An algebraic view of bacterial genome evolution

TL;DR

This paper explores how algebraic structures like braid and Coxeter groups can model bacterial genome rearrangements, potentially offering new insights into evolutionary biology.

Contribution

It introduces an algebraic framework for understanding bacterial genome evolution, connecting biological rearrangements with mathematical group theory.

Findings

Rearrangements correspond to algebraic operations in braid groups.

Topological and local genome changes share algebraic features.

Algebraic methods may reveal deeper biological structures.

Abstract

Rearrangements of bacterial chromosomes can be studied mathematically at several levels, most prominently at a local, or sequence level, as well as at a topological level. The biological changes involved locally are inversions, deletions, and transpositions, while topologically they are knotting and catenation. These two modelling approaches share some surprising algebraic features related to braid groups and Coxeter groups. The structural approach that is at the core of algebra has long found applications in sciences such as physics and analytical chemistry, but only in a small number of ways so far in biology. And yet there are examples where an algebraic viewpoint may capture a deeper structure behind biological phenomena. This article discusses a family of biological problems in bacterial genome evolution for which this may be the case, and raises the prospect that the tools developed by algebraists over the last century might provide insight to this area of evolutionary biology. .