Ab initio RNA folding by discrete molecular dynamics: from structure prediction to folding mechanisms

RNA molecules with novel functions have revived interest in the accurate prediction of RNA three-dimensional (3D) structure and folding dynamics. However, existing methods are inefficient in automated 3D structure prediction. Here, we report a robust computational approach for rapid folding of RNA molecules. We develop a simplified RNA model for discrete molecular dynamics (DMD) simulations, incorporating base-pairing and base-stacking interactions. We demonstrate correct folding of 150 structurally diverse RNA sequences. The majority of DMD-predicted 3D structures have <4 A deviations from experimental structures. The secondary structures corresponding to the predicted 3D structures consist of 94% native base-pair interactions. Folding thermodynamics and kinetics of tRNA(Phe), pseudoknots, and mRNA fragments in DMD simulations are in agreement with previous experimental findings. Folding of RNA molecules features transient, non-native conformations, suggesting non-hierarchical RNA folding. Our method allows rapid conformational sampling of RNA folding, with computational time increasing linearly with RNA length. We envision this approach as a promising tool for RNA structural and functional analyses.     

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.     

The HIV-2 Rev-response element: determining secondary structure and defining folding intermediates

Interaction between the viral protein Rev and the RNA motifs known as Rev response elements (RREs) is required for transport of unspliced and partially spliced human immunodeficiency virus (HIV)-1 and HIV-2 RNAs from the nucleus to the cytoplasm during the later stages of virus replication. A more detailed understanding of these nucleoprotein complexes and the host factors with which they interact should accelerate the development of new antiviral drugs targeting cis-acting RNA regulatory signals. In this communication, the secondary structures of the HIV-2 RRE and two RNA folding precursors have been identified using the SHAPE (selective 2′-hydroxyl acylation analyzed by primer extension) chemical probing methodology together with a novel mathematical approach for determining the secondary structures of RNA conformers present in a mixture. A complementary chemical probing technique was also used to support these secondary structure models, to confirm that the RRE2 RNA undergoes a folding transition and to obtain information about the relative positioning of RRE2 substructures in three dimensions. Our analysis collectively suggests that the HIV-2 RRE undergoes two conformational transitions before assuming the energetically most favorable conformer. The 3D models for the HIV-2 RRE and folding intermediates are also presented, wherein the Rev-binding stem–loops (IIB and I) are located coaxially in the former, which is in agreement with previous models for HIV-1 Rev-RRE binding.     

Inverse folding with RNA-As-Graphs produces a large pool of candidate sequences with target topologies

We present an RNA-As-Graphs (RAG) based inverse folding algorithm, RAG-IF, to design novel RNA sequences that fold onto target tree graph topologies. The algorithm can be used to enhance our recently reported computational design pipeline (Jain et al., NAR 2018). The RAG approach represents RNA secondary structures as tree and dual graphs, where RNA loops and helices are coarse-grained as vertices and edges, opening the usage of graph theory methods to study, predict, and design RNA structures. Our recently developed computational pipeline for design utilizes graph partitioning (RAG-3D) and atomic fragment assembly (F-RAG) to design sequences to fold onto RNA-like tree graph topologies; the atomic fragments are taken from existing RNA structures that correspond to tree subgraphs. Because F-RAG may not produce the target folds for all designs, automated mutations by RAG-IF algorithm enhance the candidate pool markedly. The crucial residues for mutation are identified by differences between the predicted and the target topology. A genetic algorithm then mutates the selected residues, and the successful sequences are optimized to retain only the minimal or essential mutations. Here we evaluate RAG-IF for 6 RNA-like topologies and generate a large pool of successful candidate sequences with a variety of minimal mutations. We find that RAG-IF adds robustness and efficiency to our RNA design pipeline, making inverse folding motivated by graph topology rather than secondary structure more productive.     

