Predicting loop–helix tertiary structural contacts in RNA pseudoknots

Tertiary interactions between loops and helical stems play critical roles in the biological function of many RNA pseudoknots. However, quantitative predictions for RNA tertiary interactions remain elusive. Here we report a statistical mechanical model for the prediction of noncanonical loop–stem base-pairing interactions in RNA pseudoknots. Central to the model is the evaluation of the conformational entropy for the pseudoknotted folds with defined loop–stem tertiary structural contacts. We develop an RNA virtual bond-based conformational model (Vfold model), which permits a rigorous computation of the conformational entropy for a given fold that contains loop–stem tertiary contacts. With the entropy parameters predicted from the Vfold model and the energy parameters for the tertiary contacts as inserted parameters, we can then predict the RNA folding thermodynamics, from which we can extract the tertiary contact thermodynamic parameters from theory–experimental comparisons. These comparisons reveal a contact enthalpy (ΔH) of −14 kcal/mol and a contact entropy (ΔS) of −38 cal/mol/K for a protonated C⁺•(G–C) base triple at pH 7.0, and (ΔH = −7 kcal/mol, ΔS = −19 cal/mol/K) for an unprotonated base triple. Tests of the model for a series of pseudoknots show good theory–experiment agreement. Based on the extracted energy parameters for the tertiary structural contacts, the model enables predictions for the structure, stability, and folding pathways for RNA pseudoknots with known or postulated loop–stem tertiary contacts from the nucleotide sequence alone.     

Predicting RNA 3D structure using a coarse-grain helix-centered model

A 3D model of RNA structure can provide information about its function and regulation that is not possible with just the sequence or secondary structure. Current models suffer from low accuracy and long running times and either neglect or presume knowledge of the long-range interactions which stabilize the tertiary structure. Our coarse-grained, helix-based, tertiary structure model operates with only a few degrees of freedom compared with all-atom models while preserving the ability to sample tertiary structures given a secondary structure. It strikes a balance between the precision of an all-atom tertiary structure model and the simplicity and effectiveness of a secondary structure representation. It provides a simplified tool for exploring global arrangements of helices and loops within RNA structures. We provide an example of a novel energy function relying only on the positions of stems and loops. We show that coupling our model to this energy function produces predictions as good as or better than the current state of the art tools. We propose that given the wide range of conformational space that needs to be explored, a coarse-grain approach can explore more conformations in less iterations than an all-atom model coupled to a fine-grain energy function. Finally, we emphasize the overarching theme of providing an ensemble of predicted structures, something which our tool excels at, rather than providing a handful of the lowest energy structures.     

Influence of specific mutations on the thermal stability of the td group I intron in vitro and on its splicing efficiency in vivo: a comparative study.

Group I introns constitute excellent systems for analyzing the relationship between RNA tertiary folding and catalysis. Within a hierarchical framework interpretation of RNA folding, secondary structure motifs subtend RNA three-dimensional (3D) architecture. Thus, mutations in two-dimensional motifs are expected to have effects different from those disrupting 3D contacts. Using UV spectroscopy, we have studied the influence of nucleotide substitutions, in both secondary and tertiary structure elements, on the thermal stability of the tertiary folding of the bacteriophage T4 td group I intron. Further, we present a quantitative analysis of the relationship between the splicing efficiency in vivo and the stability of the intron structure as monitored by UV melting curves. We conclude that the stability of the tertiary structure of a group I intron as measured by UV melting is generally a good indication of its ability to splice in vivo.     

Topological constraints are major determinants of tRNA tertiary structure and dynamics and provide basis for tertiary folding cooperativity

Recent studies have shown that basic steric and connectivity constraints encoded at the secondary structure level are key determinants of 3D structure and dynamics in simple two-way RNA junctions. However, the role of these topological constraints in higher order RNA junctions remains poorly understood. Here, we use a specialized coarse-grained molecular dynamics model to directly probe the thermodynamic contributions of topological constraints in defining the 3D architecture and dynamics of transfer RNA (tRNA). Topological constraints alone restrict tRNA''s allowed conformational space by over an order of magnitude and strongly discriminate against formation of non-native tertiary contacts, providing a sequence independent source of folding specificity. Topological constraints also give rise to long-range correlations between the relative orientation of tRNA''s helices, which in turn provides a mechanism for encoding thermodynamic cooperativity between distinct tertiary interactions. These aspects of topological constraints make it such that only several tertiary interactions are needed to confine tRNA to its native global structure and specify functionally important 3D dynamics. We further show that topological constraints are conserved across tRNA''s different naturally occurring secondary structures. Taken together, our results emphasize the central role of secondary-structure-encoded topological constraints in defining RNA 3D structure, dynamics and folding.     

