Stability and cooperativity of individual tertiary contacts in RNA revealed through chemical denaturation

For proteins, understanding tertiary interactions involved in local versus global unfolding has become increasingly important for understanding the nature of the native state ensemble, the mechanisms of unfolding, and the stability of both the native and intermediate states in folding. In this work we have addressed related questions with respect to RNA structure by combining chemical denaturation and hydroxyl radical footprinting methods. We have determined unfolding isotherms for each of 26 discrete sites of protection located throughout the Tetrahymena thermophila group I ribozyme. The cooperativity of folding, m-value, and the free energy, DeltaG degrees N-U, associated with formation of each tertiary contact was determined by analysis of the isotherms. The DeltaG degrees N-U values measured in this study vary from 1.7 +/- 0.2 to 7. 6 +/- 1.2 kcal mol-1. Thus, the stability of these discrete tertiary contacts vary by almost 104. In addition, an intradomain contact and three interdomain contacts show high cooperativity (m-values of 1.1 +/- 0.2 to 1.7 +/- 0.3 kcal mol-1 M-1) indicating that these contacts exhibit global cooperatively in their folding behavior. This new approach to examining RNA stability provides an exciting comparison to our understanding of protein structure and folding mechanisms.     

Secondary structure prediction of interacting RNA molecules

Computational tools for prediction of the secondary structure of two or more interacting nucleic acid molecules are useful for understanding mechanisms for ribozyme function, determining the affinity of an oligonucleotide primer to its target, and designing good antisense oligonucleotides, novel ribozymes, DNA code words, or nanostructures. Here, we introduce new algorithms for prediction of the minimum free energy pseudoknot-free secondary structure of two or more nucleic acid molecules, and for prediction of alternative low-energy (sub-optimal) secondary structures for two nucleic acid molecules. We provide a comprehensive analysis of our predictions against secondary structures of interacting RNA molecules drawn from the literature. Analysis of our tools on 17 sequences of up to 200 nucleotides that do not form pseudoknots shows that they have 79% accuracy, on average, for the minimum free energy predictions. When the best of 100 sub-optimal foldings is taken, the average accuracy increases to 91%. The accuracy decreases as the sequences increase in length and as the number of pseudoknots and tertiary interactions increases. Our algorithms extend the free energy minimization algorithm of Zuker and Stiegler for secondary structure prediction, and the sub-optimal folding algorithm by Wuchty et al. Implementations of our algorithms are freely available in the package MultiRNAFold.     

Salt contribution to RNA tertiary structure folding stability

Accurate quantification of the ionic contribution to RNA folding stability could greatly enhance our ability to understand and predict RNA functions. Recently, motivated by the potential importance of ion correlation and fluctuation in RNA folding, we developed the tightly bound ion (TBI) model. Extensive experimental tests showed that the TBI model can lead to better treatment of multivalent ions than the Poisson-Boltzmann equation. In this study, we use the model to quantify the contribution of salt (Na⁺ and Mg²⁺) to the RNA tertiary structure folding free energy. Folding of the RNA tertiary structure often involves intermediates. We focus on the folding transition from an intermediate state to the native state, and compute the electrostatic folding free energy of the RNA. Based on systematic calculations for a variety of RNA molecules, we derive a set of formulas for the electrostatic free energy for tertiary structural folding as a function of the sequence length and compactness of the RNA and the Na⁺ and Mg²⁺ concentrations. Extensive comparisons with experimental data suggest that our model and the extracted empirical formulas are quite reliable.     

Modeling nucleic acids

Nucleic acids are an important class of biological macromolecules that carry out a variety of cellular roles. For many functions, naturally occurring DNA and RNA molecules need to fold into precise three-dimensional structures. Due to their self-assembling characteristics, nucleic acids have also been widely studied in the field of nanotechnology, and a diverse range of intricate three-dimensional nanostructures have been designed and synthesized. Different physical terms such as base-pairing and stacking interactions, tertiary contacts, electrostatic interactions and entropy all affect nucleic acid folding and structure. Here we review general computational approaches developed to model nucleic acid systems. We focus on four key areas of nucleic acid modeling: molecular representation, potential energy function, degrees of freedom and sampling algorithm. Appropriate choices in each of these key areas in nucleic acid modeling can effectively combine to aid interpretation of experimental data and facilitate prediction of nucleic acid structure.     

