RNA-As-Graphs Research Articles

Assessing Global-Local Secondary Structure Fingerprints to Classify RNA Sequences With Deep Learning.

RNA elements that are transcribed but not translated into proteins are called non-coding RNAs (ncRNAs). They play wide-ranging roles in biological processes and disorders. Just like proteins, their structure is often intimately linked to their function. Many examples have been documented where structure is conserved across taxa despite sequence divergence. Thus, structure is often used to identify function. Specifically, the secondary structure is predicted and ncRNAs with similar structures are assumed to have same or similar functions. However, a strand of RNA can fold into multiple possible structures, and some strands even fold differently in vivo and in vitro. Furthermore, ncRNAs often function as RNA-protein complexes, which can affect structure. Because of these, we hypothesized using one structure per sequence may discard information, possibly resulting in poorer classification accuracy. Therefore, we propose using secondary structure fingerprints, comprising two categories: a higher-level representation derived from RNA-As-Graphs (RAG), and free energy fingerprints based on a curated repertoire of small structural motifs. The fingerprints take into account the difference between global and local structural matches. We also evaluated our deep learning architecture with k-mers. By combining our global-local fingerprints with 6-mer, we achieved an accuracy, precision, and recall of 91.04%, 91.10%, and 91.00%.

Evolution of coronavirus frameshifting elements: Competing stem networks explain conservation and variability

The frameshifting RNA element (FSE) in coronaviruses (CoVs) regulates the programmed -1 ribosomal frameshift (-1 PRF) mechanism common to many viruses. The FSE is of particular interest as a promising drug candidate. Its associated pseudoknot or stem loop structure is thought to play a large role in frameshifting and thus viral protein production. To investigate the FSE structural evolution, we use our graph theory-based methods for representing RNA secondary structures in the RNA-As-Graphs (RAG) framework to calculate conformational landscapes of viral FSEs with increasing sequence lengths for representative 10 Alpha and 13 Beta-CoVs. By following length-dependent conformational changes, we show that FSE sequences encode many possible competing stems which in turn favor certain FSE topologies, including a variety of pseudoknots, stem loops, and junctions. We explain alternative competing stems and topological FSE changes by recurring patterns of mutations. At the same time, FSE topology robustness can be understood by shifted stems within different sequence contexts and base pair coevolution. We further propose that the topology changes reflected by length-dependent conformations contribute to tuning the frameshifting efficiency. Our work provides tools to analyze virus sequence/structure correlations, explains how sequence and FSE structure have evolved for CoVs, and provides insights into potential mutations for therapeutic applications against a broad spectrum of CoV FSEs by targeting key sequence/structural transitions.

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.

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.

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.

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

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

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.

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.

Predicting Large RNA-Like Topologies by a Knowledge-Based Clustering Approach

An analysis and expansion of our resource for classifying, predicting, and designing RNA structures, RAG (RNA-As-Graphs), is presented, with the goal of understanding features of RNA-like and non-RNA-like motifs and exploiting this information for RNA design. RAG was first reported in 2004 for cataloging RNA secondary structure motifs using graph representations. In 2011, the RAG resource was updated with the increased availability of RNA structures and was improved by utilities for analyzing RNA structures, including substructuring and search tools. We also classified RNA structures as graphs up to 10 vertices (~200 nucleotides) into three classes: existing, RNA-like, and non-RNA-like using clustering approaches. Here, we focus on the tree graphs and evaluate the newly founded RNAs since 2011, which also support our refined predictions of RNA-like motifs. We expand the RAG resource for large tree graphs up to 13 vertices (~260 nucleotides), thereby cataloging more than 10 times as many secondary structures. We apply clustering algorithms based on features of RNA secondary structures translated from known tertiary structures to suggest which hypothetical large RNA motifs can be considered “RNA-like”. The results by the PAM (Partitioning Around Medoids) approach, in particular, reveal good accuracy, with small error for the largest cases. The RAG update here up to 13 vertices offers a useful graph-based tool for exploring RNA motifs and suggesting large RNA motifs for design.

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.

RNA graph partitioning for the discovery of RNA modularity: a novel application of graph partition algorithm to biology.