Structural basis of the enhanced stability of a mutant ribozyme domain and a detailed view of RNA--solvent interactions

BACKGROUND: The structure of P4-P6, a 160 nucleotide domain of the self-splicing Tetrahymena thermophila intron, was solved previously. Mutants of the P4-P6 RNA that form a more stable tertiary structure in solution were recently isolated by successive rounds of in vitro selection and amplification. RESULTS: We show that a single-site mutant (Delta C209) possessing greater tertiary stability than wild-type P4-P6 also crystallizes much more rapidly and under a wider variety of conditions. The crystal structure provides a satisfying explanation for the increased stability of the mutant; the deletion of C209 allows the adjacent bulged adenine to enter the P4 helix and form an A-G base pair, presumably attenuating the conformational flexibility of the helix. The structure of another mutant (Delta A210) was also solved and supports this interpretation. The crystals of Delta C209 diffract to a higher resolution limit than those of wild-type RNA (2.25 A versus 2.8 A), allowing assignment of innersphere and outersphere coordination contacts for 27 magnesium ions. Structural analysis reveals an intricate solvent scaffold with a preponderance of ordered water molecules on the inside rather than the surface of the folded RNA domain. CONCLUSIONS: In vitro evolution facilitated the identification of a highly stable, structurally homogeneous mutant RNA that was readily crystallizable. Analysis of the structure suggests that improving RNA secondary structure can stabilize tertiary structure and perhaps promote crystallization. In addition, the higher resolution model provides new details of metal ion-RNA interactions and identifies a core of ordered water molecules that may be integral to RNA tertiary structure formation.     

Use of secondary structural information and C<Emphasis Type="Italic">α</Emphasis>-C<Emphasis Type="Italic">α</Emphasis> distance restraints to model protein structures with MODELLER

Protein secondary structure predictions and amino acid long range contact map predictions from primary sequence of proteins have been explored to aid in modelling protein tertiary structures. In order to evaluate the usefulness of secondary structure and 3D-residue contact prediction methods to model protein structures we have used the known Q3 (alpha-helix, beta-strands and irregular turns/loops) secondary structure information, along with residue-residue contact information as restraints for MODELLER. We present here results of our modelling studies on 30 best resolved single domain protein structures of varied lengths. The results shows that it is very difficult to obtain useful models even with 100% accurate secondary structure predictions and accurate residue contact predictions for up to 30% of residues in a sequence. The best models that we obtained for proteins of lengths 37, 70, 118, 136 and 193 amino acid residues are of RMSDs 4.17, 5.27, 9.12, 7.89 and 9.69, respectively. The results show that one can obtain better models for the proteins which have high percent of alpha-helix content. This analysis further shows that MODELLER restrain optimization program can be useful only if we have truly homologous structure(s) as a template where it derives numerous restraints, almost identical to the templates used. This analysis also clearly indicates that even if we satisfy several true residue-residue contact distances, up to 30% of their sequence length with fully known secondary structural information, we end up predicting model structures much distant from their corresponding native structures.     

Use of secondary structural information and C alpha-C alpha distance restraints to model protein structures with MODELLER

Protein secondary structure predictions and amino acid long range contact map predictions from primary sequence of proteins have been explored to aid in modelling protein tertiary structures. In order to evaluate the usefulness of secondary structure and 3D-residue contact prediction methods to model protein structures we have used the known Q3 (alpha-helix,beta-strands and irregular turns/loops) secondary structure information, along with residue-residue contact information as restraints for MODELLER. We present here results of our modelling studies on 30 best resolved single domain protein structures of varied lengths. The results shows that it is very difficult to obtain useful models even with 100% accurate secondary structure predictions and accurate residue contact predictions for up to 30% of residues in a sequence. The best models that we obtained for proteins of lengths 37, 70, 118, 136 and 193 amino acid residues are of RMSDs 4.17, 5.27, 9.12, 7.89 and 9.69,respectively. The results show that one can obtain better models for the proteins which have high percent of alpha-helix content. This analysis further shows that MODELLER restrain optimization program can be useful only if we have truly homologous structure(s) as a template where it derives numerous restraints, almost identical to the templates used. This analysis also clearly indicates that even if we satisfy several true residue-residue contact distances, up to 30%of their sequence length with fully known secondary structural information, we end up predicting model structures much distant from their corresponding native structures.     

