interrogated using chemical mapping experiments. The usefulness and applications of RNA chemical probing technologies have expanded dramatically over the past five years because of several critical advances. These innovations include new sequence-independent RNA chemistries, algorithmic tools for high-throughput analysis of complex data sets composed of thousands of measurements, new approaches for interpreting chemical probing data for both secondary and tertiary structure prediction, facile methods for following time-dependent processes, and the willingness of individual research groups to tackle increasingly bold problems in RNA structural biology.

Evaluation of the information content of RNA structure mapping data for secondary structure prediction

Structure mapping experiments (using probes such as dimethyl sulfate [DMS], kethoxal, and T1 and V1 RNases) are used to determine the secondary structures of RNA molecules. The process is iterative, combining the results of several probes with constrained minimum free-energy calculations to produce a model of the structure. We aim to evaluate whether particular probes provide more structural information, and specifically, how noise in the data affects the predictions. Our approach involves generating "decoy" RNA structures (using the sFold Boltzmann sampling procedure) and evaluating whether we are able to identify the correct structure from this ensemble of structures. We show that with perfect information, we are always able to identify the optimal structure for five RNAs of known structure. We then collected orthogonal structure mapping data (DMS and RNase T1 digest) under several solution conditions using our high-throughput capillary automated footprinting analysis (CAFA) technique on two group I introns of known structure. Analysis of these data reveals the error rates in the data under optimal (low salt) and suboptimal solution conditions (high MgCl(2)). We show that despite these errors, our computational approach is less sensitive to experimental noise than traditional constraint-based structure prediction algorithms. Finally, we propose a novel approach for visualizing the interaction of chemical and enzymatic mapping data with RNA structure. We project the data onto the first two dimensions of a multidimensional scaling of the sFold-generated decoy structures. We are able to directly visualize the structural information content of structure mapping data and reconcile multiple data sets.

Using analytical ultracentrifugation (AUC) to measure global conformational changes accompanying equilibrium tertiary folding of RNA molecules

Analytical ultracentrifugation (AUC) is a powerful technique to determine the global conformational changes in RNA molecules mediated by cations or small molecule ligands. Although most of the developments in the field of AUC have been centered on studies involving protein molecules, the experimental methods as well as the analytical approaches have been successfully adapted and applied to the study of a variety of RNA molecules ranging from small riboswitches to large ribozymes. Most often AUC studies are performed in conjunction with other structural probing techniques that provide complementary information on local changes in the solvent accessibilities at specific regions within RNA molecules. This chapter provides a brief theoretical background, working knowledge of instrumentation, practical considerations for experimental setup, and guidelines for data analysis procedures to enable the design, execution, and interpretation of sedimentation velocity experiments that detect changes in the global dimensions of an RNA molecule during its equilibrium folding.

Rapid quantification and analysis of kinetic •OH radical footprinting data using SAFA

The use of highly reactive chemical species to probe the structure and dynamics of nucleic acids is greatly simplified by software that enables rapid quantification of the gel images that result from these experiments. Semiautomated footprinting analysis (SAFA) allows a user to quickly and reproducibly quantify a chemical footprinting gel image through a series of steps that rectify, assign, and integrate the relative band intensities. The output of this procedure is raw band intensities that report on the relative reactivity of each nucleotide with the chemical probe. We describe here how to obtain these raw band intensities using SAFA and the subsequent normalization and analysis procedures required to process these data. In particular, we focus on analyzing time-resolved hydroxyl radical ((•)OH) data, which we use to monitor the kinetics of folding of a large RNA (the L-21 T. thermophila group I intron). Exposing the RNA to bursts of (•)OH radicals at specific time points during the folding process monitors the time progress of the reaction. Specifically, we identify protected (nucleotides that become inaccessible to the (•)OH radical probe when folded) and invariant (nucleotides with constant accessibility to the (•)OH probe) residues that we use for monitoring and normalization of the data. With this analysis, we obtain time-progress curves from which we determine kinetic rates of folding. We also report on a data visualization tool implemented in SAFA that allows users to map data onto a secondary structure diagram.

