Statistics of topological RNA structures

TL;DR

This paper analyzes the statistical properties of topological RNA structures, including pseudoknots and complex loops, using generating functions to understand their distributions and expectations based on their topological genus.

Contribution

The paper introduces a new bivariate generating function for topological RNA structures and extends analysis to complex pseudoknots, providing detailed statistical insights.

Findings

Derived a new generating function for topological RNA structures.

Analyzed distributions of various RNA structural features.

Computed expectation values for complex pseudoknots.

Abstract

In this paper we study properties of topological RNA structures, i.e.~RNA contact structures with cross-serial interactions that are filtered by their topological genus. RNA secondary structures within this framework are topological structures having genus zero. We derive a new bivariate generating function whose singular expansion allows us to analyze the distributions of arcs, stacks, hairpin- , interior- and multi-loops. We then extend this analysis to H-type pseudoknots, kissing hairpins as well as $3$-knots and compute their respective expectation values. Finally we discuss our results and put them into context with data obtained by uniform sampling structures of fixed genus.