Evaluation and refinement of tmRNA structure using gene sequences from natural microbial communities

DNA harvested directly from complex natural microbial communities by PCR has been successfully used to predict RNase P RNA structure, and can potentially provide an abundant source of information for structural predictions of other RNAs. In this study, we utilized genetic variation in natural communities to test and refine the secondary and tertiary structural model for the bacterial tmRNA. The variability of proposed tmRNA secondary structures in different organisms and the lack of any predicted tertiary structure suggested that further refinement of the tmRNA could be useful. To increase the phylogenetic representation of tmRNA sequences, and thereby provide additional data for statistical comparative analysis, we amplified, sequenced, and compared tmRNA sequences from natural microbial communities. Using primers designed from gamma proteobacterial sequences, we determined 44 new tmRNA sequences from a variety of environmental DNA samples. Covariation analyses of these sequences, along with sequences from cultured organisms, confirmed most of the proposed tmRNA model but also provided evidence for a new tertiary interaction. This approach of gathering sequence information from natural microbial communities seems generally applicable in RNA structural analysis.     

A long-range pseudoknot is required for activity of the Neurospora VS ribozyme.

Four small RNA self-cleaving domains, the hammerhead, hairpin, hepatitis delta virus and Neurospora VS ribozymes, have been identified previously in naturally occurring RNAs. The secondary structures of these ribozymes are reasonably well understood, but little is known about long-range interactions that form the catalytically active tertiary conformations. Our previous work, which identified several secondary structure elements of the VS ribozyme, also showed that many additional bases were protected by magnesium-dependent interactions, implying that several tertiary contacts remained to be identified. Here we have used site-directed mutagenesis and chemical modification to characterize the first long-range interaction identified in VS RNA. This interaction contains a 3 bp pseudoknot helix that is required for tertiary folding and self-cleavage activity of the VS ribozyme.     

RNANetMotif: Identifying sequence-structure RNA network motifs in RNA-protein binding sites

RNA molecules can adopt stable secondary and tertiary structures, which are essential in mediating physical interactions with other partners such as RNA binding proteins (RBPs) and in carrying out their cellular functions. In vivo and in vitro experiments such as RNAcompete and eCLIP have revealed in vitro binding preferences of RBPs to RNA oligomers and in vivo binding sites in cells. Analysis of these binding data showed that the structure properties of the RNAs in these binding sites are important determinants of the binding events; however, it has been a challenge to incorporate the structure information into an interpretable model. Here we describe a new approach, RNANetMotif, which takes predicted secondary structure of thousands of RNA sequences bound by an RBP as input and uses a graph theory approach to recognize enriched subgraphs. These enriched subgraphs are in essence shared sequence-structure elements that are important in RBP-RNA binding. To validate our approach, we performed RNA structure modeling via coarse-grained molecular dynamics folding simulations for selected 4 RBPs, and RNA-protein docking for LIN28B. The simulation results, e.g., solvent accessibility and energetics, further support the biological relevance of the discovered network subgraphs.     

Studies on the structure and function of 16S ribosomal RNA using structure-specific chemical probes

Recent technological developments permit us to examine the accessibility of specific atoms on any nucleotide in any large RNA molecule to certain chemical probes. This can provide detailed information about the higher order structure of large RNA molecules, including secondary and tertiary structure, protein-RNA contacts, binding sites for functional ligands and possible biologically significant conformational changes. Here, we summarize recent studies on (i) the conformation of naked 16S rRNA under a variety of ionic conditions, and (ii) the behaviour of 16S rRNA in active and inactive 30S subunits, as defined by Zamir, Elson and their colleagues. The latter study reveals a reciprocal conformational change in the vicinity of the decoding region of 16S rRNA in 30S ribosomal subunits. This conformational change appears to be a rearrangement of tertiary and/or quaternary structure involving several universally conserved nucleotides. No reproducible effects are seen elsewhere in the molecule, suggesting that the active-inactive transition is a result of the observed conformational change.     

