Posets and spaces of k-noncrossing RNA structures

Moulton, Vincent ORCID: https://orcid.org/0000-0001-9371-6435 and Wu, Taoyang ORCID: https://orcid.org/0000-0002-2663-2001 (2022) Posets and spaces of k-noncrossing RNA structures. SIAM Journal on Discrete Mathematics, 36 (3). pp. 1586-1611. ISSN 0895-4801

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Abstract

RNA molecules are single-stranded analogues of DNA that can fold into various structures which influence their biological function within the cell. RNA structures can be modeled combinatorially in terms of a certain type of graph called an RNA diagram. In this paper we introduce a new poset of RNA diagrams ${\mathcal B}^r_{f,k}$, $r\ge 0$, $k \ge 1$, and $f \ge 3$, which we call the Penner--Waterman poset, and, using results from the theory of multitriangulations, we show that this is a pure poset of rank $k(2f-2k+1)+r-f-1$, whose geometric realization is the join of a simplicial sphere of dimension $k(f-2k)-1$ and an $\left((f+1)(k-1)-1\right)$-simplex in case $r=0$. As a corollary for the special case $k=1$, we obtain a result due to Penner and Waterman concerning the topology of the space of RNA secondary structures. These results could eventually lead to new ways to study landscapes of RNA $k$-noncrossing structures.

Item Type: Article
Uncontrolled Keywords: rna structures,k-noncrossing pseudoknots,multitriangulations,poset topology,mathematics(all) ,/dk/atira/pure/subjectarea/asjc/2600
Faculty \ School: Faculty of Science > School of Computing Sciences
Related URLs:
Depositing User: LivePure Connector
Date Deposited: 13 Apr 2022 10:30
Last Modified: 23 Oct 2022 03:43
URI: https://ueaeprints.uea.ac.uk/id/eprint/84621
DOI: 10.1137/21M1413316

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