Interaction with capsid protein alters RNA structure and the pathway for in vitro assembly of cowpea chlorotic mottle virus

Viruses use sophisticated mechanisms to allow the specific packaging of their genome over that of host nucleic acids. We examined the in vitro assembly of the Cowpea chlorotic mottle virus (CCMV) and observed that assembly with viral RNA follows two different mechanisms. Initially, CCMV capsid protein (CP) dimers bind RNA with low cooperativity and form virus-like particles of 90 CP dimers and one copy of RNA. Longer incubation reveals a different assembly path. At a stoichiometry of about ten CP dimers per RNA, the CP slowly folds the RNA into a compact structure that can be bound with high cooperativity by additional CP dimers. This folding process is exclusively a function of CP quaternary structure and is independent of RNA sequence. CP-induced folding is distinct from RNA folding that depends on base-pairing to stabilize tertiary structure. We hypothesize that specific encapsidation of viral RNA is a three-step process: specific binding by a few copies of CP, RNA folding, and then cooperative binding of CP to the "labeled" nucleoprotein complex. This mechanism, observed in a plant virus, may be applicable to other viruses that do not halt synthesis of host nucleic acid, including HIV.     

Comparison of crystal structure interactions and thermodynamics for stabilizing mutations in the Tetrahymena ribozyme

Although general mechanisms of RNA folding and catalysis have been elucidated, little is known about how ribozymes achieve structural stability at high temperature. A previous in vitro evolution experiment identified a small number of mutations that significantly increase the thermostability of the tertiary structure of the Tetrahymena ribozyme. Because we also determined the crystal structure of this thermostable ribozyme, we have for the first time the opportunity to compare the structural interactions and thermodynamic contributions of individual nucleotides in a ribozyme. We investigated the contribution of five mutations to thermostability by using temperature gradient gel electrophoresis. Unlike the case with several well-studied proteins, the effects of individual mutations on thermostability of this RNA were highly context dependent. The three most important mutations for thermostability were actually destabilizing in the wild-type background. A269G and A304G contributed to stability only when present as a pair, consistent with their proximity in the ribozyme structure. In an evolutionary context, this work supports and extends the idea that one advantage of protein enzyme systems over an RNA world is the ability of proteins to accumulate stabilizing single-site mutations, whereas RNA may often require much rarer double mutations to improve the stability of both its tertiary and secondary structures.     

Molecular crowders and cosolutes promote folding cooperativity of RNA under physiological ionic conditions

Folding mechanisms of functional RNAs under idealized in vitro conditions of dilute solution and high ionic strength have been well studied. Comparatively little is known, however, about mechanisms for folding of RNA in vivo where Mg²⁺ ion concentrations are low, K⁺ concentrations are modest, and concentrations of macromolecular crowders and low-molecular-weight cosolutes are high. Herein, we apply a combination of biophysical and structure mapping techniques to tRNA to elucidate thermodynamic and functional principles that govern RNA folding under in vivo–like conditions. We show by thermal denaturation and SHAPE studies that tRNA folding cooperativity increases in physiologically low concentrations of Mg²⁺ (0.5–2 mM) and K⁺ (140 mM) if the solution is supplemented with physiological amounts (∼20%) of a water-soluble neutral macromolecular crowding agent such as PEG or dextran. Low-molecular-weight cosolutes show varying effects on tRNA folding cooperativity, increasing or decreasing it based on the identity of the cosolute. For those additives that increase folding cooperativity, the gain is manifested in sharpened two-state-like folding transitions for full-length tRNA over its secondary structural elements. Temperature-dependent SHAPE experiments in the absence and presence of crowders and cosolutes reveal extent of cooperative folding of tRNA on a nucleotide basis and are consistent with the melting studies. Mechanistically, crowding agents appear to promote cooperativity by stabilizing tertiary structure, while those low molecular cosolutes that promote cooperativity stabilize tertiary structure and/or destabilize secondary structure. Cooperative folding of functional RNA under physiological-like conditions parallels the behavior of many proteins and has implications for cellular RNA folding kinetics and evolution.     

Properties of an LNA-modified ricin RNA aptamer

'Locked nucleic acids' (LNAs) are sugar modified nucleic acids containing the 2'-O-4'C-methylene-β-D-ribofuranoses. The substitution of RNAs with LNAs leads to an enhanced thermostability. Aptamers are nucleic acids, which are selected for specific target binding from a large library pool by the 'SELEX' method. Introduction of modified nucleic acids into aptamers can improve their stability. The stem region of a ricin A chain RNA aptamer was substituted by locked nucleic acids. Different constructs of the LNA-substituted aptamers were examined for their thermostability, binding activity, folding and RNase sensitivity as compared to the natural RNA counterpart. The LNA-modified aptamers were active in target binding, while the loop regions and the adjacent stem nucleotides remained unsubstituted. The thermostability and RNase resistance of LNA substituted aptamers were enhanced as compared to the native RNA aptamer. This study supports the approach to substitute the aptamer stem region by LNAs and to leave the loop region unmodified, which is responsible for ligand binding. Thus, LNAs possess an encouraging potential for the development of new stabilized nucleic acids and will promote future diagnostic and therapeutic applications.     

