Partitioning RNAs into pseudonotted and pseudoknot-free regions modeled as Dual Graphs

TL;DR

This paper introduces a graph-theoretic approach using dual graphs to efficiently partition RNA structures into pseudoknotted and pseudoknot-free regions, enabling better analysis and potential applications in RNA design.

Contribution

It presents new properties of dual graphs for RNA analysis and a linear-time algorithm to classify RNA regions based on their topological features.

Findings

A block contains a pseudoknot if and only if it has a vertex of degree 3 or more.

The algorithm efficiently isolates and classifies RNA fragments.

Structural properties of dual graphs offer a novel perspective for RNA analysis.

Abstract

Dual graphs have been applied to model RNA secondary structures. The purpose of the paper is two-fold: we present new graph-theoretic properties of dual graphs to validate the further analysis and classification of RNAs using these topological representations; we also present a linear-time algorithm to partition dual graphs into topological components called {\it blocks} and determine if each block contains a {\it 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. Even though non-topological techniques to detect and classify pseudoknots have been efficiently applied, structural properties of dual graphs provide a unique perspective for the further analysis of RNAs. Applications to RNA design can be envisioned since modular building blocks with intact pseudoknots can be combined to form new constructs.\end{abstract}