A phase transition in energy-filtered RNA secondary structures

TL;DR

This paper investigates how energy parameters influence RNA secondary structures, revealing a phase transition in their complexity and distribution, with implications for computational efficiency in RNA folding predictions.

Contribution

It proves a dichotomy in mfe structures based on energy parameters, identifying a phase transition point and analyzing its impact on structure complexity and computational sparsification.

Findings

Mfe structures contain finitely many complex irreducibles under certain parameters

A phase transition occurs from discrete to normal distribution of irreducibles

Sparsification reduces computational complexity differently depending on parameters

Abstract

In this paper we study the effect of energy parameters on minimum free energy (mfe) RNA secondary structures. Employing a simplified combinatorial energy model, that is only dependent on the diagram representation and that is not sequence specific, we prove the following dichotomy result. Mfe structures derived via the Turner energy parameters contain only finitely many complex irreducible substructures and just minor parameter changes produce a class of mfe-structures that contain a large number of small irreducibles. We localize the exact point where the distribution of irreducibles experiences this phase transition from a discrete limit to a central limit distribution and subsequently put our result into the context of quantifying the effect of sparsification of the folding of these respective mfe-structures. We show that the sparsification of realistic mfe-structures leads to a constant time and space reduction and that the sparsifcation of the folding of structures with modified parameters leads to a linear time and space reduction. We furthermore identify the limit distribution at the phase transition as a Rayleigh distribution.