Stepwise conversion of a mesophilic to a thermophilic ribozyme

A fundamental question in RNA folding is the mechanism of thermodynamic stability. We investigated the equilibrium folding of a series of sequence variants in which one to three motifs of a 255-nucleotide mesophilic ribozyme were substituted with the corresponding motifs from its thermophilic homologue. Substitution of three crucial motifs individually or in groups results in a continual increase in the stability and folding cooperativity in a stepwise fashion. We find an unexpected relationship between stability and folding cooperativity. Without changing the folding cooperativity, RNAs having a similar native structure can only achieve moderate change in stability and likewise, without changing stability, RNAs having a similar native structure can only achieve moderate change in folding cooperativity. This intricate relationship must be included in the predictions of tertiary RNA stability.     

Mg2+ Impacts the Twister Ribozyme through Push-Pull Stabilization of Nonsequential Phosphate Pairs

RNA molecules perform a variety of biological functions for which the correct three-dimensional structure is essential, including as ribozymes where they catalyze chemical reactions. Metal ions, especially Mg²⁺, neutralize these negatively charged nucleic acids and specifically stabilize RNA tertiary structures as well as impact the folding landscape of RNAs as they assume their tertiary structures. Specific binding sites of Mg²⁺ in folded conformations of RNA have been studied extensively; however, the full range of interactions of the ion with compact intermediates and unfolded states of RNA is challenging to investigate, and the atomic details of the mechanism by which the ion facilitates tertiary structure formation is not fully known. Here, umbrella sampling combined with oscillating chemical potential Grand Canonical Monte Carlo/molecular dynamics simulations are used to capture the energetics and atomic-level details of Mg²⁺-RNA interactions that occur along an unfolding pathway of the Twister ribozyme. The free energy profiles reveal stabilization of partially unfolded states by Mg²⁺, as observed in unfolding experiments, with this stabilization being due to increased sampling of simultaneous interactions of Mg²⁺ with two or more nonsequential phosphate groups. Notably, these results indicate a push-pull mechanism in which the Mg²⁺-RNA interactions actually lead to destabilization of specific nonsequential phosphate-phosphate interactions (i.e., pushed apart), whereas other interactions are stabilized (i.e., pulled together), a balance that stabilizes unfolded states and facilitates the folding of Twister, including the formation of hydrogen bonds associated with the tertiary structure. This study establishes a better understanding of how Mg²⁺-ion interactions contribute to RNA structural properties and stability.     

Cooperative tertiary interaction network guides RNA folding

Noncoding RNAs form unique 3D structures, which perform many regulatory functions. To understand how RNAs fold uniquely despite a small number of tertiary interaction motifs, we mutated the major tertiary interactions in a group I ribozyme by single-base substitutions. The resulting perturbations to the folding energy landscape were measured using SAXS, ribozyme activity, hydroxyl radical footprinting, and native PAGE. Double- and triple-mutant cycles show that most tertiary interactions have?a small effect on the stability of the native state. Instead, the formation of core and peripheral structural motifs is cooperatively linked in near-native folding intermediates, and this cooperativity depends on the native helix orientation. The emergence of a cooperative interaction network at an early stage of folding suppresses nonnative structures and guides the search for the native state. We suggest that cooperativity in noncoding RNAs arose from natural selection of architectures conducive to forming?a unique, stable fold.     

A DEAD-box RNA helicase promotes thermodynamic equilibration of kinetically trapped RNA structures in vivo

