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

RNA-As-Graphs Motif Atlas—Dual Graph Library of RNA Modules and Viral Frameshifting-Element Applications

RNA motif classification is important for understanding structure/function connections and building phylogenetic relationships. Using our coarse-grained RNA-As-Graphs (RAG) representations, we identify recurrent dual graph motifs in experimentally solved RNA structures based on an improved search algorithm that finds and ranks independent RNA substructures. Our expanded list of 183 existing dual graph motifs reveals five common motifs found in transfer RNA, riboswitch, and ribosomal 5S RNA components. Moreover, we identify three motifs for available viral frameshifting RNA elements, suggesting a correlation between viral structural complexity and frameshifting efficiency. We further partition the RNA substructures into 1844 distinct submotifs, with pseudoknots and junctions retained intact. Common modules are internal loops and three-way junctions, and three submotifs are associated with riboswitches that bind nucleotides, ions, and signaling molecules. Together, our library of existing RNA motifs and submotifs adds to the growing universe of RNA modules, and provides a resource of structures and substructures for novel RNA design.

Length-dependent motions of SARS-CoV-2 frameshifting RNA pseudoknot and alternative conformations suggest avenues for frameshifting suppression

The SARS-CoV-2 frameshifting element (FSE), a highly conserved mRNA region required for correct translation of viral polyproteins, defines an excellent therapeutic target against Covid-19. As discovered by our prior graph-theory analysis with SHAPE experiments, the FSE adopts a heterogeneous, length-dependent conformational landscape consisting of an assumed 3-stem H-type pseudoknot (graph motif 3_6), and two alternative motifs (3_3 and 3_5). Here, for the first time, we build and simulate, by microsecond molecular dynamics, 30 models for all three motifs plus motif-stabilizing mutants at different lengths. Our 3_6 pseudoknot systems, which agree with experimental structures, reveal interconvertible L and linear conformations likely related to ribosomal pausing and frameshifting. The 3_6 mutant inhibits this transformation and could hamper frameshifting. Our 3_3 systems exhibit length-dependent stem interactions that point to a potential transition pathway connecting the three motifs during ribosomal elongation. Together, our observations provide new insights into frameshifting mechanisms and anti-viral strategies.

RNAloops: a database of RNA multiloops

MOTIVATION

Knowledge of the 3D structure of RNA supports discovering its functions and is crucial for designing drugs and modern therapeutic solutions. Thus, much attention is devoted to experimental determination and computational prediction targeting the global fold of RNA and its local substructures. The latter include multi-branched loops-functionally significant elements that highly affect the spatial shape of the entire molecule. Unfortunately, their computational modeling constitutes a weak point of structural bioinformatics. A remedy for this is in collecting these motifs and analyzing their features.

RESULTS

RNAloops is a self-updating database that stores multi-branched loops identified in the PDB-deposited RNA structures. A description of each loop includes angular data-planar and Euler angles computed between pairs of adjacent helices to allow studying their mutual arrangement in space. The system enables search and analysis of multiloops, presents their structure details numerically and visually, and computes data statistics.

AVAILABILITY AND IMPLEMENTATION

RNAloops is freely accessible at https://rnaloops.cs.put.poznan.pl.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

GrAfSS: a webserver for substructure similarity searching and comparisons in the structures of proteins and RNA

The GrAfSS (Graph theoretical Applications for Substructure Searching) webserver is a platform to search for three-dimensional substructures of: (i) amino acid side chains in protein structures; and (ii) base arrangements in RNA structures. The webserver interfaces the functions of five different graph theoretical algorithms – ASSAM, SPRITE, IMAAAGINE, NASSAM and COGNAC – into a single substructure searching suite. Users will be able to identify whether a three-dimensional (3D) arrangement of interest, such as a ligand binding site or 3D motif, observed in a protein or RNA structure can be found in other structures available in the Protein Data Bank (PDB). The webserver also allows users to determine whether a protein or RNA structure of interest contains substructural arrangements that are similar to known motifs or 3D arrangements. These capabilities allow for the functional annotation of new structures that were either experimentally determined or computationally generated (such as the coordinates generated by AlphaFold2) and can provide further insights into the diversity or conservation of functional mechanisms of structures in the PDB. The computed substructural superpositions are visualized using integrated NGL viewers. The GrAfSS server is available at http://mfrlab.org/grafss/.

