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

Prediction of 3D RNA Structures from Sequence Using Energy Landscapes of RNA Dimers: Application to RNA Tetraloops

Access to the three-dimensional structure of RNA enables an ability to gain a more profound understanding of its biological mechanisms, as well as the ability to design RNA-targeting drugs, which can take advantage of the unique chemical environment imposed by a folded RNA structure. Due to the dynamic and structurally complex properties of RNA, both experimental and traditional computational methods have difficulty in determining RNA's 3D structure. Herein, we introduce TAPERSS (Theoretical Analyses, Prediction, and Evaluation of RNA Structures from Sequence), a physics-based fragment assembly method for predicting 3D RNA structures from sequence. Using a fragment library created using discrete path sampling calculations of RNA dinucleoside monophosphates, TAPERSS can sample the physics-based energy landscapes of any RNA sequence with relatively low computational complexity. We have benchmarked TAPERSS on 21 RNA tetraloops, using a combinatorial algorithm as a proof-of-concept. We show that TAPERSS was successfully able to predict the apo-state structures of all 21 RNA hairpins, with 16 of those structures also having low predicted energies as well. We demonstrate that TAPERSS performs most accurately on GNRA-like tetraloops with mostly stacked loop-nucleotides, while having limited success with more dynamic UNCG and CUYG tetraloops, most likely due to the influence of the RNA force field used to create the fragment library. Moreover, we show that TAPERSS can successfully predict the majority of the experimental non-apo states, highlighting its potential in anticipating biologically significant yet unobserved states. This holds great promise for future applications in drug design and related studies. With discussed improvements and implementation of more efficient sampling algorithms, we believe TAPERSS may serve as a useful tool for a physics-based conformational sampling of large RNA structures.

Predicting 3D RNA structure from the nucleotide sequence using Euclidean neural networks

Fast and accurate 3D RNA structure prediction remains a major challenge in structural biology, mostly due to the size and flexibility of RNA molecules, as well as the lack of diverse experimentally determined structures of RNA molecules. Unlike DNA structure, RNA structure is far less constrained by basepair hydrogen bonding, resulting in an explosion of potential stable states. Here, we propose a convolutional neural network that predicts all pairwise distances between residues in an RNA, using a recently described smooth parametrization of Euclidean distance matrices. We achieve high-accuracy predictions on RNAs up to 100 nt in length in fractions of a second, a factor of 107 faster than existing molecular dynamics-based methods. We also convert our coarse-grained machine learning output into an all-atom model using discrete molecular dynamics with constraints. Our proposed computational pipeline predicts all-atom RNA models solely from the nucleotide sequence. However, this method suffers from the same limitation as nucleic acid molecular dynamics: the scarcity of available RNA crystal structures for training.

Advances in RNA 3D Structure Prediction

RNA molecules carry out various cellular functions, and understanding the mechanisms behind their functions requires the knowledge of their 3D structures. Different types of computational methods have been developed to model RNA 3D structures over the past decade. These methods were widely used by researchers although their performance needs to be further improved. Recently, along with these traditional methods, machine-learning techniques have been increasingly applied to RNA 3D structure prediction and show significant improvement in performance. Here we shall give a brief review of the traditional methods and recent related advances in machine-learning approaches for RNA 3D structure prediction.

FebRNA: An automated fragment-ensemble-based model for building RNA 3D structures

Knowledge of RNA three-dimensional (3D) structures is critical to understanding the important biological functions of RNAs. Although various structure prediction models have been developed, the high-accuracy predictions of RNA 3D structures are still limited to the RNAs with short lengths or with simple topology. In this work, we proposed a new model, namely FebRNA, for building RNA 3D structures through fragment assembly based on coarse-grained (CG) fragment ensembles. Specifically, FebRNA is composed of four processes: establishing the library of different types of non-redundant CG fragment ensembles regardless of the sequences, building CG 3D structure ensemble through fragment assembly, identifying top-scored CG structures through a specific CG scoring function, and rebuilding the all-atom structures from the top-scored CG ones. Extensive examination against different types of RNA structures indicates that FebRNA consistently gives the reliable predictions on RNA 3D structures, including pseudoknots, three-way junctions, four-way and five-way junctions, and RNAs in the RNA-Puzzles. FebRNA is available on the Web site: https://github.com/Tan-group/FebRNA.

