Algebraic double cut and join

  title={Algebraic double cut and join},
  author={Sangeeta Bhatia and Attila Egri-Nagy and Andrew R. Francis},
  journal={Journal of Mathematical Biology},
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… 


  • S. Bhatia
  • Biology
    Bulletin of the Australian Mathematical Society
  • 2019
This work is the first to apply the theory of rewriting systems to a problem in phylogenetics, thereby linking these two separate fields and contributing to the conversation between algebra and biology.

The Complexity of Genome Rearrangement Combinatorics under the Infinite Sites Model.

Position and Content Paradigms in Genome Rearrangements: The Wild and Crazy World of Permutations in Genomics

The different ways in which permutations have been used to model genomes and genome rearrangement events are described, presenting some features and limitations of each approach, and how the various models are related are shown.

A five-element transformation monoid on labelled trees

Maximum of the sum of consecutive terms in random permutations



A Unifying View of Genome Rearrangements

A simple way to apply the double cut and join operation to the most general type of genomes with a mixed collection of linear and circular chromosomes is shown and a graph structure is described that allows simplifying the theory and distance computation considerably, as neither capping nor concatenation of the linear chromosomes are necessary.

Efficient sorting of genomic permutations by translocation, inversion and block interchange

A universal double-cut-and-join operation that accounts for inversions, translocations, fissions and fusions, but also produces circular intermediates which can be reabsorbed, which converts one multi-linear chromosome genome to another in the minimum distance.

The Solution Space of Sorting by DCJ

An easy-to-compute formula is given that corresponds to the exact number of optimal DCJ sorting sequences for a particular subset of instances of the problem and the demonstration of the possibility of obtaining one optimal sorting sequence by properly replacing any pair of consecutive operations in another optimal sequence.

Group-theoretic models of the inversion process in bacterial genomes

A group-theoretic framework is suggested that by lifting the problem from circular permutations to the affine symmetric group, the inversion distance can be found in polynomial time for a model in which inversions are restricted to acting on two regions.

Extending the Algebraic Formalism for Genome Rearrangements to Include Linear Chromosomes

  • P. FeijãoJ. Meidanis
  • Computer Science
    IEEE/ACM Transactions on Computational Biology and Bioinformatics
  • 2013
The adjacency algebraic theory is introduced, extending the original mathematics to linear chromosomes in a very natural way, and allowing the original algebraic distance formula to be used to the general multichromosomal case, with both linear and circular chromosomes.

An algebraic view of bacterial genome evolution

  • A. Francis
  • Mathematics
    Journal of mathematical biology
  • 2014
A family of biological problems in bacterial genome evolution for which an algebraic viewpoint may capture a deeper structure behind biological phenomena is discussed, and the prospect that the tools developed by algebraists over the last century might provide insight to this area of evolutionary biology is raised.

Combinatorial Structure of Genome Rearrangements Scenarios

An exact formula is given for the number of double-cut-and-join (DCJ) rearrangement scenarios between two genomes and effective bijections are constructed between the set of scenarios that sort a component as well studied combinatorial objects such as parking functions, labeled trees, and prüfer codes.

Analysis of circular genome rearrangement by fusions, fissions and block-interchanges

FFBI is a useful tool for the bioinformatics analysis of circular and multiple genome rearrangement by fusions, fissions and block-interchange events altogether and is implemented as a web server, called FFBI.

The chromosome inversion problem