Large Deviations for Random Trees and the Branching of RNA Secondary Structures

TL;DR

This paper establishes a Large Deviation Principle for vertex degrees in plane trees, modeling RNA secondary structures, and compares theoretical predictions with actual RNA data, revealing general agreement and notable deviations.

Contribution

It introduces an explicit LDP for vertex degrees in plane trees and applies it to analyze RNA secondary structures, providing new insights into their branching patterns.

Findings

Theoretical degree distributions match observed RNA structures broadly.

Substantial agreement between model predictions and RNA data.

Some deviations suggest areas for further investigation.

Abstract

We give a Large Deviation Principle (LDP) with explicit rate function for the distribution of vertex degrees in plane trees, a combinatorial model of RNA secondary structures. We calculate the typical degree distributions based on nearest neighbor free energies, and compare our results with the branching configurations found in two sets of large RNA secondary structures. We find substantial agreement overall, with some interesting deviations which merit further study.