Vernal: a tool for mining fuzzy network motifs in RNA

MOTIVATION

RNA 3D motifs are recurrent substructures, modeled as networks of base pair interactions, which are crucial for understanding structure-function relationships. The task of automatically identifying such motifs is computationally hard, and remains a key challenge in the field of RNA structural biology and network analysis. State-of-the-art methods solve special cases of the motif problem by constraining the structural variability in occurrences of a motif, and narrowing the substructure search space.

RESULTS

Here, we relax these constraints by posing the motif finding problem as a graph representation learning and clustering task. This framing takes advantage of the continuous nature of graph representations to model the flexibility and variability of RNA motifs in an efficient manner. We propose a set of node similarity functions, clustering methods and motif construction algorithms to recover flexible RNA motifs. Our tool, Vernal can be easily customized by users to desired levels of motif flexibility, abundance and size. We show that Vernal is able to retrieve and expand known classes of motifs, as well as to propose novel motifs.

AVAILABILITY AND IMPLEMENTATION

The source code, data and a webserver are available at vernal.cs.mcgill.ca. We also provide a flexible interface and a user-friendly webserver to browse and download our results.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Length-dependent motions of SARS-CoV-2 frameshifting RNA pseudoknot and alternative conformations suggest avenues for frameshifting suppression

Conserved SARS-CoV-2 RNA regions of critical biological functions define excellent targets for anti-viral therapeutics against Covid-19 variants. One such region is the frameshifting element (FSE), responsible for correct translation of viral polyproteins. Here, we analyze molecular-dynamics motions of three FSE conformations, discovered by graph-theory analysis, and associated mutants designed by graph-based inverse folding: two distinct 3-stem H-type pseudoknots and a 3-way junction. We find that the prevalent H-type pseudoknot in literature adopts ring-like conformations, which in combination with 5' end threading could promote ribosomal pausing. An inherent shape switch from "L" to linear that may help trigger the frameshifting is suppressed in our designed mutant. The alternative conformation trajectories suggest a stable intermediate structure with mixed stem interactions of all three conformations, pointing to a possible transition pathway during ribosomal translation. These observations provide new insights into anti-viral strategies and frameshifting mechanisms.

A Fiedler Vector Scoring Approach for Novel RNA Motif Selection

Novel RNA motif design is of great practical importance for technology and medicine. Increasingly, computational design plays an important role in such efforts. Our coarse-grained RAG (RNA-As-Graphs) framework offers strategies for enumerating the universe of RNA 2D folds, selecting "RNA-like" candidates for design, and determining sequences that fold onto these candidates. In RAG, RNA secondary structures are represented as tree or dual graphs. Graphs with known RNA structures are called "existing", and the others are labeled "hypothetical". By using simplified features for RNA graphs, we have clustered the hypothetical graphs into "RNA-like" and "non-RNA-like" groups and proposed RNA-like graphs as candidates for design. Here, we propose a new way of designing graph features by using Fiedler vectors. The new features reflect graph shapes better, and they lead to a more clustered organization of existing graphs. We show significant increases in K-means clustering accuracy by using the new features (e.g., up to 95% and 98% accuracy for tree and dual graphs, respectively). In addition, we propose a scoring model for top graph candidate selection. This scoring model allows users to set a threshold for candidates, and it incorporates weighing of existing graphs based on their corresponding number of known RNAs. We include a list of top scored RNA-like candidates, which we hope will stimulate future novel RNA design.