Graph representations have been widely used to analyze and design various economic, social, military, political, and biological networks. In systems biology, networks of cells and organs are useful for understanding disease and medical treatments and, in structural biology, structures of molecules can be described, including RNA structures. In our RNA-As-Graphs (RAG) framework, we represent RNA structures as tree graphs by translating unpaired regions into vertices and helices into edges. Here we explore the modularity of RNA structures by applying graph partitioning known in graph theory to divide an RNA graph into subgraphs. To our knowledge, this is the first application of graph partitioning to biology, and the results suggest a systematic approach for modular design in general. The graph partitioning algorithms utilize mathematical properties of the Laplacian eigenvector (µ2) corresponding to the second eigenvalues (λ2) associated with the topology matrix defining the graph: λ2 describes the overall topology, and the sum of µ2′s components is zero. The three types of algorithms, termed median, sign, and gap cuts, divide a graph by determining nodes of cut by median, zero, and largest gap of µ2′s components, respectively. We apply these algorithms to 45 graphs corresponding to all solved RNA structures up through 11 vertices (∼220 nucleotides). While we observe that the median cut divides a graph into two similar-sized subgraphs, the sign and gap cuts partition a graph into two topologically-distinct subgraphs. We find that the gap cut produces the best biologically-relevant partitioning for RNA because it divides RNAs at less stable connections while maintaining junctions intact. The iterative gap cuts suggest basic modules and assembly protocols to design large RNA structures. Our graph substructuring thus suggests a systematic approach to explore the modularity of biological networks. In our applications to RNA structures, subgraphs also suggest design strategies for novel RNA motifs.

Classifying multigraph models of secondary RNA structure using graph-theoretic descriptors.

The prediction of secondary RNA folds from primary sequences continues to be an important area of research given the significance of RNA molecules in biological processes such as gene regulation. To facilitate this effort, graph models of secondary structure have been developed to quantify and thereby characterize the topological properties of the secondary folds. In this work we utilize a multigraph representation of a secondary RNA structure to examine the ability of the existing graph-theoretic descriptors to classify all possible topologies as either RNA-like or not RNA-like. We use more than one hundred descriptors and several different machine learning approaches, including nearest neighbor algorithms, one-class classifiers, and several clustering techniques. We predict that many more topologies will be identified as those representing RNA secondary structures than currently predicted in the RAG (RNA-As-Graphs) database. The results also suggest which descriptors and which algorithms are more informative in classifying and exploring secondary RNA structures.

RAG: an update to the RNA-As-Graphs resource.

BackgroundIn 2004, we presented a web resource for stimulating the search for novel RNAs, RNA-As-Graphs (RAG), which classified, catalogued, and predicted RNA secondary structure motifs using clustering and build-up approaches. With the increased availability of secondary structures in recent years, we update the RAG resource and provide various improvements for analyzing RNA structures.DescriptionOur RAG update includes a new supervised clustering algorithm that can suggest RNA motifs that may be "RNA-like". We use this utility to describe RNA motifs as three classes: existing, RNA-like, and non-RNA-like. This produces 126 tree and 16,658 dual graphs as candidate RNA-like topologies using the supervised clustering algorithm with existing RNAs serving as the training data. A comparison of this clustering approach to an earlier method shows considerable improvements. Additional RAG features include greatly expanded search capabilities, an interface to better utilize the benefits of relational database, and improvements to several of the utilities such as directed/labeled graphs and a subgraph search program.ConclusionsThe RAG updates presented here augment the database's intended function - stimulating the search for novel RNA functionality - by classifying available motifs, suggesting new motifs for design, and allowing for more specific searches for specific topologies. The updated RAG web resource offers users a graph-based tool for exploring available RNA motifs and suggesting new RNAs for design.

RAG: RNA-As-Graphs database—concepts, analysis, and features

Close birth spacing increases the risk of miscarriage, congenital malformation and perinatal death because it does not give a mother time to recover from the nutritional depletion caused by the first pregnancy or time to recover a normal hormonal profile before the beginning of the next pregnancy. The placental vitamin pump causes maternal vitamin depletion. Nutritional deficits do more damage to reproduction around the time of conception than later during pregnancy. Vitamin and mineral deficiencies can cause not only direct damage to embryonic development but damage to both male and female germ cells resulting in new mutations before a conception. New mutations can cause pregnancy failure or maldevelopment of the embryo. The realisation that nutritional deficits can be mutagenic opened a new chapter in nutritional science. Some nutrients are antimutagenic and already act as such within the digestive tract, but foods contain many other antimutagenic substances. The juices of many fresh vegetables in particular are antimutagenic.