Combinatorics of RNA-RNA interaction

TL;DR

This paper explores the combinatorial properties of RNA-RNA interaction structures, providing mathematical tools like generating functions and asymptotic formulas to understand their complexity and enumeration.

Contribution

It introduces the combinatorics of RNA interaction structures, including generating functions, singularity analysis, and recurrence relations, advancing the mathematical understanding of RNA joint structures.

Findings

Derived explicit recurrence relations for RNA interaction structures.

Provided asymptotic formulas for counting joint structures.

Analyzed the singularity structure of the generating functions.

Abstract

RNA-RNA binding is an important phenomenon observed for many classes of non-coding RNAs and plays a crucial role in a number of regulatory processes. Recently several MFE folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Here joint structure means that in a diagram representation the intramolecular bonds of each partner are pseudoknot-free, that the intermolecular binding pairs are noncrossing, and that there is no so-called ``zig-zag'' configuration. This paper presents the combinatorics of RNA interaction structures including their generating function, singularity analysis as well as explicit recurrence relations. In particular, our results imply simple asymptotic formulas for the number of joint structures.