Structure-altering mutations of the SARS-CoV-2 frameshifting RNA element

With the rapid rate of COVID-19 infections and deaths, treatments and cures besides hand washing, social distancing, masks, isolation, and quarantines are urgently needed. The treatments and vaccines rely on the basic biophysics of the complex viral apparatus. Although proteins are serving as main drug and vaccine targets, therapeutic approaches targeting the 30,000 nucleotide RNA viral genome form important complementary approaches. Indeed, the high conservation of the viral genome, its close evolutionary relationship to other viruses, and the rise of gene editing and RNA-based vaccines all argue for a focus on the RNA agent itself. One of the key steps in the viral replication cycle inside host cells is the ribosomal frameshifting required for translation of overlapping open reading frames. The RNA frameshifting element (FSE), one of three highly conserved regions of coronaviruses, is believed to include a pseudoknot considered essential for this ribosomal switching. In this work, we apply our graph-theory-based framework for representing RNA secondary structures, "RAG (or RNA-As-Graphs)," to alter key structural features of the FSE of the SARS-CoV-2 virus. Specifically, using RAG machinery of genetic algorithms for inverse folding adapted for RNA structures with pseudoknots, we computationally predict minimal mutations that destroy a structurally important stem and/or the pseudoknot of the FSE, potentially dismantling the virus against translation of the polyproteins. Our microsecond molecular dynamics simulations of mutant structures indicate relatively stable secondary structures. These findings not only advance our computational design of RNAs containing pseudoknots, they pinpoint key residues of the SARS-CoV-2 virus as targets for antiviral drugs and gene editing approaches.

Structure-Altering Mutations of the SARS-CoV-2 Frame Shifting RNA Element

With the rapid rate of Covid-19 infections and deaths, treatments and cures besides hand washing, social distancing, masks, isolation, and quarantines are urgently needed. The treatments and vaccines rely on the basic biophysics of the complex viral apparatus. While proteins are serving as main drug and vaccine targets, therapeutic approaches targeting the 30,000 nucleotide RNA viral genome form important complementary approaches. Indeed, the high conservation of the viral genome, its close evolutionary relationship to other viruses, and the rise of gene editing and RNA-based vaccines all argue for a focus on the RNA agent itself. One of the key steps in the viral replication cycle inside host cells is the ribosomal frameshifting required for translation of overlapping open reading frames. The frameshifting element (FSE), one of three highly conserved regions of coronaviruses, includes an RNA pseudoknot considered essential for this ribosomal switching. In this work, we apply our graph-theory-based framework for representing RNA secondary structures, "RAG" (RNA-As Graphs), to alter key structural features of the FSE of the SARS-CoV-2 virus. Specifically, using RAG machinery of genetic algorithms for inverse folding adapted for RNA structures with pseudoknots, we computationally predict minimal mutations that destroy a structurally-important stem and/or the pseudoknot of the FSE, potentially dismantling the virus against translation of the polyproteins. Additionally, our microsecond molecular dynamics simulations of mutant structures indicate relatively stable secondary structures. These findings not only advance our computational design of RNAs containing pseudoknots; they pinpoint to key residues of the SARS-CoV-2 virus as targets for anti-viral drugs and gene editing approaches.

NAPS update: network analysis of molecular dynamics data and protein-nucleic acid complexes

Network theory is now a method of choice to gain insights in understanding protein structure, folding and function. In combination with molecular dynamics (MD) simulations, it is an invaluable tool with widespread applications such as analyzing subtle conformational changes and flexibility regions in proteins, dynamic correlation analysis across distant regions for allosteric communications, in drug design to reveal alternative binding pockets for drugs, etc. Updated version of NAPS now facilitates network analysis of the complete repertoire of these biomolecules, i.e., proteins, protein–protein/nucleic acid complexes, MD trajectories, and RNA. Various options provided for analysis of MD trajectories include individual network construction and analysis of intermediate time-steps, comparative analysis of these networks, construction and analysis of average network of the ensemble of trajectories and dynamic cross-correlations. For protein–nucleic acid complexes, networks of the whole complex as well as that of the interface can be constructed and analyzed. For analysis of proteins, protein–protein complexes and MD trajectories, network construction based on inter-residue interaction energies with realistic edge-weights obtained from standard force fields is provided to capture the atomistic details. Updated version of NAPS also provides improved visualization features, interactive plots and bulk execution. URL: http://bioinf.iiit.ac.in/NAPS/

Identification of novel RNA design candidates by clustering the extended RNA-As-Graphs library

BACKGROUND

We re-evaluate our RNA-As-Graphs clustering approach, using our expanded graph library and new RNA structures, to identify potential RNA-like topologies for design. Our coarse-grained approach represents RNA secondary structures as tree and dual graphs, with vertices and edges corresponding to RNA helices and loops. The graph theoretical framework facilitates graph enumeration, partitioning, and clustering approaches to study RNA structure and its applications.

