Irreducibility in RNA structures

TL;DR

This paper investigates the concept of irreducibility in RNA structures, analyzing distributions and sizes of irreducible substructures in both random and minimum free energy configurations, with implications for RNA folding times.

Contribution

It provides a detailed analysis of irreducibility in RNA structures, contrasting random and mfe configurations, and explores distributions related to irreducible substructures based on crossing arcs and stack sizes.

Findings

Distribution of irreducible substructures characterized

Largest irreducible substructure size analyzed

Implications for RNA folding time discussed

Abstract

In this paper we study irreducibility in RNA structures. By RNA structure we mean RNA secondary as well as RNA pseudoknot structures. In our analysis we shall contrast random and minimum free energy (mfe) configurations. We compute various distributions: of the numbers of irreducible substructures, their locations and sizes, parameterized in terms of the maximal number of mutually crossing arcs, $k-1$, and the minimal size of stacks $\sigma$. In particular, we analyze the size of the largest irreducible substructure for random and mfe structures, which is the key factor for the folding time of mfe configurations.