Hydroxyl-radical footprinting to probe equilibrium changes in RNA tertiary structure

Hydroxyl-radical footprinting utilizes the ability of a highly reactive species to nonspecifically cleave the solvent accessible regions of a nucleic acid backbone. Thus, changes in a nucleic acids structure can be probed either as a function of time or of a reagent's concentration. When combined with techniques that allow single nucleotide resolution of the resulting fragments, footprinting experiments provide richly detailed information about local changes in tertiary structure of a nucleic acid accompanying its folding or ligand binding. In this chapter, we present two protocols of equilibrium hydroxyl-radical footprinting based on peroxidative and oxidative Fenton chemistry and discuss how to adjust the Fenton reagent concentrations for a specific experimental condition. We also discuss the choice of the techniques to separate the reaction products and specifics of the data analysis for equilibrium footprinting experiments. Protocols addressing the use of peroxidative Fenton chemistry for time-resolved studies have been published [Schlatterer and Brenowitz, 2009. Methods; Shcherbakova and Brenowitz, 2008. Nat. Protoc.3(2), 288-302; Shcherbakova et al., 2006. Nucleic Acids Res.34(6), e48; Shcherbakova et al., 2007. Methods Cell Biol.84, 589-615].

Complementing global measures of RNA folding with local reports of backbone solvent accessibility by time resolved hydroxyl radical footprinting

A variety of analytical techniques are used to probe the mechanisms by which RNA molecules fold to discrete three dimensional structures. Methods such as small angle X-ray scattering (SAXS) report global properties like overall size and shape of the RNA. Other methods such as chemical or enzymatic mapping (footprinting) report properties with resolution as fine as single nucleotide. The hydroxyl radical (*OH) is a footprinting probe which cleaves the oligonucleotide backbone independently of sequence and thus is a valuable reporter of backbone solvent accessibility. Combinations of global and local measures of folding reactions are uniquely able to distinguish specific from nonspecific processes. This article highlights the application of *OH footprinting as a complement to SAXS for kinetics analysis of RNA folding. We illustrate this combination of techniques using a study of the role played by the stiffness of a hinge in determining the rate limiting step of a Mg(2+)-mediated RNA folding reaction.

A complex assembly landscape for the 30S ribosomal subunit

The ribosome is a complex macromolecular machine responsible for protein synthesis in the cell. It consists of two subunits, each of which contains both RNA and protein components. Ribosome assembly is subject to intricate regulatory control and is aided by a multitude of assembly factors in vivo, but can also be carried out in vitro. The details of the assembly process remain unknown even in the face of atomic structures of the entire ribosome and after more than three decades of research. Some of the earliest research on ribosome assembly produced the Nomura assembly map of the small subunit, revealing a hierarchy of protein binding dependencies for the 20 proteins involved and suggesting the possibility of a single intermediate. Recent work using a combination of RNA footprinting and pulse-chase quantitative mass spectrometry paints a picture of small subunit assembly as a dynamic and varied landscape, with sequential and hierarchical RNA folding and protein binding events finally converging on complete subunits. Proteins generally lock tightly into place in a 5' to 3' direction along the ribosomal RNA, stabilizing transient RNA conformations, while RNA folding and the early stages of protein binding are initiated from multiple locations along the length of the RNA.

Exhaustive Enumeration of Kinetic Model Topologies for the Analysis of Time-Resolved RNA Folding

Unlike protein folding, the process by which a large RNA molecule adopts a functionally active conformation remains poorly understood. Chemical mapping techniques, such as Hydroxyl Radical (·OH) footprinting report on local structural changes in an RNA as it folds with single nucleotide resolution. The analysis and interpretation of this kinetic data requires the identification and subsequent optimization of a kinetic model and its parameters. We detail our approach to this problem, specifically focusing on a novel strategy to overcome a factorial explosion in the number of possible models that need to be tested to identify the best fitting model. Previously, smaller systems (less than three intermediates) were computationally tractable using a distributed computing approach. However, for larger systems with three or more intermediates, the problem became computationally intractable. With our new enumeration strategy, we are able to significantly reduce the number of models that need to be tested using non-linear least squares optimization, allowing us to study systems with up to five intermediates. Furthermore, two intermediate systems can now be analyzed on a desktop computer, which eliminates the need for a distributed computing solution for most medium-sized data sets. Our new approach also allows us to study potential degeneracy in kinetic model selection, elucidating the limits of the method when working with large systems. This work establishes clear criteria for determining if experimental ·OH data is sufficient to determine the underlying kinetic model, or if other experimental modalities are required to resolve any degeneracy.

Energy barriers, pathways, and dynamics during folding of large, multidomain RNAs

Large, multidomain RNA molecules are generally thought to fold following multiple pathways down rugged landscapes populated with intermediates and traps. A challenge to understanding RNA folding reactions is the complex relationships that exist between the structure of the RNA and its folding landscape. The identification of intermediate species that populate folding landscapes and characterization of elements of their structures are the key components to solving the RNA folding problem. This review explores recent studies that characterize the dominant pathways by which RNA folds, structural and dynamic features of intermediates that populate the folding landscape, and the energy barriers that separate the distinct steps of the folding process.

