Graph applications to RNA structure and function

RNA's modular, hierarchical, and versatile structure makes possible diverse, essential regulatory and catalytic roles in the cell. It also invites systematic modeling and simulation approaches. Among the diverse computational and theoretical approaches to model RNA structures, graph theory has been applied in various contexts to study RNA structure and function. Here, we describe graph-theoretical approaches for predicting and designing novel RNA topologies using graphical representations of RNA secondary structure, clustering tools, and a build-up procedure. Recent applications to noncoding RNA classification, RNA structure analysis and prediction, and novel RNA design are also described. As evident from the work of many groups in the mathematical and biological sciences, graph-theoretical approaches offer a fruitful avenue for discovering novel RNA topologies and designing new structural classes of RNAs.