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

Yuri Bakhtin; Christine E. Heitsch

doi:10.1007/s11538-008-9353-y

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

Yuri Bakhtin, Christine E. Heitsch

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	84-106
Number of pages	23
Journal	Bulletin of Mathematical Biology
Volume	71
Issue number	1
DOIs	https://doi.org/10.1007/s11538-008-9353-y
State	Published - Jan 2009

Keywords

Branching loops
Gibbs distributions
Large deviations
Picornavirus
RNA secondary structure
Random trees
Ribosome
Vertex degree

ASJC Scopus subject areas

Neuroscience(all)
Immunology
Mathematics(all)
Biochemistry, Genetics and Molecular Biology(all)
Environmental Science(all)
Pharmacology
Agricultural and Biological Sciences(all)
Computational Theory and Mathematics

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10.1007/s11538-008-9353-y

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title = "Large deviations for random trees and the branching of RNA secondary structures",

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.",

keywords = "Branching loops, Gibbs distributions, Large deviations, Picornavirus, RNA secondary structure, Random trees, Ribosome, Vertex degree",

author = "Yuri Bakhtin and Heitsch, {Christine E.}",

note = "Funding Information: This research of Yuri Bakhtin, Ph.D., is supported in part by NSF CAREER DMS-0742424. This research of Christine E. Heitsch, Ph.D., is supported in part by a Career Award at the Scientific Interface (CASI) from the Burroughs Wellcome Fund (BWF) and by NIH NIGMS R01 GM083621. Funding Information: ∗Corresponding author. E-mail addresses: bakhtin@math.gatech.edu (Yuri Bakhtin), heitsch@math.gatech.edu (Christine E. Heitsch). Y. Bakhtin partially supported by NSF CAREER DMS-0742424. C.E. Heitsch partially supported by a BWF CASI and NIH NIGMS R01 GM083621.",

year = "2009",

month = jan,

doi = "10.1007/s11538-008-9353-y",

language = "English (US)",

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T1 - Large deviations for random trees and the branching of RNA secondary structures

AU - Bakhtin, Yuri

AU - Heitsch, Christine E.

N1 - Funding Information: This research of Yuri Bakhtin, Ph.D., is supported in part by NSF CAREER DMS-0742424. This research of Christine E. Heitsch, Ph.D., is supported in part by a Career Award at the Scientific Interface (CASI) from the Burroughs Wellcome Fund (BWF) and by NIH NIGMS R01 GM083621. Funding Information: ∗Corresponding author. E-mail addresses: bakhtin@math.gatech.edu (Yuri Bakhtin), heitsch@math.gatech.edu (Christine E. Heitsch). Y. Bakhtin partially supported by NSF CAREER DMS-0742424. C.E. Heitsch partially supported by a BWF CASI and NIH NIGMS R01 GM083621.

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N2 - 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.

AB - 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.

KW - Branching loops

KW - Gibbs distributions

KW - Large deviations

KW - Picornavirus

KW - RNA secondary structure

KW - Random trees

KW - Ribosome

KW - Vertex degree

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JO - Bulletin of Mathematical Biology

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

Abstract

Keywords

ASJC Scopus subject areas

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