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.

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.

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.

Partitioning and Classification of RNA Secondary Structures into Pseudonotted and Pseudoknot-free Regions Using a Graph-Theoretical Approach.

Dual graphs have been applied to model RNA secondary structures with pseudoknots, or intertwined base pairs. In this paper we present a linear-time algorithm to partition dual graphs into maximal topological components called blocks and determine whether each block contains a pseudoknot or not. We show that a block contains a pseudoknot if and only if the block has a vertex of degree 3 or more; this characterization allows us to efficiently isolate smaller RNA fragments and classify them as pseudoknotted or pseudoknot-free regions, while keeping these sub-structures intact.

Network Theory Tools for RNA Modeling.

An introduction into the usage of graph or network theory tools for the study of RNA molecules is presented. By using vertices and edges to define RNA secondary structures as tree and dual graphs, we can enumerate, predict, and design RNA topologies. Graph connectivity and associated Laplacian eigenvalues relate to biological properties of RNA and help understand RNA motifs as well as build, by computational design, various RNA target structures.