Extended Structures in RNA Folding Intermediates Are Due to Nonnative Interactions Rather than Electrostatic Repulsion

RNA folding occurs via a series of transitions between metastable intermediate states for Mg²⁺ concentrations below those needed to fold the native structure. In general, these folding intermediates are considerably less compact than their respective native states. Our previous work demonstrates that the major equilibrium intermediate of the 154-residue specificity domain (S-domain) of the Bacillus subtilis RNase P RNA is more extended than its native structure. We now investigate two models with falsifiable predictions regarding the origins of the extended intermediate structures in the S-domains of the B. subtilis and the Escherichia coli RNase P RNA that belong to different classes of P RNA and have distinct native structures. The first model explores the contribution of electrostatic repulsion, while the second model probes specific interactions in the core of the folding intermediate. Using small-angle X-ray scattering and Langevin dynamics simulations, we show that electrostatics plays only a minor role, whereas specific interactions largely account for the extended nature of the intermediate. Structural contacts in the core, including a nonnative base pair, help to stabilize the intermediate conformation. We conclude that RNA folding intermediates adopt extended conformations due to short-range, nonnative interactions rather than generic electrostatic repulsion of helical domains. These principles apply to other ribozymes and riboswitches that undergo functionally relevant conformational changes.     

Prediction of RNA pseudoknots using heuristic modeling with mapping and sequential folding

Predicting RNA secondary structure is often the first step to determining the structure of RNA. Prediction approaches have historically avoided searching for pseudoknots because of the extreme combinatorial and time complexity of the problem. Yet neglecting pseudoknots limits the utility of such approaches. Here, an algorithm utilizing structure mapping and thermodynamics is introduced for RNA pseudoknot prediction that finds the minimum free energy and identifies information about the flexibility of the RNA. The heuristic approach takes advantage of the 5' to 3' folding direction of many biological RNA molecules and is consistent with the hierarchical folding hypothesis and the contact order model. Mapping methods are used to build and analyze the folded structure for pseudoknots and to add important 3D structural considerations. The program can predict some well known pseudoknot structures correctly. The results of this study suggest that many functional RNA sequences are optimized for proper folding. They also suggest directions we can proceed in the future to achieve even better results.     

Coarse-grained modeling of large RNA molecules with knowledge-based potentials and structural filters

Understanding the function of complex RNA molecules depends critically on understanding their structure. However, creating three-dimensional (3D) structural models of RNA remains a significant challenge. We present a protocol (the nucleic acid simulation tool [NAST]) for RNA modeling that uses an RNA-specific knowledge-based potential in a coarse-grained molecular dynamics engine to generate plausible 3D structures. We demonstrate NAST's capabilities by using only secondary structure and tertiary contact predictions to generate, cluster, and rank structures. Representative structures in the best ranking clusters averaged 8.0 ± 0.3 Å and 16.3 ± 1.0 Å RMSD for the yeast phenylalanine tRNA and the P4-P6 domain of the Tetrahymena thermophila group I intron, respectively. The coarse-grained resolution allows us to model large molecules such as the 158-residue P4-P6 or the 388-residue T. thermophila group I intron. One advantage of NAST is the ability to rank clusters of structurally similar decoys based on their compatibility with experimental data. We successfully used ideal small-angle X-ray scattering data and both ideal and experimental solvent accessibility data to select the best cluster of structures for both tRNA and P4-P6. Finally, we used NAST to build in missing loops in the crystal structures of the Azoarcus and Twort ribozymes, and to incorporate crystallographic data into the Michel–Westhof model of the T. thermophila group I intron, creating an integrated model of the entire molecule. Our software package is freely available at https://simtk.org/home/nast.     

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.     

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.     

Structural Rearrangements Linked to Global Folding Pathways of the Azoarcus Group I Ribozyme

Stable RNAs must fold into specific three-dimensional structures to be biologically active, yet many RNAs form metastable structures that compete with the native state. Our previous time-resolved footprinting experiments showed that Azoarcus group I ribozyme forms its tertiary structure rapidly (τ < 30 ms) without becoming significantly trapped in kinetic intermediates. Here, we use stopped-flow fluorescence spectroscopy to probe the global folding kinetics of a ribozyme containing 2-aminopurine in the loop of P9. The modified ribozyme was catalytically active and exhibited two equilibrium folding transitions centered at 0.3 and 1.6 mM Mg²⁺, consistent with previous results. Stopped-flow fluorescence revealed four kinetic folding transitions with observed rate constants of 100, 34, 1, and 0.1 s^− 1 at 37 °C. From comparison with time-resolved Fe(II)-ethylenediaminetetraacetic acid footprinting of the modified ribozyme under the same conditions, these folding transitions were assigned to formation of the I_C intermediate, tertiary folding and docking of the nicked P9 tetraloop, reorganization of the P3 pseudoknot, and refolding of nonnative conformers, respectively. The footprinting results show that 50-60% of the modified ribozyme folds in less than 30 ms, while the rest of the RNA population undergoes slow structural rearrangements that control the global folding rate. The results show how small perturbations to the structure of the RNA, such as a nick in P9, populate kinetic folding intermediates that are not observed in the natural ribozyme.     

