Large deviations for random trees and the branching of RNA secondary structures

Area of Science:

• Computational Biology
• Bioinformatics
• RNA Structure Analysis

Background:

• RNA secondary structures are often modeled using combinatorial plane trees.
• Understanding the distribution of vertex degrees in these models is crucial for predicting RNA behavior.

Purpose of the Study:

• To establish a Large Deviation Principle (LDP) with an explicit rate function for vertex degree distributions in plane trees.
• To compute typical degree distributions using nearest neighbor free energies.
• To compare these theoretical distributions with empirical data from large RNA secondary structures.

Main Methods:

• Application of Large Deviation Principle (LDP) theory to plane trees.
• Calculation of vertex degree distributions based on nearest neighbor free energy models.
• Comparative analysis of theoretical and empirical branching configurations in RNA structures.

Main Results:

• An explicit rate function for the LDP of vertex degrees in plane trees was derived.
• Calculated typical degree distributions showed substantial agreement with observed branching patterns in large RNA datasets.
• Identified specific deviations between theoretical predictions and empirical data that warrant further investigation.

Conclusions:

• The study provides a robust theoretical framework for analyzing RNA secondary structure complexity using LDP.
• The findings validate the use of plane trees as a combinatorial model for RNA structures.
• The observed deviations suggest potential limitations of current free energy models or novel structural motifs in RNA.