Algebraic double cut and join : A group-theoretic approach to the operator on multichromosomal genomes

Sangeeta Bhatia; Attila Egri-Nagy; Andrew R Francis

doi:10.1007/s00285-014-0852-1

Algebraic double cut and join : A group-theoretic approach to the operator on multichromosomal genomes

J Math Biol. 2015 Nov;71(5):1149-78. doi: 10.1007/s00285-014-0852-1. Epub 2014 Dec 11.

Authors

Sangeeta Bhatia¹, Attila Egri-Nagy², Andrew R Francis³

Affiliations

¹ Centre for Research in Mathematics, University of Western Sydney, Penrith, NSW, 2751, Australia. s.bhatia@uws.edu.au.
² Centre for Research in Mathematics, University of Western Sydney, Penrith, NSW, 2751, Australia. a.egri-nagy@uws.edu.au.
³ Centre for Research in Mathematics, University of Western Sydney, Penrith, NSW, 2751, Australia. a.francis@uws.edu.au.

PMID: 25502846
DOI: 10.1007/s00285-014-0852-1

Abstract

Establishing a distance between genomes is a significant problem in computational genomics, because its solution can be used to establish evolutionary relationships including phylogeny. The "double cut and join" (DCJ) model of chromosomal rearrangement proposed by Yancopoulos et al. (Bioinformatics 21:3340-3346, 2005) has received attention as it can model inversions, translocations, fusion and fission on a multichromosomal genome that may contain both linear and circular chromosomes. In this paper, we realize the DCJ operator as a group action on the space of multichromosomal genomes. We study this group action, deriving some properties of the group and finding group-theoretic analogues for the key results in the DCJ theory.

Keywords: Algebraic biology; Double cut and join; Genome rearrangements; Group theory; Inversion.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Chromosomes / genetics
Evolution, Molecular
Gene Rearrangement*
Genome*
Genomics
Mathematical Concepts
Models, Genetic*
Phylogeny