On the Loop Homology of a Certain Complex of RNA Structures

Thomas J. X. Li and Christian M. Reidys
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Thomas J. X. Li: Biocomplexity Institute and Initiative, University of Virginia, Charlottesville, VA 22904-4298, USA
Christian M. Reidys: Biocomplexity Institute and Initiative, University of Virginia, Charlottesville, VA 22904-4298, USA

Mathematics, 2021, vol. 9, issue 15, 1-22

Abstract: In this paper, we establish a topological framework of ? -structures to quantify the evolutionary transitions between two RNA sequence–structure pairs. ? -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 ? -structure captures the intersections of loops in both secondary structures. We compute the loop homology of ? -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 ? of certain arc-components in a ? -structure and that the rank of the first homology is given by ? ? ? + 1 , where ? is the Euler characteristic of the loop complex.

Keywords: topology; simplicial complex; homology; Mayer–Vietoris sequence; RNA; secondary structure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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