Measurements of protein sequence-structure correlations

Correlations between protein structures and amino acid sequences are widely used for protein structure prediction. For example, secondary structure predictors generally use correlations between a secondary structure sequence and corresponding primary structure sequence, whereas threading algorithms and similar tertiary structure predictors typically incorporate interresidue contact potentials. To investigate the relative importance of these sequence-structure interactions, we measured the mutual information among the primary structure, secondary structure and side-chain surface exposure, both for adjacent residues along the amino acid sequence and for tertiary structure contacts between residues distantly separated along the backbone. We found that local interactions along the amino acid chain are far more important than non-local contacts and that correlations between proximate amino acids are essentially uninformative. This suggests that knowledge-based contact potentials may be less important for structure predication than is generally believed.     

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.     

The fastest global events in RNA folding: electrostatic relaxation and tertiary collapse of the Tetrahymena ribozyme

Large RNAs can collapse into compact conformations well before the stable formation of the tertiary contacts that define their final folds. This study identifies likely physical mechanisms driving these early compaction events in RNA folding. We have employed time-resolved small-angle X-ray scattering to monitor the fastest global shape changes of the Tetrahymena ribozyme under different ionic conditions and with RNA mutations that remove long-range tertiary contacts. A partial collapse in each of the folding time-courses occurs within tens of milliseconds with either monovalent or divalent cations. Combined with comparison to predictions from structural models, this observation suggests a relaxation of the RNA to a more compact but denatured conformational ensemble in response to enhanced electrostatic screening at higher ionic concentrations. Further, the results provide evidence against counterion-correlation-mediated attraction between RNA double helices, a recently proposed model for early collapse. A previous study revealed a second 100 ms phase of collapse to a globular state. Surprisingly, we find that progression to this second early folding intermediate requires RNA sequence motifs that eventually mediate native long-range tertiary interactions, even though these regions of the RNA were observed to be solvent-accessible in previous footprinting studies under similar conditions. These results help delineate an analogy between the early conformational changes in RNA folding and the "burst phase" changes and molten globule formation in protein folding.     

An RNA tertiary structure in the 3' untranslated region of enteroviruses is necessary for efficient replication.

RNA tertiary structures, such as pseudoknots, are known to be biologically significant in a number of virus systems. The 3' untranslated regions of the RNA genomes of all members of the Enterovirus genus of Picornaviridae exhibit a potential, pseudoknot-like, tertiary structure interaction of an unusual type. This is formed by base pairing between loop regions of two secondary structure domains. It is distinct from a potential, conventional pseudoknot, studied previously in poliovirus, which is less conserved phylogenetically. We have analyzed the tertiary structure feature in one enterovirus, coxsackievirus A9, using specific mutagenesis. A double mutant in which the potential interaction was destroyed was nonviable, and viability was restored by introducing compensating mutations, predicted to allow the interaction to reform. Phenotypic pseudorevertants of virus mutants, having mutations designed to disrupt the interaction, were all found to have acquired nucleotide changes which restored the potential interaction. Analysis of one mutant containing a single-base mutation indicated a greatly increased temperature sensitivity due to a step early in replication. The results show that, in addition to secondary structures, tertiary RNA structural interactions can play an important role in the biology of picornaviruses.     

Structural constraints identified with covariation analysis in ribosomal RNA

Covariation analysis is used to identify those positions with similar patterns of sequence variation in an alignment of RNA sequences. These constraints on the evolution of two positions are usually associated with a base pair in a helix. While mutual information (MI) has been used to accurately predict an RNA secondary structure and a few of its tertiary interactions, early studies revealed that phylogenetic event counting methods are more sensitive and provide extra confidence in the prediction of base pairs. We developed a novel and powerful phylogenetic events counting method (PEC) for quantifying positional covariation with the Gutell lab's new RNA Comparative Analysis Database (rCAD). The PEC and MI-based methods each identify unique base pairs, and jointly identify many other base pairs. In total, both methods in combination with an N-best and helix-extension strategy identify the maximal number of base pairs. While covariation methods have effectively and accurately predicted RNAs secondary structure, only a few tertiary structure base pairs have been identified. Analysis presented herein and at the Gutell lab's Comparative RNA Web (CRW) Site reveal that the majority of these latter base pairs do not covary with one another. However, covariation analysis does reveal a weaker although significant covariation between sets of nucleotides that are in proximity in the three-dimensional RNA structure. This reveals that covariation analysis identifies other types of structural constraints beyond the two nucleotides that form a base pair.     