RNAs must assemble into specific structures in order to carry out their biological functions, but in vitro RNA folding reactions produce multiple misfolded structures that fail to exchange with functional structures on biological time scales. We used carefully designed self-cleaving mRNAs that assemble through well-defined folding pathways to identify factors that differentiate intracellular and in vitro folding reactions. Our previous work showed that simple base-paired RNA helices form and dissociate with the same rate and equilibrium constants in vivo and in vitro. However, exchange between adjacent secondary structures occurs much faster in vivo, enabling RNAs to quickly adopt structures with the lowest free energy. We have now used this approach to probe the effects of an extensively characterized DEAD-box RNA helicase, Mss116p, on a series of well-defined RNA folding steps in yeast. Mss116p overexpression had no detectable effect on helix formation or dissociation kinetics or on the stability of interdomain tertiary interactions, consistent with previous evidence that intracellular factors do not affect these folding parameters. However, Mss116p overexpression did accelerate exchange between adjacent helices. The nonprocessive nature of RNA duplex unwinding by DEAD-box RNA helicases is consistent with a branch migration mechanism in which Mss116p lowers barriers to exchange between otherwise stable helices by the melting and annealing of one or two base pairs at interhelical junctions. These results suggest that the helicase activity of DEAD-box proteins like Mss116p distinguish intracellular RNA folding pathways from nonproductive RNA folding reactions in vitro and allow RNA structures to overcome kinetic barriers to thermodynamic equilibration in vivo.     

Principles of protein folding--a perspective from simple exact models.

General principles of protein structure, stability, and folding kinetics have recently been explored in computer simulations of simple exact lattice models. These models represent protein chains at a rudimentary level, but they involve few parameters, approximations, or implicit biases, and they allow complete explorations of conformational and sequence spaces. Such simulations have resulted in testable predictions that are sometimes unanticipated: The folding code is mainly binary and delocalized throughout the amino acid sequence. The secondary and tertiary structures of a protein are specified mainly by the sequence of polar and nonpolar monomers. More specific interactions may refine the structure, rather than dominate the folding code. Simple exact models can account for the properties that characterize protein folding: two-state cooperativity, secondary and tertiary structures, and multistage folding kinetics--fast hydrophobic collapse followed by slower annealing. These studies suggest the possibility of creating "foldable" chain molecules other than proteins. The encoding of a unique compact chain conformation may not require amino acids; it may require only the ability to synthesize specific monomer sequences in which at least one monomer type is solvent-averse.     

Salt-Dependent Folding Energy Landscape of RNA Three-Way Junction

RNAs are highly negatively charged chain molecules. Metal ions play a crucial role in RNA folding stability and conformational changes. In this work, we employ the recently developed tightly bound ion (TBI) model, which accounts for the correlation between ions and the fluctuation of ion distributions, to investigate the ion-dependent free energy landscape for the three-way RNA junction in a 16S rRNA domain. The predicted electrostatic free energy landscape suggests that 1), ion-mediated electrostatic interactions cause an ensemble of unfolded conformations narrowly populated around the maximally extended structure; and 2), Mg²⁺ ion-induced correlation effects help bring the helices to the folded state. Nonelectrostatic interactions, such as noncanonical interactions within the junctions and between junctions and helix stems, might further limit the conformational diversity of the unfolded state, resulting in a more ordered unfolded state than the one predicted from the electrostatic effect. Moreover, the folded state is predominantly stabilized by the coaxial stacking force. The TBI-predicted folding stability agrees well with the experimental measurements for the different Na⁺ and Mg²⁺ ion concentrations. For Mg²⁺ solutions, the TBI model, which accounts for the Mg²⁺ ion correlation effect, gives more improved predictions than the Poisson-Boltzmann theory, which tends to underestimate the role of Mg²⁺ in stabilizing the folded structure. Detailed control tests indicate that the dominant ion correlation effect comes from the charge-charge Coulombic correlation rather than the size (excluded volume) correlation between the ions. Furthermore, the model gives quantitative predictions for the ion size effect in the folding energy landscape and folding cooperativity.     

Structural details,pathways, and energetics of unfolding apomyoglobin

Protein folding is often difficult to characterize experimentally because of the transience of intermediate states, and the complexity of the protein-solvent system. Atomistic simulations, which could provide more detailed information, have had to employ highly simplified models or high temperatures, to cope with the long time scales of unfolding; direct simulation of folding is even more problematic. We report a fully atomistic simulation of the acid-induced unfolding of apomyoglobin in which the protonation of acidic side-chains to simulate low pH is sufficient to induce unfolding at room temperature with no added biasing forces or other unusual conditions; and the trajectory is validated by comparison to experimental characterization of intermediate states. Novel insights provided by their analysis include: characterization of a dry swollen globule state forming a barrier to initial unfolding or final folding; observation of cooperativity in secondary and tertiary structure formation and its explanation in terms of dielectric environments; and structural details of the intermediate and the completely unfolded states. These insights involve time scales and levels of structural detail that are presently beyond the range of experiment, but come within reach through the simulation methods described here. An implicit solvation model is used to analyze the energetics of protein folding at various pH and ionic strength values, and a reasonable estimate of folding free energy is obtained. Electrostatic interactions are found to disfavor folding.     