Monitoring structural changes in nucleic acids with single residue spatial and millisecond time resolution by quantitative hydroxyl radical footprinting

Hydroxyl radical (.OH) footprinting provides comprehensive site-specific quantitative information about the structural changes associated with macromolecular folding, interactions and ligand binding. 'Fast Fenton' footprinting is a laboratory-based method for time-resolved .OH footprinting capable of millisecond time resolution readily applicable to DNA and RNA. This protocol utilizes inexpensive chemical reagents (H2O2, Fe(NH4)2(SO4)2, EDTA, thiourea or ethanol) and widely available quench-flow mixers to reveal transient, often short-lived, intermediate states of complex biochemical processes. We describe a protocol developed to study RNA folding that can be readily tailored to particular applications. Once familiar with quench-flow mixer operation and its calibration, nucleic acid labeling and the conduct of a dose-response experiment, a single kinetic experiment of 30 time points takes about 1 h to perform. Sample processing and separation of the .OH reaction products takes several hours. Data analysis can take 45 min to several weeks depending on the depth of analysis conducted.

Unwinding RNA's secrets: advances in the biology, physics, and modeling of complex RNAs

The rapid development of our understanding of the diverse biological roles fulfilled by non-coding RNA has motivated interest in the basic macromolecular behavior, structure, and function of RNA. We focus on two areas in the behavior of complex RNAs. First, we present advances in the understanding of how RNA folding is accomplished in vivo by presenting a mechanism for the action of DEAD-box proteins. Members of this family are intimately associated with almost all cellular processes involving RNA, mediating RNA structural rearrangements and chaperoning their folding. Next, we focus on advances in understanding, and characterizing the basic biophysical forces that govern the folding of complex RNAs. Ultimately we expect that a confluence and synergy between these approaches will lead to profound understanding of RNA and its biology.

High-throughput single-nucleotide structural mapping by capillary automated footprinting analysis

The use of capillary electrophoresis with fluorescently labeled nucleic acids revolutionized DNA sequencing, effectively fueling the genomic revolution. We present an application of this technology for the high-throughput structural analysis of nucleic acids by chemical and enzymatic mapping ('footprinting'). We achieve the throughput and data quality necessary for genomic-scale structural analysis by combining fluorophore labeling of nucleic acids with novel quantitation algorithms. We implemented these algorithms in the CAFA (capillary automated footprinting analysis) open-source software that is downloadable gratis from https://simtk.org/home/cafa. The accuracy, throughput and reproducibility of CAFA analysis are demonstrated using hydroxyl radical footprinting of RNA. The versatility of CAFA is illustrated by dimethyl sulfate mapping of RNA secondary structure and DNase I mapping of a protein binding to a specific sequence of DNA. Our experimental and computational approach facilitates the acquisition of high-throughput chemical probing data for solution structural analysis of nucleic acids.

Semiautomated and rapid quantification of nucleic acid footprinting and structure mapping experiments

We have developed protocols for rapidly quantifying the band intensities from nucleic acid chemical mapping gels at single-nucleotide resolution. These protocols are implemented in the software SAFA (semi-automated footprinting analysis) that can be downloaded without charge from http://safa.stanford.edu. The protocols implemented in SAFA have five steps: (i) lane identification, (ii) gel rectification, (iii) band assignment, (iv) model fitting and (v) band-intensity normalization. SAFA enables the rapid quantitation of gel images containing thousands of discrete bands, thereby eliminating a bottleneck to the analysis of chemical mapping experiments. An experienced user of the software can quantify a gel image in approximately 20 min. Although SAFA was developed to analyze hydroxyl radical (*OH) footprints, it effectively quantifies the gel images obtained with other types of chemical mapping probes. We also present a series of tutorial movies that illustrate the best practices and different steps in the SAFA analysis as a supplement to this protocol.

Informatics challenges in structured RNA

The world of regulatory RNAs is fast expanding into mainstream molecular biology as both a subject of intense mechanistic study and as a tool for functional characterization. The RNA world is one of complex structures that carry out catalysis, sense metabolites and synthesize proteins. The dynamic and structural nature of RNAs presents a whole new set of informatics challenges to the computational community. The ability to relate structure and dynamics to function will be key to understanding this complex world. I review several important classes of structured RNAs that present our community with a series of biologically novel informatics challenges. I also review available informatics tools that have been recently developed in the field.