# Combinatorial Structure of Genome Rearrangements Scenarios

@article{Ouangraoua2010CombinatorialSO, title={Combinatorial Structure of Genome Rearrangements Scenarios}, author={A{\"i}da Ouangraoua and Anne Bergeron}, journal={Journal of computational biology : a journal of computational molecular cell biology}, year={2010}, volume={17 9}, pages={ 1129-44 } }

In genome rearrangement theory, one of the elusive questions raised in recent years is the enumeration of rearrangement scenarios between two genomes. This problem is related to the uniform generation of rearrangement scenarios and the derivation of tests of statistical significance of the properties of these scenarios. Here we give an exact formula for the number of double-cut-and-join (DCJ) rearrangement scenarios between two genomes. We also construct effective bijections between the set of…

## 19 Citations

### ALGEBRAIC MODELS OF LARGE SCALE GENOME REARRANGEMENT EVENTS

- BiologyBulletin 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.

### Implicit Transpositions in Shortest DCJ Scenarios

- BiologyAlCoB
- 2015

The results imply that implicit transpositions may be unavoidable and even appear in a significant proportion for some genomes, and it is estimated that in mammalian evolution transposition constitute at least at least 17% of genome rearrangements.

### Models and algorithms for genome rearrangement with positional constraints

- Computer ScienceAlgorithms for Molecular Biology
- 2016

A model for weighting genome rearrangements is introduced and it is shown that under simple yet reasonable conditions, a fundamental distance can be computed in polynomial time.

### Finding local genome rearrangements

- BiologyAlgorithms for Molecular Biology
- 2018

A solution to this problem provides a lower bound on the number of unlikely moves necessary when transforming one gene order into another, and could eventually be used in the design of a fixed parameter algorithm with a more general objective function.

### Counting Sorting Scenarios and Intermediate Genomes for the Rank Distance

- Computer ScienceAlCoB
- 2019

This paper shows how to count the number of optimal sorting scenarios and the numberof intermediate genomes between any two given genomes, under the rank distance.

### Approximating the number of Double Cut-and-Join scenarios

- Computer ScienceTheor. Comput. Sci.
- 2012

### Models and algorithms for genome rearrangement with positional constraints

- BiologyAlgorithms for molecular biology : AMB
- 2016

A model for weighting genome rearrangements is introduced and it is shown that under simple yet reasonable conditions, a fundamental distance can be computed in polynomial time.

### Algebraic double cut and join

- BiologyJournal of mathematical biology
- 2015

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.

### Implicit Transpositions in DCJ Scenarios

- BiologyFront. Genet.
- 2017

The results imply that implicit appearance of transpositions in DCJ scenarios may be unavoidable or even abundant for some pairs of genomes.

### Weighted Minimum-Length Rearrangement Scenarios

- Computer ScienceWABI
- 2019

An O(n 4)-time dynamic programming algorithm solving the Minimum Cost Parsimonious Scenario (MCPS) problem for co-tailed genomes with n genes (or syntenic blocks) yields a polynomial-time algorithm for general genomes.

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