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

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 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.

Diagrammatic approaches to RNA structures with trinucleotide repeats

Trinucleotide repeat expansion disorders are associated with the overexpansion of (CNG) repeats on the genome. Messenger RNA transcripts of sequences with greater than 60–100 (CNG) tandem units have been implicated in trinucleotide repeat expansion disorder pathogenesis. In this work, we develop a diagrammatic theory to study the structural diversity of these (CNG)_n RNA sequences. Representing structural elements on the chain’s conformation by a set of graphs and employing elementary diagrammatic methods, we have formulated a renormalization procedure to re-sum these graphs and arrive at a closed-form expression for the ensemble partition function. With a simple approximation for the renormalization and applied to extended (CNG)_n sequences, this theory can comprehensively capture an infinite set of conformations with any number and any combination of duplexes, hairpins, multiway junctions, and quadruplexes. To quantify the diversity of different (CNG)_n ensembles, the analytical equations derived from the diagrammatic theory were solved numerically to derive equilibrium estimates for the secondary structural contents of the chains. The results suggest that the structural ensembles of (CNG)_n repeat sequence with n ∼60 are surprisingly diverse, and the distribution is sensitive to the ability of the N nucleotide to make noncanonical pairs and whether the (CNG)_n sequence can sustain stable quadruplexes. The results show how perturbations in the form of biases on the stabilities of the various structural motifs, duplexes, junctions, helices, and quadruplexes could affect the secondary structures of the chains and how these structures may switch when they are perturbed.

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.

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.

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.

Special Issue: Computational Analysis of RNA Structure and Function

RNA structure often plays a key role in determining the function of non-coding and coding transcripts [...].

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.