Topological Constraints and Their Conformational Entropic Penalties on RNA Folds

Functional RNAs can fold into intricate structures using a number of different secondary and tertiary structural motifs. Many factors contribute to the overall free energy of the target fold. This study aims at quantifying the entropic costs coming from the loss of conformational freedom when the sugar-phosphate backbone is subjected to constraints imposed by secondary and tertiary contacts. Motivated by insights from topology theory, we design a diagrammatic scheme to represent different types of RNA structures so that constraints associated with a folded structure may be segregated into mutually independent subsets, enabling the total conformational entropy loss to be easily calculated as a sum of independent terms. We used high-throughput Monte Carlo simulations to simulate large ensembles of single-stranded RNA sequences in solution to validate the assumptions behind our diagrammatic scheme, examining the entropic costs for hairpin initiation and formation of many multiway junctions. Our diagrammatic scheme aids in the factorization of secondary/tertiary constraints into distinct topological classes and facilitates the discovery of interrelationships among multiple constraints on RNA folds. This perspective, which to our knowledge is novel, leads to useful insights into the inner workings of some functional RNA sequences, demonstrating how they might operate by transforming their structures among different topological classes.     

An alternative route for the folding of large RNAs: apparent two-state folding by a group II intron ribozyme

Despite a growing literature on the folding of RNA, our understanding of tertiary folding in large RNAs derives from studies on a small set of molecular examples, with primary focus on group I introns and RNase P RNA. To broaden the scope of RNA folding models and to better understand group II intron function, we have examined the tertiary folding of a ribozyme (D135) that is derived from the self-splicing ai5gamma intron from yeast mitochondria. The D135 ribozyme folds homogeneously and cooperatively into a compact, well-defined tertiary structure that includes all regions critical for active-site organization and substrate recognition. When D135 was treated with increasing concentrations of Mg(2+) and then subjected to hydroxyl radical footprinting, similar Mg(2+) dependencies were seen for internalization of all regions of the molecule, suggesting a highly cooperative folding behavior. In this work, we show that global folding and compaction of the molecule have the same magnesium dependence as the local folding previously observed. Furthermore, urea denaturation studies indicate highly cooperative unfolding of the ribozyme that is governed by thermodynamic parameters similar to those for forward folding. In fact, D135 folds homogeneously and cooperatively from the unfolded state to its native, active structure, thereby demonstrating functional reversibility in RNA folding. Taken together, the data are consistent with two-state folding of the D135 ribozyme, which is surprising given the size and multi-domain structure of the RNA. The findings establish that the accumulation of stable intermediates prior to formation of the native state is not a universal feature of RNA folding and that there is an alternative paradigm in which the folding landscape is relatively smooth, lacking rugged features that obstruct folding to the native state.     

Automated 3D structure composition for large RNAs

Understanding the numerous functions that RNAs play in living cells depends critically on knowledge of their three-dimensional structure. Due to the difficulties in experimentally assessing structures of large RNAs, there is currently great demand for new high-resolution structure prediction methods. We present the novel method for the fully automated prediction of RNA 3D structures from a user-defined secondary structure. The concept is founded on the machine translation system. The translation engine operates on the RNA FRABASE database tailored to the dictionary relating the RNA secondary structure and tertiary structure elements. The translation algorithm is very fast. Initial 3D structure is composed in a range of seconds on a single processor. The method assures the prediction of large RNA 3D structures of high quality. Our approach needs neither structural templates nor RNA sequence alignment, required for comparative methods. This enables the building of unresolved yet native and artificial RNA structures. The method is implemented in a publicly available, user-friendly server RNAComposer. It works in an interactive mode and a batch mode. The batch mode is designed for large-scale modelling and accepts atomic distance restraints. Presently, the server is set to build RNA structures of up to 500 residues.     

