Counting All DCJ Sorting Scenarios

  title={Counting All DCJ Sorting Scenarios},
  author={Mar{\'i}lia Dias Vieira Braga and Jens Stoye},
In genome rearrangements, the double cut and join (DCJ) operation, introduced by Yancopoulos et al. , allows to represent most rearrangement events that could happen in multichromosomal genomes, such as inversions, translocations, fusions and fissions. No restriction on the genome structure considering linear and circular chromosomes is imposed. An advantage of this general model is that it leads to considerable algorithmic simplifications. Recently several works concerning the DCJ operation… 

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.

All Possible Optimal Solutions for Multichromosomal Genome Rearrangements using DCJ

The whole space of solutions for this problem and some propositions are given, on the basis of which a theoretical algorithm has been proposed, to find one optimal DCJ rearrangement sequence for sorting one genome into the another one.

Algebraic double cut and join

This paper realizes the double cut and join operator as a group action on the space of multichromosomal genomes, deriving some properties of the group and finding group-theoretic analogues for the key results in the DCJ theory.

Visualization of genome rearrangements using DCJ operations

A novel visualization program is introduced, DCJVis, to create a diagram of each DCJ operations necessary to transform between the genomes of two distinct organisms by describing a possible sequence of genome graphs based on the selected gene adjacency for the DCJ operation.


  • 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.

DCJVis: visualization of genome rearrangements using DCJ operations

A new visualization program is introduced, DCJVis, to create a diagram of each DCJ operation necessary to transform between the genomes of two distinct organisms by describing a possible sequence of genome graphs based on the selected gene adjacency on the source genome for theDCJ operation.

Bayesian sampling of genomic rearrangement scenarios via double cut and join

Two theorems underlying the theoretical mixing properties of the Double Cut and Join model are introduced, based on a parallel MCMC method that cools down DCJ scenarios to HP scenarios, and allowed us to provide estimates of the different modes of evolution in diverse lineages.

Sampling and counting genome rearrangement scenarios

A Gibbs sampler for sampling most parsimonious labeling of evolutionary trees under the SCJ model and a mini-review about the state of the art of sampling and counting rearrangement scenarios, focusing on the reversal, DCJ and SCJ models are given.

Phylogenetic Reconstruction Analysis on Gene Order and Copy Number Variation

A new median solver for gene order data that combines double-cut-join (DCJ) sorting with the Simulated Annealing algorithm (SAMedian) is proposed and a new phylogenetic inference method is built to solve both SPP and BPP problems.

Gene order rearrangement methods for the reconstruction of phylogeny

Two fundamental genome rearrangement problems are studied in this thesis and it is shown that increased plausibility can be accompanied by an efficient solution.



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.

Exploring the Solution Space of Sorting by Reversals, with Experiments and an Application to Evolution

An algorithm which gives all the classes of solutions and counts the number of solutions in each class, with a better theoretical and practical complexity than the complete enumeration method is proposed.

Parking Functions, Labeled Trees and DCJ Sorting Scenarios

An exact formula is given for the number of double-cut-and-join (DCJ) rearrangement scenarios of co-tailed genomes and effective bijections are constructed between the set of scenarios that sort a cycle and well studied combinatorial objects.

An Algorithm to Enumerate Sorting Reversals for Signed Permutations

  • A. Siepel
  • Computer Science
    J. Comput. Biol.
  • 2003
An efficient algorithm is derived to solve the problem of finding all sorting reversals, and experimental results are presented indicating that, while the new algorithm does not represent a significant improvement in asymptotic terms, it performs dramatically better in practice than the best known alternative.

On the Properties of Sequences of Reversals that Sort a Signed Permutation

Experimental and theoretical evidence is provided showing that, typically, there is a huge number of optimal sequences of reversals that sort a given signed permutation.

Transforming men into mice (polynomial algorithm for genomic distance problem)

A duality theorem is proved which expresses the genomic distance in terms of easily computable parameters reflecting different combinatorial properties of sets of strings and leads to a polynomial time algorithm for computing most parsimonious rearrangement scenarios for human-mouse evolution.

Edit Distances for Genome Comparisons Based on Non-Local Operations

A number of measures of gene order rearrangement are defined, algorithm design and software development for the calculation of some of these quantities in single-chromosome genomes are described, and the results of applying these tools to a database of mitochondrial gene orders inferred from genomic sequences are reported on.

Breakpoint graphs and ancestral genome reconstructions.

An algorithm MGRA for reconstructing ancestral genomes is developed and used to study the rearrangement history of seven mammalian genomes: human, chimpanzee, macaque, mouse, rat, dog, and opossum.

Algorithms in Bioinformatics, 5th International Workshop, WABI 2005, Mallorca, Spain, October 3-6, 2005, Proceedings

A Lookahead Branch-and-Bound Algorithm for the Maximum Quartet Consistency Problem and Semi-definite Programming to Enhance Supertree Resolvability are presented.

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.