Quantifying the energetic interplay of RNA tertiary and secondary structure interactions

To understand the RNA-folding problem, we must know the extent to which RNA structure formation is hierarchical (tertiary folding of preformed secondary structure). Recently, nuclear magnetic resonance (NMR) spectroscopy was used to show that Mg2+-dependent tertiary interactions force secondary structure rearrangement in the 56-nt tP5abc RNA, a truncated subdomain of the Tetrahymena group I intron. Here we combine mutagenesis with folding computations, nondenaturing gel electrophoresis, high-resolution NMR spectroscopy, and chemical-modification experiments to probe further the energetic interplay of tertiary and secondary interactions in tP5abc. Point mutations predicted to destabilize the secondary structure of folded tP5abc greatly disrupt its Mg2+-dependent folding, as monitored by nondenaturing gels. Imino proton assignments and sequential NOE walks of the two-dimensional NMR spectrum of one of the tP5abc mutants confirm the predicted secondary structure, which does not change in the presence of Mg2+. In contrast to these data on tP5abc, the same point mutations in the context of the P4-P6 domain (of which P5abc is a subdomain) shift the Mg2+ dependence of P4-P6 folding only moderately, and dimethyl sulfate (DMS) modification experiments demonstrate that Mg2+ does cause secondary structure rearrangement of the P4-P6 mutants' P5abc subdomains. Our data provide experimental support for two simple conclusions: (1) Even single point mutations at bases involved only in secondary structure can be enough to tip the balance between RNA tertiary and secondary interactions. (2) Domain context must be considered in evaluating the relative importance of tertiary and secondary contributions. This tertiary/secondary interplay is likely relevant to the folding of many large RNA and to bimolecular snRNA-snRNA and snRNA-intron RNA interactions.     

Predicting Helical Topologies in RNA Junctions as Tree Graphs

RNA molecules are important cellular components involved in many fundamental biological processes. Understanding the mechanisms behind their functions requires knowledge of their tertiary structures. Though computational RNA folding approaches exist, they often require manual manipulation and expert intuition; predicting global long-range tertiary contacts remains challenging. Here we develop a computational approach and associated program module (RNAJAG) to predict helical arrangements/topologies in RNA junctions. Our method has two components: junction topology prediction and graph modeling. First, junction topologies are determined by a data mining approach from a given secondary structure of the target RNAs; second, the predicted topology is used to construct a tree graph consistent with geometric preferences analyzed from solved RNAs. The predicted graphs, which model the helical arrangements of RNA junctions for a large set of 200 junctions using a cross validation procedure, yield fairly good representations compared to the helical configurations in native RNAs, and can be further used to develop all-atom models as we show for two examples. Because junctions are among the most complex structural elements in RNA, this work advances folding structure prediction methods of large RNAs. The RNAJAG module is available to academic users upon request.     

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

There are potentially several ways Mg2+ might promote formation of an RNA tertiary structure: by causing a general "collapse" of the unfolded ensemble to more compact conformations, by favoring a reorganization of structure within a domain to a form with specific tertiary contacts, and by enhancing cooperative linkages between different sets of tertiary contacts. To distinguish these different modes of action, we have studied Mg2+ interactions with the adenine riboswitch, in which a set of tertiary interactions that forms around a purine-binding pocket is thermodynamically linked to the tertiary "docking" of two hairpin loops in another part of the molecule. Each of four RNA forms with different extents of tertiary structure were characterized by small-angle X-ray scattering. The free energy of interconversion between different conformations in the absence of Mg2+ and the free energy of Mg2+ interaction with each form have been estimated, yielding a complete picture of the folding energy landscape as a function of Mg2+ concentration. At 1 mM Mg2+ (50 mM K+), the overall free energy of stabilization by Mg2+ is large, -9.8 kcal/mol, and about equally divided between its effect on RNA collapse to a partially folded structure and on organization of the binding pocket. A strong cooperative linkage between the two sets of tertiary contacts is intrinsic to the RNA. This quantitation of the effects of Mg2+ on an RNA with two distinct sets of tertiary interactions suggests ways that Mg2+ may work to stabilize larger and more complex RNA structures.