Loops in canonical RNA pseudoknot structures

TL;DR

This paper analyzes the statistical distribution of different loop types in complex RNA pseudoknot structures, providing a mathematical framework for understanding their structural variability.

Contribution

It introduces a method to compute limit distributions of loop counts in k-noncrossing RNA structures using generating functions and central limit theorems.

Findings

Limit distributions of hairpin-loops, interior-loops, and bulges are derived.

Central limit theorems are proved for these distributions.

The approach applies to coarse-grained RNA structures with crossing interactions.

Abstract

In this paper we compute the limit distributions of the numbers of hairpin-loops, interior-loops and bulges in k-noncrossing RNA structures. The latter are coarse grained RNA structures allowing for cross-serial interactions, subject to the constraint that there are at most k-1 mutually crossing arcs in the diagram representation of the molecule. We prove central limit theorems by means of studying the corresponding bivariate generating functions. These generating functions are obtained by symbolic inflation of Ik5-shapes.