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

@article{Bakhtin2009LargeDF,
  title={Large Deviations for Random Trees and the Branching of RNA Secondary Structures},
  author={Yuri Bakhtin and Christine E. Heitsch},
  journal={Bulletin of Mathematical Biology},
  year={2009},
  volume={71},
  pages={84-106}
}
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. 
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19 Citations
Highly Influential Citations
4
Background Citations
7
Methods Citations
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19 Citations

Large Deviations for Random Trees
TLDR
A Large Deviation Principle (LDP) is proved for the distribution of degrees of vertices of the tree in a large random tree under Gibbs distributions from the analysis of RNA secondary structures.
Parametric Analysis of RNA Branching Configurations
TLDR
The results indicate that variation of these specific parameters does not have a dramatic effect on the structures predicted by the free energy model.
Parametric analysis of RNA folding
TLDR
The results indicate that variation of these specific parameters does not have a dramatic effect on the structures predicted by the free energy model.
Combinatorial Insights into RNA Secondary Structure
TLDR
Results based on these mathematical abstractions have been used to count, compare, classify, and otherwise analyze RNA secondary structures and provide important insights into the base pairing of RNA sequences, thereby advancing the understanding of RNA folding.
Markov Chain-Based Sampling for Exploring RNA Secondary Structure under the Nearest Neighbor Thermodynamic Model and Extended Applications
Ribonucleic acid (RNA) secondary structures and branching properties are important for determining functional ramifications in biology. While energy minimization of the Nearest Neighbor Thermodynamic…
Markov Chain-based Sampling for Exploring RNA Secondary Structure under the Nearest Neighbor Thermodynamic Model
We study plane trees as a model for RNA secondary structure, assigning energy to each tree based on the Nearest Neighbor Thermodynamic Model, and defining a corresponding Gibbs distribution on the…
Graph Applications to RNA Structure and Function
TLDR
Graph-theoretical approaches for predicting and designing novel RNA topologies using graphical representations of RNA secondary structure, clustering tools, and a build-up procedure are described.
Predicting Large RNA-Like Topologies by a Knowledge-Based Clustering Approach.
Viral RNAs Are Unusually Compact
TLDR
The extent to which these viral RNAs have evolved to be physically compact molecules to facilitate encapsulation is examined, and it is demonstrated that their sizes correlate with the compactness of branching patterns in predicted secondary structure ensembles.
Thermodynamic limit for large random trees
TLDR
An infinite random tree consistent with Gibbs distributions on finite random plane trees with bounded branching is introduced and it is shown that it satisfies a certain form of the Markov property.
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