Melting of Branched RNA Molecules

TL;DR

This study investigates how the branching geometry of RNA molecules, modeled as Cayley Trees, affects their melting thermodynamics, revealing that complex branching can lead to non-traditional melting behavior with singularities.

Contribution

It demonstrates analytically that the melting thermodynamics of branched RNA molecules with Cayley Tree structures differ fundamentally from linear ones, showing a hidden singularity.

Findings

Linear RNA melts via a continuous phase transition.

Cayley Tree RNA exhibits a smooth free energy with a mathematical singularity.

Correlation length diverges near the stability limit.

Abstract

Stability of the branching structure of an RNA molecule is an important condition for its function. In this letter we show that the melting thermodynamics of RNA molecules is very sensitive to their branching geometry for the case of a molecule whose groundstate has the branching geometry of a Cayley Tree and whose pairing interactions are described by the Go model. Whereas RNA molecules with a linear geometry melt via a conventional continuous phase transition with classical exponents, molecules with a Cayley Tree geometry are found to have a free energy that seems smooth, at least within our precision. Yet, we show analytically that this free energy in fact has a mathematical singularity at the stability limit of the ordered structure. The correlation length appears to diverge on the high-temperature side of this singularity.