Spaces of RNA secondary structures
type: Item
instance of: scholarly article
title: Spaces of RNA secondary structures
zbMATH Open document ID: 0810.92011
author: Michael S. Waterman
author: Robert Penner
published in: Advances in Mathematics
publication date: 1994-02-10T00:00:00Z
review text: The primary goal of the authors is to contribute to investigations of the secondary structure of RNA. The starting point are bond pictures that give rise to partially ordered sets of macromolecules. For such posets corresponding to classes of ``arbitrary'' and ``binary'' macromolecules (the latter being motivated by the study of secondary structures of RNA) geometric realizations are derived utilizing isomorphisms of posets and certain classes of rooted trees. A geometrical realization is a construction which associates a simplicial decomposition of a topological space to a given poset. The main result of the paper is that the geometrical realization of both the posets of arbitrary and of binary macromolecules are topological spheres. The proof uses techniques from Teichmüller theory and the theory of train tracks.
Mathematics Subject Classification ID: 92C40
Mathematics Subject Classification ID: 30F60
Mathematics Subject Classification ID: 92E10
Mathematics Subject Classification ID: 57Q05
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 495494
zbMATH Keywords: linear macromolecules
zbMATH Keywords: sphericity
zbMATH Keywords: secondary structure of RNA
zbMATH Keywords: bond pictures
zbMATH Keywords: partially ordered sets of macromolecules
zbMATH Keywords: posets
zbMATH Keywords: geometric realizations
zbMATH Keywords: isomorphisms of posets
zbMATH Keywords: classes of rooted trees
zbMATH Keywords: simplicial decomposition of a topological space
zbMATH Keywords: topological spheres
zbMATH Keywords: Teichmüller theory
zbMATH Keywords: train tracks
reviewed by: Dietmar Dorninger
MaRDI profile type: Publication
full work available at URL: aima.1993.1039
OpenAlex ID: W2008468762
DOI: 10.1006/AIMA.1993.1039
description: scientific article; zbMATH DE number 495494