Involve: A Journal of Mathematics

  • Involve
  • Volume 12, Number 2 (2019), 257-280.

Properties of RNA secondary structure matching models

Nicole Anderson, Michael Breunig, Kyle Goryl, Hannah Lewis, Manda Riehl, and McKenzie Scanlan

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Abstract

RNA secondary structures have been modeled using a variety of matching families. We first explore the intersections of different matching families which are models for likely RNA secondary structures. We then introduce their respective enumeration sequences and prove our proposed equations for enumeration. Next, we prove a formula for the number of matchings with a given crossing number for a variety of matching families. Then we develop a new statistic called the pseudoknot number and find the maximum pseudoknot number on a given set of matchings. We end by providing a comparison between the crossing number, nesting number, and pseudoknot number for three matching families on nine edges.

Article information

Source
Involve, Volume 12, Number 2 (2019), 257-280.

Dates
Received: 22 July 2017
Revised: 3 April 2018
Accepted: 4 April 2018
First available in Project Euclid: 25 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.involve/1540432915

Digital Object Identifier
doi:10.2140/involve.2019.12.257

Mathematical Reviews number (MathSciNet)
MR3864217

Zentralblatt MATH identifier
06980501

Subjects
Primary: 05C30: Enumeration in graph theory 92E10: Molecular structure (graph-theoretic methods, methods of differential topology, etc.)

Keywords
RNA secondary structure perfect matchings crossing number nesting number pseudoknot

Citation

Anderson, Nicole; Breunig, Michael; Goryl, Kyle; Lewis, Hannah; Riehl, Manda; Scanlan, McKenzie. Properties of RNA secondary structure matching models. Involve 12 (2019), no. 2, 257--280. doi:10.2140/involve.2019.12.257. https://projecteuclid.org/euclid.involve/1540432915


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