METHODS

Clustering graph topologies based on features derived from graph Laplacian matrices and known RNA structures allows us to classify topologies into 'existing' or hypothetical, and the latter into, 'RNA-like' or 'non RNA-like' topologies. Here we update our list of existing tree graph topologies and RAG-3D database of atomic fragments to include newly determined RNA structures. We then use linear and quadratic regression, optionally with dimensionality reduction, to derive graph features and apply several clustering algorithms on our tree-graph library and recently expanded dual-graph library to classify them into the three groups.

RESULTS

The unsupervised PAM and K-means clustering approaches correctly classify 72-77% of all existing graph topologies and 75-82% of newly added ones as RNA-like. For supervised k-NN clustering, the cross-validation accuracy ranges from 57 to 81%.

CONCLUSIONS

Using linear regression with unsupervised clustering, or quadratic regression with supervised clustering, provides better accuracies than supervised/linear clustering. All accuracies are better than random, especially for newly added existing topologies, thus lending credibility to our approach.

GENERAL SIGNIFICANCE

Our updated RAG-3D database and motif classification by clustering present new RNA substructures and RNA-like motifs as novel design candidates.

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.

Identification of Structural Motifs Using Networks of Hydrogen-Bonded Base Interactions in RNA Crystallographic Structures

RNA structural motifs can be identified using methods that analyze base–base interactions and the conformation of a structure’s backbone; however, these approaches do not necessarily take into consideration the hydrogen bonds that connect the bases or the networks of inter-connected hydrogen-bonded bases that are found in RNA structures. Large clusters of RNA bases that are tightly inter-connected by a network of hydrogen bonds are expected to be stable and relatively rigid substructures. Such base arrangements could therefore be present as structural motifs in RNA structures, especially when there is a requirement for a highly stable support platform or substructure to ensure the correct folding and spatial maintenance of functional sites that partake in catalysis or binding interactions. In order to test this hypothesis, we conducted a search in available RNA crystallographic structures in the Protein Data Bank database using queries that searched for profiles of bases inter-connected by hydrogen bonds. This method of searching does not require to have prior knowledge of the arrangement being searched. Our search results identified two clusters of six bases that are inter-connected by a network of hydrogen bonds. These arrangements of base sextuples have never been previously reported, thus making this the first report that proposes them as novel RNA tertiary motifs.

RAG-Web: RNA structure prediction/design using RNA-As-Graphs

SUMMARY

We launch a webserver for RNA structure prediction and design corresponding to tools developed using our RNA-As-Graphs (RAG) approach. RAG uses coarse-grained tree graphs to represent RNA secondary structure, allowing the application of graph theory to analyze and advance RNA structure discovery. Our webserver consists of three modules: (a) RAG Sampler: samples tree graph topologies from an RNA secondary structure to predict corresponding tertiary topologies, (b) RAG Builder: builds three-dimensional atomic models from candidate graphs generated by RAG Sampler, and (c) RAG Designer: designs sequences that fold onto novel RNA motifs (described by tree graph topologies). Results analyses are performed for further assessment/selection. The Results page provides links to download results and indicates possible errors encountered. RAG-Web offers a user-friendly interface to utilize our RAG software suite to predict and design RNA structures and sequences.

