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

TL;DR

This paper models the double cut and join (DCJ) operation in genome rearrangements as a group action, providing a group-theoretic framework that enhances understanding of genome evolution and rearrangement distances.

Contribution

It introduces a novel group-theoretic approach to the DCJ model, establishing properties of the group and analogues of key results in genome rearrangement theory.

Findings

Group action representation of DCJ operator

Derived properties of the associated group

Found group-theoretic analogues for DCJ results

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. 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.