Inverse folding of RNA pseudoknot structures

Background  

RNA exhibits a variety of structural configurations. Here we consider a structure to be tantamount to the noncrossing Watson-Crick and G-U-base pairings (secondary structure) and additional cross-serial base pairs. These interactions are called pseudoknots and are observed across the whole spectrum of RNA functionalities. In the context of studying natural RNA structures, searching for new ribozymes and designing artificial RNA, it is of interest to find RNA sequences folding into a specific structure and to analyze their induced neutral networks. Since the established inverse folding algorithms, RNAinverse, RNA-SSD as well as INFO-RNA are limited to RNA secondary structures, we present in this paper the inverse folding algorithm Inv which can deal with 3-noncrossing, canonical pseudoknot structures.     

Design, construction, and analysis of a novel class of self-folding RNA

RNA can play multiple biological roles through use of its three-dimensional (3-D) structures. Recent advances in RNA structural biology have revealed that complex RNA 3D structures are assemblages of double-stranded helices with a variety of tertiary structural motifs. By employing RNA tertiary structural motifs together with the helices, we designed a novel class of self-folding RNA. In RNA composed of three helices (P1, P2, and P3), P1 interacts with P3 via a tetraloop-receptor interaction and P2 forms consecutive base-triples. Two designed RNAs of this class were prepared and their folding properties indicate that they form defined tertiary structures as designed. These RNAs may be used as modular units for constructing artificial ribozymes or nanometer-scale materials.     

A novel SHAPE reagent enables the analysis of RNA structure in living cells with unprecedented accuracy

Due to the mounting evidence that RNA structure plays a critical role in regulating almost any physiological as well as pathological process, being able to accurately define the folding of RNA molecules within living cells has become a crucial need. We introduce here 2-aminopyridine-3-carboxylic acid imidazolide (2A3), as a general probe for the interrogation of RNA structures in vivo. 2A3 shows moderate improvements with respect to the state-of-the-art selective 2′-hydroxyl acylation analyzed by primer extension (SHAPE) reagent NAI on naked RNA under in vitro conditions, but it significantly outperforms NAI when probing RNA structure in vivo, particularly in bacteria, underlining its increased ability to permeate biological membranes. When used as a restraint to drive RNA structure prediction, data derived by SHAPE-MaP with 2A3 yields more accurate predictions than NAI-derived data. Due to its extreme efficiency and accuracy, we can anticipate that 2A3 will rapidly take over conventional SHAPE reagents for probing RNA structures both in vitro and in vivo.     

Comparative 3-D Modeling of tmRNA

Background

Trans-translation releases stalled ribosomes from truncated mRNAs and tags defective proteins for proteolytic degradation using transfer-messenger RNA (tmRNA). This small stable RNA represents a hybrid of tRNA- and mRNA-like domains connected by a variable number of pseudoknots. Comparative sequence analysis of tmRNAs found in bacteria, plastids, and mitochondria provides considerable insights into their secondary structures. Progress toward understanding the molecular mechanism of template switching, which constitutes an essential step in trans-translation, is hampered by our limited knowledge about the three-dimensional folding of tmRNA.

Results

To facilitate experimental testing of the molecular intricacies of trans-translation, which often require appropriately modified tmRNA derivatives, we developed a procedure for building three-dimensional models of tmRNA. Using comparative sequence analysis, phylogenetically-supported 2-D structures were obtained to serve as input for the program ERNA-3D. Motifs containing loops and turns were extracted from the known structures of other RNAs and used to improve the tmRNA models. Biologically feasible 3-D models for the entire tmRNA molecule could be obtained. The models were characterized by a functionally significant close proximity between the tRNA-like domain and the resume codon. Potential conformational changes which might lead to a more open structure of tmRNA upon binding to the ribosome are discussed. The method, described in detail for the tmRNAs of Escherichia coli, Bacillus anthracis, and Caulobacter crescentus, is applicable to every tmRNA.

Conclusion

Improved molecular models of biological significance were obtained. These models will guide in the design of experiments and provide a better understanding of trans-translation. The comparative procedure described here for tmRNA is easily adopted for the modeling the members of other RNA families.