Journal of Mathematical Biology

, Volume 69, Issue 6–7, pp 1693–1718 | Cite as

An algebraic view of bacterial genome evolution

  • Andrew R. FrancisEmail author


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.


Bacteria Genome rearrangement Inversion Knotting  Tangle algebra Coxeter group DNA 

Mathematics Subject Classification

20F55 92-02 92B05 92D15 57M25 



I would like to thank Mark M. Tanaka, Leonard L. Scott Jr, John J. Graham and Attila Egri-Nagy, who read and commented on the manuscript. Particular thanks to MMT who introduced me to the field of bacterial genomics in the first place.


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Authors and Affiliations

  1. 1.Centre for Research in Mathematics, School of Computing, Engineering and MathematicsUniversity of Western SydneySydneyAustralia

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