Shapes of interacting RNA complexes

TL;DR

This paper introduces a topological approach to classify and analyze RNA complexes by their shapes, providing a finite set of simplified structures, a bijection with RNA structures, and an efficient sampling algorithm.

Contribution

It presents a novel topological framework for RNA complex shapes, establishing a bijection with RNA structures and developing a linear-time sampling algorithm.

Findings

Finite set of shapes for fixed topological genus

Bijection between RNA complex shapes and RNA structures

Linear-time uniform sampling algorithm

Abstract

Shapes of interacting RNA complexes are studied using a filtration via their topological genus. A shape of an RNA complex is obtained by (iteratively) collapsing stacks and eliminating hairpin loops. This shape-projection preserves the topological core of the RNA complex and for fixed topological genus there are only finitely many such shapes.Our main result is a new bijection that relates the shapes of RNA complexes with shapes of RNA structures.This allows to compute the shape polynomial of RNA complexes via the shape polynomial of RNA structures. We furthermore present a linear time uniform sampling algorithm for shapes of RNA complexes of fixed topological genus.