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.

Length-Dependent Deep Learning Model for RNA Secondary Structure Prediction

Deep learning methods for RNA secondary structure prediction have shown higher performance than traditional methods, but there is still much room to improve. It is known that the lengths of RNAs are very different, as are their secondary structures. However, the current deep learning methods all use length-independent models, so it is difficult for these models to learn very different secondary structures. Here, we propose a length-dependent model that is obtained by further training the length-independent model for different length ranges of RNAs through transfer learning. 2dRNA, a coupled deep learning neural network for RNA secondary structure prediction, is used to do this. Benchmarking shows that the length-dependent model performs better than the usual length-independent model.

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.

rsRNASP: A residue-separation-based statistical potential for RNA 3D structure evaluation

Knowledge-based statistical potentials have been shown to be rather effective in protein 3-dimensional (3D) structure evaluation and prediction. Recently, several statistical potentials have been developed for RNA 3D structure evaluation, while their performances are either still at a low level for the test datasets from structure prediction models or dependent on the "black-box" process through neural networks. In this work, we have developed an all-atom distance-dependent statistical potential based on residue separation for RNA 3D structure evaluation, namely rsRNASP, which is composed of short- and long-ranged potentials distinguished by residue separation. The extensive examinations against available RNA test datasets show that rsRNASP has apparently higher performance than the existing statistical potentials for the realistic test datasets with large RNAs from structure prediction models, including the newly released RNA-Puzzles dataset, and is comparable to the existing top statistical potentials for the test datasets with small RNAs or near-native decoys. In addition, rsRNASP is superior to RNA3DCNN, a recently developed scoring function through 3D convolutional neural networks. rsRNASP and the relevant databases are available to the public.

Biomolecular Modeling and Simulation: A Prospering Multidisciplinary Field

We reassess progress in the field of biomolecular modeling and simulation, following up on our perspective published in 2011. By reviewing metrics for the field's productivity and providing examples of success, we underscore the productive phase of the field, whose short-term expectations were overestimated and long-term effects underestimated. Such successes include prediction of structures and mechanisms; generation of new insights into biomolecular activity; and thriving collaborations between modeling and experimentation, including experiments driven by modeling. We also discuss the impact of field exercises and web games on the field's progress. Overall, we note tremendous success by the biomolecular modeling community in utilization of computer power; improvement in force fields; and development and application of new algorithms, notably machine learning and artificial intelligence. The combined advances are enhancing the accuracy andscope of modeling and simulation, establishing an exemplary discipline where experiment and theory or simulations are full partners.

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.

3dRNA: Building RNA 3D structure with improved template library

Most of computational methods of building RNA tertiary structure are template-based. The template-based methods usually can give more accurate 3D structures due to the use of native 3D templates, but they cannot work if the 3D templates are not available. So, a more complete library of the native 3D templates is very important for this type of methods. 3dRNA is a template-based method for building RNA tertiary structure previously proposed by us. In this paper we report improved 3D template libraries of 3dRNA by using two different schemes that give two libraries 3dRNA_Lib1 and 3dRNA_Lib2. These libraries expand the original one by nearly ten times. Benchmark shows that they can significantly increase the accuracy of 3dRNA, especially in building complex and large RNA 3D structures.

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.