A new way to see RNA

Unlike proteins, the RNA backbone has numerous degrees of freedom (eight, if one counts the sugar pucker), making RNA modeling, structure building and prediction a multidimensional problem of exceptionally high complexity. And yet RNA tertiary structures are not infinite in their structural morphology; rather, they are built from a limited set of discrete units. In order to reduce the dimensionality of the RNA backbone in a physically reasonable way, a shorthand notation was created that reduced the RNA backbone torsion angles to two (η and θ, analogous to φ and ψ in proteins). When these torsion angles are calculated for nucleotides in a crystallographic database and plotted against one another, one obtains a plot analogous to a Ramachandran plot (the η/θ plot), with highly populated and unpopulated regions. Nucleotides that occupy proximal positions on the plot have identical structures and are found in the same units of tertiary structure. In this review, we describe the statistical validation of the η/θ formalism and the exploration of features within the η/θ plot. We also describe the application of the η/θ formalism in RNA motif discovery, structural comparison, RNA structure building and tertiary structure prediction. More than a tool, however, the η/θ formalism has provided new insights into RNA structure itself, revealing its fundamental components and the factors underlying RNA architectural form.     

Lead-catalyzed cleavage of ribonuclease P RNA as a probe for integrity of tertiary structure.

Pb(2+)-catalyzed cleavage of RNA has been shown previously to be a useful probe for tertiary structure. In the present study, Pb2+ cleavage patterns were identified for ribonuclease P RNAs from three phylogenetically disparate organisms, Escherichia coli, Chromatium vinosum, Bacillus subtilis, and for E. coli RNase P RNAs that had been altered by deletions. Each of the native RNAs undergoes cleavage at several sites in the core structure that is common to all bacterial RNase P RNAs. All the cleavages occur in non-paired regions of the secondary structure models of the RNAs, in regions likely to be involved in tertiary interactions. Two cleavage sites occur at homologous positions in all the native RNAs, regardless of sequence variation, suggesting common tertiary structural features. The Pb2+ cleavage sites in four deletion mutants of E. coli RNase P RNA differed from the native pattern, indicating alterations in the tertiary structures of the mutant RNAs. This conclusion is consistent with previously characterized properties of the mutant RNAs. The Pb2+ cleavage assay is thus a useful probe to reveal alteration of tertiary structure in RNase P RNA.     

RAG-3D: a search tool for RNA 3D substructures

To address many challenges in RNA structure/function prediction, the characterization of RNA''s modular architectural units is required. Using the RNA-As-Graphs (RAG) database, we have previously explored the existence of secondary structure (2D) submotifs within larger RNA structures. Here we present RAG-3D—a dataset of RNA tertiary (3D) structures and substructures plus a web-based search tool—designed to exploit graph representations of RNAs for the goal of searching for similar 3D structural fragments. The objects in RAG-3D consist of 3D structures translated into 3D graphs, cataloged based on the connectivity between their secondary structure elements. Each graph is additionally described in terms of its subgraph building blocks. The RAG-3D search tool then compares a query RNA 3D structure to those in the database to obtain structurally similar structures and substructures. This comparison reveals conserved 3D RNA features and thus may suggest functional connections. Though RNA search programs based on similarity in sequence, 2D, and/or 3D structural elements are available, our graph-based search tool may be advantageous for illuminating similarities that are not obvious; using motifs rather than sequence space also reduces search times considerably. Ultimately, such substructuring could be useful for RNA 3D structure prediction, structure/function inference and inverse folding.     

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.     

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.     

In vitro selection of RNAs with increased tertiary structure stability.

An in vitro selection system was devised to select RNAs based on their tertiary structural stability, independent of RNA activity. Selection studies were conducted on the P4-P6 domain from the Tetrahymena thermophila group I intron, an autonomous self-folding unit that contains several important tertiary folding motifs including the tetraloop receptor and the A-rich bulge. Partially randomized P4-P6 molecules were selected based on their ability to fold into compact structures using native gel electrophoresis in the presence of decreasing concentrations of MgCl2. After 10 rounds of the selection process, a number of sequence alterations were identified that stabilized the P4-P6 RNA. One of these, a single base deletion of C209 within the P4 helix, significantly stabilized the P4-P6 molecule and would not have been identified by an activity-based selection because of its essential role for ribozyme function. Additionally, the sequence analysis provided evidence that stabilization of secondary structure may contribute to overall tertiary stability for RNAs. This system for probing RNA structure irrespective of RNA activity allows analysis of RNA structure/function relationships by identifying nucleotides or motifs important for folding and then comparing them with RNA sequences required for function.     