AVAILABILITY AND IMPLEMENTATION

The webserver is freely available online at: http://www.biomath.nyu.edu/ragtop/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A pipeline for computational design of novel RNA-like topologies

Designing novel RNA topologies is a challenge, with important therapeutic and industrial applications. We describe a computational pipeline for design of novel RNA topologies based on our coarse-grained RNA-As-Graphs (RAG) framework. RAG represents RNA structures as tree graphs and describes RNA secondary (2D) structure topologies (currently up to 13 vertices, ≈260 nucleotides). We have previously identified novel graph topologies that are RNA-like among these. Here we describe a systematic design pipeline and illustrate design for six broad design problems using recently developed tools for graph-partitioning and fragment assembly (F-RAG). Following partitioning of the target graph, corresponding atomic fragments from our RAG-3D database are combined using F-RAG, and the candidate atomic models are scored using a knowledge-based potential developed for 3D structure prediction. The sequences of the top scoring models are screened further using available tools for 2D structure prediction. The results indicate that our modular approach based on RNA-like topologies rather than specific 2D structures allows for greater flexibility in the design process, and generates a large number of candidate sequences quickly. Experimental structure probing using SHAPE-MaP for two sequences agree with our predictions and suggest that our combined tools yield excellent candidates for further sequence and experimental screening.

An extended dual graph library and partitioning algorithm applicable to pseudoknotted RNA structures

Exploring novel RNA topologies is imperative for understanding RNA structure and pursuing its design. Our RNA-As-Graphs (RAG) approach exploits graph theory tools and uses coarse-grained tree and dual graphs to represent RNA helices and loops by vertices and edges. Only dual graphs represent pseudoknotted RNAs fully. Here we develop a dual graph enumeration algorithm to generate an expanded library of dual graph topologies for 2-9 vertices, and extend our dual graph partitioning algorithm to identify all possible RNA subgraphs. Our enumeration algorithm connects smaller-vertex graphs, using all possible edge combinations, to build larger-vertex graphs and retain all non-isomorphic graph topologies, thereby more than doubling the size of our prior library to a total of 110,667 dual graph topologies. We apply our dual graph partitioning algorithm, which keeps pseudoknots and junctions intact, to all existing RNA structures to identify all possible substructures up to 9 vertices. In addition, our expanded dual graph library assigns graph topologies to all RNA graphs and subgraphs, rectifying prior inconsistencies. We update our RAG-3Dual database of RNA atomic fragments with all newly identified substructures and their graph IDs, increasing its size by more than 50 times. The enlarged dual graph library and RAG-3Dual database provide a comprehensive repertoire of graph topologies and atomic fragments to study yet undiscovered RNA molecules and design RNA sequences with novel topologies, including a variety of pseudoknotted RNAs.

Dual Graph Partitioning Highlights a Small Group of Pseudoknot-Containing RNA Submotifs

RNA molecules are composed of modular architectural units that define their unique structural and functional properties. Characterization of these building blocks can help interpret RNA structure/function relationships. We present an RNA secondary structure motif and submotif library using dual graph representation and partitioning. Dual graphs represent RNA helices as vertices and loops as edges. Unlike tree graphs, dual graphs can represent RNA pseudoknots (intertwined base pairs). For a representative set of RNA structures, we construct dual graphs from their secondary structures, and apply our partitioning algorithm to identify non-separable subgraphs (or blocks) without breaking pseudoknots. We report 56 subgraph blocks up to nine vertices; among them, 22 are frequently occurring, 15 of which contain pseudoknots. We then catalog atomic fragments corresponding to the subgraph blocks to define a library of building blocks that can be used for RNA design, which we call RAG-3Dual, as we have done for tree graphs. As an application, we analyze the distribution of these subgraph blocks within ribosomal RNAs of various prokaryotic and eukaryotic species to identify common subgraphs and possible ancestry relationships. Other applications of dual graph partitioning and motif library can be envisioned for RNA structure analysis and design.

Adventures with RNA graphs

The structure of RNA has been a natural subject for mathematical modeling, inviting many innovative computational frameworks. This single-stranded polynucleotide chain can fold upon itself in numerous ways to form hydrogen-bonded segments, imperfect with single-stranded loops. Illustrating these paired and non-paired interaction networks, known as RNA's secondary (2D) structure, using mathematical graph objects has been illuminating for RNA structure analysis. Building upon such seminal work from the 1970s and 1980s, graph models are now used to study not only RNA structure but also describe RNA's recurring modular units, sample the conformational space accessible to RNAs, predict RNA's three-dimensional folds, and apply the combined aspects to novel RNA design. In this article, we outline the development of the RNA-As-Graphs (or RAG) approach and highlight current applications to RNA structure prediction and design.

