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

Abstract

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.

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

“…However, this led to the exclusion of non-isomorphic dual graphs with identical eigenvalue spectra. The prior dual graph library also missed some dual graph topologies that corresponded to known RNA molecules, as we found recently [46].…”

“…We have recently applied this partitioning algorithm to study most common subgraph blocks with and without pseudoknots in RNA structures, and identify possible ancestry relationships between ribosomal RNAs in different species [46]. However, the above algorithm only identifies non-separable blocks for dual graphs.…”

“…For V = 2, 3, and 4, no new graphs were added to the expanded library. For V = 5, 6, and 7, the enumeration algorithm adds 2, 14, and 164 new graphs, respectively, including the dual graph corresponding to a 7-way junction (7_2389) that was manually assigned a dual graph ID in our recent study [46]. We also removed two dual graphs labeled 4_15 and 7_174 as they were isomorphic (and hence duplicates) to 4_16 and 7_74, respectively.…”

“…We have previously used graph representations in many contexts, such as to: create a library of graph topologies up to 13 vertices for tree graphs (that correspond to RNA molecules of ≈ 260 residues) [34] and 9 vertices for dual graphs [35]; partition tree graphs [36] to create a database of RNA atomic fragments (RAG-3D [37]); predict junction topologies for RNA [38,39]; sample RNA tree graphs for the prediction of RNA topologies (RAGTOP) [40,41]; build atomic models from tree graphs by fragment assembly (F-RAG) [42]; and design novel RNA topologies [43]. We have also partitioned dual graphs into non-separable subgraph blocks, i.e., subgraphs that cannot be partitioned further without breaking junctions and pseudoknots [44,45], to identify commonly occurring subgraph motifs in RNA structures and create a database of corresponding RNA atomic fragments called RAG-3Dual [46].…”

“…With the newly generated and correctly classified subgraphs, we extend our RAG-3Dual database (available at https://github.com/Schlicklab/RAG-3Dual) to include atomic fragments for all possible subgraphs (not only for basic building blocks) between 2 and 9 vertices and update our previous list [46] of RNA topologies for existing RNA graphs and subgraphs. The enlarged dual graph library, combined with the extended partitioning algorithm and the RAG-3Dual database, makes available a more comprehensive repertoire of graph topologies and fragments to study yet undiscovered pseudoknot-containing RNA molecules and design RNA sequences with novel topologies.…”