Prediction of geometrically feasible three-dimensional structures of pseudoknotted RNA through free energy estimation

Accurate free energy estimation is essential for RNA structure prediction. The widely used Turner''s energy model works well for nested structures. For pseudoknotted RNAs, however, there is no effective rule for estimation of loop entropy and free energy. In this work we present a new free energy estimation method, termed the pseudoknot predictor in three-dimensional space (pk3D), which goes beyond Turner''s model. Our approach treats nested and pseudoknotted structures alike in one unifying physical framework, regardless of how complex the RNA structures are. We first test the ability of pk3D in selecting native structures from a large number of decoys for a set of 43 pseudoknotted RNA molecules, with lengths ranging from 23 to 113. We find that pk3D performs slightly better than the Dirks and Pierce extension of Turner''s rule. We then test pk3D for blind secondary structure prediction, and find that pk3D gives the best sensitivity and comparable positive predictive value (related to specificity) in predicting pseudoknotted RNA secondary structures, when compared with other methods. A unique strength of pk3D is that it also generates spatial arrangement of structural elements of the RNA molecule. Comparison of three-dimensional structures predicted by pk3D with the native structure measured by nuclear magnetic resonance or X-ray experiments shows that the predicted spatial arrangement of stems and loops is often similar to that found in the native structure. These close-to-native structures can be used as starting points for further refinement to derive accurate three-dimensional structures of RNA molecules, including those with pseudoknots.     

Near native structure in an RNA collapsed state

Many large RNAs form conformationally collapsed, but non-native, states prior to folding to the native state or assembling with protein cofactors. Although RNA collapsed states play fundamental roles in RNA folding and ribonucleoprotein assembly processes, their structures have been poorly understood. We obtained 12 high-quality structural constraints for the collapsed state formed by the catalytic core of the bI5 intron RNA using site-specific cross-linking mediated by a short-lived reactant. RNA tertiary structures in the collapsed and native states are indistinguishable, even though only the native state forms a solvent-inaccessible core. Thus, structural neighbors in the collapsed state, including several long-range tertiary interactions, are approximately as close in space as in the native state, but RNA packing is sufficiently loose or dynamic to allow access by solvent. Binding by the obligate CBP2 protein cofactor has almost no effect on structural neighbors reported by cross-linking, even though protein binding chases the RNA from the collapsed state to the native state. Protein binding thus appears to promote only the final few angstroms of RNA folding rather than mediate global conformational rearrangements in the catalytic core. The bI5 RNA collapsed state functions to self-chaperone ribonucleoprotein assembly because this conformationally restrained structure lies very near that of the native state and excludes structures that otherwise misassemble efficiently.     

An obligate intermediate along the slow folding pathway of a group II intron ribozyme

Most RNA molecules collapse rapidly and reach the native state through a pathway that contains numerous traps and unproductive intermediates. The D135 group II intron ribozyme is unusual in that it can fold slowly and directly to the native state, despite its large size and structural complexity. Here we use hydroxyl radical footprinting and native gel analysis to monitor the timescale of tertiary structure collapse and to detect the presence of obligate intermediates along the folding pathway of D135. We find that structural collapse and native folding of Domain 1 precede assembly of the entire ribozyme, indicating that D1 contains an on-pathway intermediate to folding of the D135 ribozyme. Subsequent docking of Domains 3 and 5, for which D1 provides a preorganized scaffold, appears to be very fast and independent of one another. In contrast to other RNAs, the D135 ribozyme undergoes slow tertiary collapse to a compacted state, with a rate constant that is also limited by the formation D1. These findings provide a new paradigm for RNA folding and they underscore the diversity of RNA biophysical behaviors.     

Fully differentiable coarse-grained and all-atom knowledge-based potentials for RNA structure evaluation

RNA molecules play integral roles in gene regulation, and understanding their structures gives us important insights into their biological functions. Despite recent developments in template-based and parameterized energy functions, the structure of RNA--in particular the nonhelical regions--is still difficult to predict. Knowledge-based potentials have proven efficient in protein structure prediction. In this work, we describe two differentiable knowledge-based potentials derived from a curated data set of RNA structures, with all-atom or coarse-grained representation, respectively. We focus on one aspect of the prediction problem: the identification of native-like RNA conformations from a set of near-native models. Using a variety of near-native RNA models generated from three independent methods, we show that our potential is able to distinguish the native structure and identify native-like conformations, even at the coarse-grained level. The all-atom version of our knowledge-based potential performs better and appears to be more effective at discriminating near-native RNA conformations than one of the most highly regarded parameterized potential. The fully differentiable form of our potentials will additionally likely be useful for structure refinement and/or molecular dynamics simulations.     

