Combinatorial analysis of interacting RNA molecules

TL;DR

This paper provides a combinatorial framework for analyzing joint structures of interacting RNA molecules, introducing new shape-based enumeration methods and deriving asymptotic formulas relevant for RNA interaction prediction algorithms.

Contribution

It introduces a novel shape-based combinatorial approach to enumerate RNA-RNA interaction structures with specific constraints, advancing understanding of their complexity.

Findings

Derived asymptotic formulas with small exponential growth rates

Introduced a new shape-based enumeration method

Implications for designing RNA-RNA interaction prediction algorithms

Abstract

Recently several minimum free energy (MFE) folding algorithms for predicting the joint structure of two interacting RNA molecules have been proposed. Their folding targets are interaction structures, that can be represented as diagrams with two backbones drawn horizontally on top of each other such that (1) intramolecular and intermolecular bonds are noncrossing and (2) there is no "zig-zag" configuration. This paper studies joint structures with arc-length at least four in which both, interior and exterior stack-lengths are at least two (no isolated arcs). The key idea in this paper is to consider a new type of shape, based on which joint structures can be derived via symbolic enumeration. Our results imply simple asymptotic formulas for the number of joint structures with surprisingly small exponential growth rates. They are of interest in the context of designing prediction algorithms for RNA-RNA interactions.