Structure folding of RNA kissing complexes in salt solutions: predicting 3D structure, stability, and folding pathway

RNA kissing complexes are essential for genomic RNA dimerization and regulation of gene expression, and their structures and stability are critical to their biological functions. In this work, we used our previously developed coarse-grained model with an implicit structure-based electrostatic potential to predict three-dimensional (3D) structures and stability of RNA kissing complexes in salt solutions. For extensive RNA kissing complexes, our model shows great reliability in predicting 3D structures from their sequences, and our additional predictions indicate that the model can capture the dependence of 3D structures of RNA kissing complexes on monovalent/divalent ion concentrations. Moreover, the comparisons with extensive experimental data show that the model can make reliable predictions on the stability for various RNA kissing complexes over wide ranges of monovalent/divalent ion concentrations. Notably, for RNA kissing complexes, our further analyses show the important contribution of coaxial stacking to the 3D structures and stronger stability than the corresponding kissing-interface duplexes at high salts. Furthermore, our comprehensive analyses for RNA kissing complexes reveal that the thermally folding pathway for a complex sequence is mainly determined by the relative stability of two possible folded states of kissing complex and extended duplex, which can be significantly modulated by its sequence.

3dRNA v2.0: An Updated Web Server for RNA 3D Structure Prediction

3D structures of RNAs are the basis for understanding their biological functions. However, experimentally solved RNA 3D structures are very limited in comparison with known RNA sequences up to now. Therefore, many computational methods have been proposed to solve this problem, including our 3dRNA. In recent years, 3dRNA has been greatly improved by adding several important features, including structure sampling, structure ranking and structure optimization under residue-residue restraints. Particularly, the optimization procedure with restraints enables 3dRNA to treat pseudoknots in a new way. These new features of 3dRNA can greatly promote its performance and have been integrated into the 3dRNA v2.0 web server. Here we introduce these new features in the 3dRNA v2.0 web server for the users.

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.

What is the best reference state for building statistical potentials in RNA 3D structure evaluation?

Knowledge-based statistical potentials have been shown to be efficient in protein structure evaluation/prediction, and the core difference between various statistical potentials is attributed to the choice of reference states. However, for RNA 3D structure evaluation, a comprehensive examination on reference states is still lacking. In this work, we built six statistical potentials based on six reference states widely used in protein structure evaluation, including averaging, quasi-chemical approximation, atom-shuffled, finite-ideal-gas, spherical-noninteracting, and random-walk-chain reference states, and we examined the six reference states against three RNA test sets including six subsets. Our extensive examinations show that, overall, for identifying native structures and ranking decoy structures, the finite-ideal-gas and random-walk-chain reference states are slightly superior to others, while for identifying near-native structures, there is only a slight difference between these reference states. Our further analyses show that the performance of a statistical potential is apparently dependent on the quality of the training set. Furthermore, we found that the performance of a statistical potential is closely related to the origin of test sets, and for the three realistic test subsets, the six statistical potentials have overall unsatisfactory performance. This work presents a comprehensive examination on the existing reference states and statistical potentials for RNA 3D structure evaluation.

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.

Modeling Structure, Stability, and Flexibility of Double-Stranded RNAs in Salt Solutions

Double-stranded (ds) RNAs play essential roles in many processes of cell metabolism. The knowledge of three-dimensional (3D) structure, stability, and flexibility of dsRNAs in salt solutions is important for understanding their biological functions. In this work, we further developed our previously proposed coarse-grained model to predict 3D structure, stability, and flexibility for dsRNAs in monovalent and divalent ion solutions through involving an implicit structure-based electrostatic potential. The model can make reliable predictions for 3D structures of extensive dsRNAs with/without bulge/internal loops from their sequences, and the involvement of the structure-based electrostatic potential and corresponding ion condition can improve the predictions for 3D structures of dsRNAs in ion solutions. Furthermore, the model can make good predictions for thermal stability for extensive dsRNAs over the wide range of monovalent/divalent ion concentrations, and our analyses show that the thermally unfolding pathway of dsRNA is generally dependent on its length as well as its sequence. In addition, the model was employed to examine the salt-dependent flexibility of a dsRNA helix, and the calculated salt-dependent persistence lengths are in good accordance with experiments.

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.

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.