3dRNAscore: a distance and torsion angle dependent evaluation function of 3D RNA structures

Model evaluation is a necessary step for better prediction and design of 3D RNA structures. For proteins, this has been widely studied and the knowledge-based statistical potential has been proved to be one of effective ways to solve this problem. Currently, a few knowledge-based statistical potentials have also been proposed to evaluate predicted models of RNA tertiary structures. The benchmark tests showed that they can identify the native structures effectively but further improvements are needed to identify near-native structures and those with non-canonical base pairs. Here, we present a novel knowledge-based potential, 3dRNAscore, which combines distance-dependent and dihedral-dependent energies. The benchmarks on different testing datasets all show that 3dRNAscore are more efficient than existing evaluation methods in recognizing native state from a pool of near-native states of RNAs as well as in ranking near-native states of RNA models.     

Modeling RNA tertiary structure motifs by graph-grammars

A new approach, graph-grammars, to encode RNA tertiary structure patterns is introduced and exemplified with the classical sarcin-ricin motif. The sarcin-ricin motif is found in the stem of the crucial ribosomal loop E (also referred to as the sarcin-ricin loop), which is sensitive to the alpha-sarcin and ricin toxins. Here, we generate a graph-grammar for the sarcin-ricin motif and apply it to derive putative sequences that would fold in this motif. The biological relevance of the derived sequences is confirmed by a comparison with those found in known sarcin-ricin sites in an alignment of over 800 bacterial 23S ribosomal RNAs. The comparison raised alternative alignments in few sarcin-ricin sites, which were assessed using tertiary structure predictions and 3D modeling. The sarcin-ricin motif graph-grammar was built with indivisible nucleotide interaction cycles that were recently observed in structured RNAs. A comparison of the sequences and 3D structures of each cycle that constitute the sarcin-ricin motif gave us additional insights about RNA sequence-structure relationships. In particular, this analysis revealed the sequence space of an RNA motif depends on a structural context that goes beyond the single base pairing and base-stacking interactions.     

Arrangement of 3D structural motifs in ribosomal RNA

Structural 3D motifs in RNA play an important role in the RNA stability and function. Previous studies have focused on the characterization and discovery of 3D motifs in RNA secondary and tertiary structures. However, statistical analyses of the distribution of 3D motifs along the RNA appear to be lacking. Herein, we present a novel strategy for evaluating the distribution of 3D motifs along the RNA chain and those motifs whose distributions are significantly non-random are identified. By applying it to the X-ray structure of the large ribosomal subunit from Haloarcula marismortui, helical motifs were found to cluster together along the chain and in the 3D structure, whereas the known tetraloops tend to be sequentially and spatially dispersed. That the distribution of key structural motifs such as tetraloops differ significantly from a random one suggests that our method could also be used to detect novel 3D motifs of any size in sufficiently long/large RNA structures. The motif distribution type can help in the prediction and design of 3D structures of large RNA molecules.     

Topological constraints: using RNA secondary structure to model 3D conformation, folding pathways, and dynamic adaptation

Accompanying recent advances in determining RNA secondary structure is the growing appreciation for the importance of relatively simple topological constraints, encoded at the secondary structure level, in defining the overall architecture, folding pathways, and dynamic adaptability of RNA. A new view is emerging in which tertiary interactions do not define RNA 3D structure, but rather, help select specific conformers from an already narrow, topologically pre-defined conformational distribution. Studies are providing fundamental insights into the nature of these topological constraints, how they are encoded by the RNA secondary structure, and how they interplay with other interactions, breathing new meaning to RNA secondary structure. New approaches have been developed that take advantage of topological constraints in determining RNA backbone conformation based on secondary structure, and a limited set of other, easily accessible constraints. Topological constraints are also providing a much-needed framework for rationalizing and describing RNA dynamics and structural adaptation. Finally, studies suggest that topological constraints may play important roles in steering RNA folding pathways. Here, we review recent advances in our understanding of topological constraints encoded by the RNA secondary structure.