R3D-BLAST2: an improved search tool for similar RNA 3D substructures

Background

RNA molecules have been known to play a variety of significant roles in cells. In principle, the functions of RNAs are largely determined by their three-dimensional (3D) structures. As more and more RNA 3D structures are available in the Protein Data Bank (PDB), a bioinformatics tool, which is able to rapidly and accurately search the PDB database for similar RNA 3D structures or substructures, is helpful to understand the structural and functional relationships of RNAs.

Results

Since its first release in 2011, R3D-BLAST has become a useful tool for searching the PDB database for similar RNA 3D structures and substructures. It was implemented by a structural-alphabet (SA)-based method, which utilizes an SA with 23 structural letters to encode RNA 3D structures into one-dimensional (1D) structural sequences and applies BLAST to the resulting structural sequences for searching similar substructures of RNAs. In this study, we have upgraded R3D-BLAST to develop a new web server named R3D-BLAST2 based on a higher quality SA newly constructed from a representative and sufficiently non-redundant list of RNA 3D structures. In addition, we have modified the kernel program in R3D-BLAST2 so that it can accept an RNA structure in the mmCIF format as an input. The results of our experiments on a benchmark dataset have demonstrated that R3D-BLAST2 indeed performs very well in comparison to its earlier version R3D-BLAST and other similar tools RNA FRABASE, FASTR3D and RAG-3D by searching a larger number of RNA 3D substructures resembling those of the input RNA.

Conclusions

R3D-BLAST2 is a valuable BLAST-like search tool that can more accurately scan the PDB database for similar RNA 3D substructures. It is publicly available at http://genome.cs.nthu.edu.tw/R3D-BLAST2/.

F-RAG: Generating Atomic Coordinates from RNA Graphs by Fragment Assembly

Coarse-grained models represent attractive approaches to analyze and simulate ribonucleic acid (RNA) molecules, for example, for structure prediction and design, as they simplify the RNA structure to reduce the conformational search space. Our structure prediction protocol RAGTOP (RNA-As-Graphs Topology Prediction) represents RNA structures as tree graphs and samples graph topologies to produce candidate graphs. However, for a more detailed study and analysis, construction of atomic from coarse-grained models is required. Here we present our graph-based fragment assembly algorithm (F-RAG) to convert candidate three-dimensional (3D) tree graph models, produced by RAGTOP into atomic structures. We use our related RAG-3D utilities to partition graphs into subgraphs and search for structurally similar atomic fragments in a data set of RNA 3D structures. The fragments are edited and superimposed using common residues, full atomic models are scored using RAGTOP's knowledge-based potential, and geometries of top scoring models is optimized. To evaluate our models, we assess all-atom RMSDs and Interaction Network Fidelity (a measure of residue interactions) with respect to experimentally solved structures and compare our results to other fragment assembly programs. For a set of 50 RNA structures, we obtain atomic models with reasonable geometries and interactions, particularly good for RNAs containing junctions. Additional improvements to our protocol and databases are outlined. These results provide a good foundation for further work on RNA structure prediction and design applications.

Using sequence signatures and kink-turn motifs in knowledge-based statistical potentials for RNA structure prediction

Kink turns are widely occurring motifs in RNA, located in internal loops and associated with many biological functions including translation, regulation and splicing. The associated sequence pattern, a 3-nt bulge and G-A, A-G base-pairs, generates an angle of ∼50° along the helical axis due to A-minor interactions. The conserved sequence and distinct secondary structures of kink-turns (k-turn) suggest computational folding rules to predict k-turn-like topologies from sequence. Here, we annotate observed k-turn motifs within a non-redundant RNA dataset based on sequence signatures and geometrical features, analyze bending and torsion angles, and determine distinct knowledge-based potentials with and without k-turn motifs. We apply these scoring potentials to our RAGTOP (RNA-As-Graph-Topologies) graph sampling protocol to construct and sample coarse-grained graph representations of RNAs from a given secondary structure. We present graph-sampling results for 35 RNAs, including 12 k-turn and 23 non k-turn internal loops, and compare the results to solved structures and to RAGTOP results without special k-turn potentials. Significant improvements are observed with the updated scoring potentials compared to the k-turn-free potentials. Because k-turns represent a classic example of sequence/structure motif, our study suggests that other such motifs with sequence signatures and unique geometrical features can similarly be utilized for RNA structure prediction and design.

