Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

On the Loop Homology of a Certain Complex of RNA Structures

Version 1 : Received: 6 July 2021 / Approved: 8 July 2021 / Online: 8 July 2021 (10:43:11 CEST)

A peer-reviewed article of this Preprint also exists.

Li, T.J.X.; Reidys, C.M. On the Loop Homology of a Certain Complex of RNA Structures. Mathematics 2021, 9, 1749. Li, T.J.X.; Reidys, C.M. On the Loop Homology of a Certain Complex of RNA Structures. Mathematics 2021, 9, 1749.

Journal reference: Mathematics 2021, 9, 1749
DOI: 10.3390/math9151749

Abstract

In this paper we establish a topological framework of τ-structures to quantify the evolutionary transitions between two RNA sequence-structure pairs. τ-structures developed here consist of a pair of RNA secondary structures together with a non-crossing partial matching between the two backbones. The loop complex of a τ-structure captures the intersections of loops in both secondary structures. We compute the loop homology of τ-structures. We show that only the zeroth, first and second homology groups are free. In particular, we prove that the rank of the second homology group equals the number γ of certain arc-components in a τ-structure, and the rank of the first homology is given by γ−χ+1, where χ is the Euler characteristic of the loop complex.

Keywords

topology; simplicial complex; homology; Mayer-Vietoris sequence; RNA; secondary structure

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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