Correlation of RNA Secondary Structure Statistics with Thermodynamic Stability and Applications to Folding

The accurate prediction of the secondary and tertiary structure of an RNA with different folding algorithms is dependent on several factors, including the energy functions. However, an RNA higher-order structure cannot be predicted accurately from its sequence based on a limited set of energy parameters. The inter- and intramolecular forces between this RNA and other small molecules and macromolecules, in addition to other factors in the cell such as pH, ionic strength, and temperature, influence the complex dynamics associated with transition of a single stranded RNA to its secondary and tertiary structure. Since all of the factors that affect the formation of an RNAs 3D structure cannot be determined experimentally, statistically derived potential energy has been used in the prediction of protein structure. In the current work, we evaluate the statistical free energy of various secondary structure motifs, including base-pair stacks, hairpin loops, and internal loops, using their statistical frequency obtained from the comparative analysis of more than 50,000 RNA sequences stored in the RNA Comparative Analysis Database (rCAD) at the Comparative RNA Web (CRW) Site. Statistical energy was computed from the structural statistics for several datasets. While the statistical energy for a base-pair stack correlates with experimentally derived free energy values, suggesting a Boltzmann-like distribution, variation is observed between different molecules and their location on the phylogenetic tree of life. Our statistical energy values calculated for several structural elements were utilized in the Mfold RNA-folding algorithm. The combined statistical energy values for base-pair stacks, hairpins and internal loop flanks result in a significant improvement in the accuracy of secondary structure prediction; the hairpin flanks contribute the most.     

Structure of a folding intermediate reveals the interplay between core and peripheral elements in RNA folding

Though the molecular architecture of many native RNA structures has been characterized, the structures of folding intermediates are poorly defined. Here, we present a nucleotide-level model of a highly structured equilibrium folding intermediate of the specificity domain of the Bacillus subtilis RNase P RNA, obtained using chemical and nuclease mapping, circular dichroism spectroscopy, small-angle X-ray scattering and molecular modeling. The crystal structure indicates that the 154 nucleotide specificity domain is composed of several secondary and tertiary structural modules. The structure of the intermediate contains modules composed of secondary structures and short-range tertiary interactions, implying a sequential order of tertiary structure formation during folding. The intermediate lacks the native core and several long-range interactions among peripheral regions, such as a GAAA tetraloop and its receptor. Folding to the native structure requires the local rearrangement of a T-loop in the core in concert with the formation of the GAAA tetraloop-receptor interaction. The interplay of core and peripheral structure formation rationalizes the high degree of cooperativity observed in the folding transition leading to the native structure.     

The GAAA tetraloop-receptor interaction contributes differentially to folding thermodynamics and kinetics for the P4-P6 RNA domain

Tetraloops with the generic sequence GNRA are commonly found in RNA secondary structure, and interactions of such tetraloops with "receptors" elsewhere in RNA play important roles in RNA structure and folding. However, the contributions of tetraloop-receptor interactions specifically to the kinetics of RNA tertiary folding, rather than the thermodynamics of maintaining tertiary structure once folded, have not been reported. Here we investigate the role of the key GAAA tetraloop-receptor motif in folding of the P4-P6 domain of the Tetrahymena group I intron RNA. Insertions of one or more nucleotides into the tetraloop significantly disrupt the thermodynamics of tertiary folding; single-nucleotide insertions shift the folding free energy by 2-4 kcal/mol (DeltaDeltaG(o)'). The folding kinetics of several modified P4-P6 domains were determined by stopped-flow fluorescence spectroscopy, using an internally incorporated pyrene residue as the chromophore. In contrast to the thermodynamic results, the kinetics of Mg(2+)-induced folding were barely affected by the tetraloop modifications, with a DeltaDeltaG(++) of 0.2-0.4 kcal/mol and a Phi value (ratio of the kinetic and thermodynamic contributions) of <0.1. These data indicate an early transition state for folding of P4-P6 with respect to forming the tetraloop-receptor contact, consistent with previous results for modifications elsewhere in P4-P6. We conclude that the GAAA tetraloop-receptor motif contributes little to the stabilization of the transition state for Mg(2+)-induced P4-P6 folding. Rather, the tetraloop-receptor motif acts to clamp the RNA once folding has occurred. This is the first report to correlate the kinetic and thermodynamic contributions of an important RNA tertiary motif, the GNRA tetraloop-receptor. The results are related to possible models for the Mg(2+)-induced folding of the P4-P6 RNA, including a model invoking rapid nonspecific electrostatic collapse.