RNA structure prediction: from 2D to 3D

We summarize different levels of RNA structure prediction, from classical 2D structure to extended secondary structure and motif-based research toward 3D structure prediction of RNA. We outline the importance of classical secondary structure during all those levels of structure prediction.

Opportunities and Challenges in RNA Structural Modeling and Design

We describe opportunities and challenges in RNA structural modeling and design, as recently discussed during the second Telluride Science Research Center workshop organized in June 2016. Topics include fundamental processes of RNA, such as structural assemblies (hierarchical folding, multiple conformational states and their clustering), RNA motifs, and chemical reactivity of RNA, as used for structural prediction and functional inference. We also highlight the software and database issues associated with RNA structures, such as the multiple approaches for motif annotation, the need for frequent database updating, and the importance of quality control of RNA structures. We discuss various modeling approaches for structure prediction, mechanistic analysis of RNA reactions, and RNA design, and the complementary roles that both atomistic and coarse-grained approaches play in such simulations. Collectively, as scientists from varied disciplines become familiar and drawn into these unique challenges, new approaches and collaborative efforts will undoubtedly be catalyzed.

Capturing RNA Folding Free Energy with Coarse-Grained Molecular Dynamics Simulations

We introduce a coarse-grained RNA model for molecular dynamics simulations, RACER (RnA CoarsE-gRained). RACER achieves accurate native structure prediction for a number of RNAs (average RMSD of 2.93 Å) and the sequence-specific variation of free energy is in excellent agreement with experimentally measured stabilities (R2 = 0.93). Using RACER, we identified hydrogen-bonding (or base pairing), base stacking, and electrostatic interactions as essential driving forces for RNA folding. Also, we found that separating pairing vs. stacking interactions allowed RACER to distinguish folded vs. unfolded states. In RACER, base pairing and stacking interactions each provide an approximate stability of 3-4 kcal/mol for an A-form helix. RACER was developed based on PDB structural statistics and experimental thermodynamic data. In contrast with previous work, RACER implements a novel effective vdW potential energy function, which led us to re-parameterize hydrogen bond and electrostatic potential energy functions. Further, RACER is validated and optimized using a simulated annealing protocol to generate potential energy vs. RMSD landscapes. Finally, RACER is tested using extensive equilibrium pulling simulations (0.86 ms total) on eleven RNA sequences (hairpins and duplexes).

Sizes of Long RNA Molecules Are Determined by the Branching Patterns of Their Secondary Structures

Long RNA molecules are at the core of gene regulation across all kingdoms of life, while also serving as genomes in RNA viruses. Few studies have addressed the basic physical properties of long single-stranded RNAs. Long RNAs with nonrepeating sequences usually adopt highly ramified secondary structures and are better described as branched polymers. To test whether a branched polymer model can estimate the overall sizes of large RNAs, we employed fluorescence correlation spectroscopy to examine the hydrodynamic radii of a broad spectrum of biologically important RNAs, ranging from viral genomes to long noncoding regulatory RNAs. The relative sizes of long RNAs measured at low ionic strength correspond well to those predicted by two theoretical approaches that treat the effective branching associated with secondary structure formation-one employing the Kramers theorem for calculating radii of gyration, and the other featuring the metric of maximum ladder distance. Upon addition of multivalent cations, most RNAs are found to be compacted as compared with their original, low ionic-strength sizes. These results suggest that sizes of long RNA molecules are determined by the branching pattern of their secondary structures. We also experimentally validate the proposed computational approaches for estimating hydrodynamic radii of single-stranded RNAs, which use generic RNA structure prediction tools and thus can be universally applied to a wide range of long RNAs.