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Counting All DCJ Sorting Scenarios [chapter]

Marília D. V. Braga, Jens Stoye
2009 Lecture Notes in Computer Science  
Recently several works concerning the DCJ operation have been published, and in particular an algorithm was proposed to find an optimal DCJ sequence for sorting one genome into another one.  ...  Here we study the solution space of this problem and give an easy to compute formula that corresponds to the exact number of optimal DCJ sorting sequences to a particular subset of instances of the problem  ...  In this model, the space of all sorting scenarios has been well characterized, allowing to group sorting scenarios into classes of equivalence [2] .  ... 
doi:10.1007/978-3-642-04744-2_4 fatcat:3iqxdkbuibcufbc7jt3tc3z7ry

Approximating the number of Double Cut-and-Join scenarios

István Miklós, Eric Tannier
2012 Theoretical Computer Science  
A closed formula exists for counting the number of DCJ scenarios between cotailed genomes, but no polynomial result has been published so far for arbitrary genomes.  ...  The MCMC can be used to quickly draw a sample of DCJ scenarios from a prescribed distribution and test some hypotheses on genome evolution.  ...  In Section 4, we prove some partial results on counting the number of DCJ scenarios.  ... 
doi:10.1016/j.tcs.2012.03.006 fatcat:f3vn2cvcaranzocsfrntokurdi

Restricted DCJ-Indel Model Revisited [chapter]

Marília D. V. Braga, Jens Stoye
2013 Lecture Notes in Computer Science  
We also present a simpler algorithm for computing an optimal restricted DCJ-indel sorting scenario in O(n log n) time.  ...  (BMC Bioinformatics 13, Suppl. 19, S14), but only an upper bound for the restricted DCJ-indel distance was provided.  ...  In Figure 1 we give examples of a general and a restricted DCJ sorting scenarios.  ... 
doi:10.1007/978-3-319-02624-4_4 fatcat:wavtm5iu4vhtvfa6n4glejfhdu

Genomic distance under gene substitutions

Marília D V Braga, Raphael Machado, Leonardo C Ribeiro, Jens Stoye
2011 BMC Bioinformatics  
In these models, a deletion and a subsequent insertion that occur at the same position of the genome count for two sorting steps.  ...  A deletion and an insertion that occur at the same position of the genome can be modeled as a substitution, counting for a single sorting step.  ...  scenario with DCJ operations and indels.  ... 
doi:10.1186/1471-2105-12-s9-s8 pmid:22151231 pmcid:PMC3271670 fatcat:vic4mhkdcbgthli2llijakuzru

Rearrangement Problems with Duplicated Genomic Markers [article]

Antoine Thomas
2014 arXiv   pre-print
Distances formulae as well as scenario computing algorithms were established, along with their complexity proofs.  ...  This means that there exists a BI halving scenario S such that all BI operations in S, possibly excluding the last one, are equivalent to two successive sorting DCJ operations.  ...  Moreover, all BI operations, possibly excluding the last one, are computed as pairs of compatible intervals, ie. pairs of sorting DCJ operations, which ensures that the length of the scenario is n−C 2  ... 
arXiv:1410.5415v1 fatcat:t3slxmig65a6rihwxgvp66xqlu

The Problem of Chromosome Reincorporation in DCJ Sorting and Halving [chapter]

Jakub Kováč, Marília D. V. Braga, Jens Stoye
2010 Lecture Notes in Computer Science  
We study two problems in the double cut and join (DCJ) model: sorting -transforming one multilinear genome into another and halving -transforming a duplicated genome into a perfectly duplicated one.  ...  The DCJ model includes rearrangement operations such as reversals, translocations, fusions and fissions.  ...  DCJ distance and scenarios. A sequence of k DCJ operations transforming a given genome Π into Γ is called a DCJ scenario of length k.  ... 
doi:10.1007/978-3-642-16181-0_2 fatcat:5wbkuahcdfaobebjqdzspvbiqy

Algebraic double cut and join -- A group-theoretic approach to the operator on multichromosomal genomes [article]

Sangeeta Bhatia, Attila Egri-Nagy, Andrew R. Francis
2014 arXiv   pre-print
In this paper, we realize the DCJ operator as a group action on the space of multichromosomal genomes.  ...  We study this group action, deriving some properties of the group and finding group-theoretic analogues for the key results in the DCJ theory.  ...  Counting the optimal sorting scenarios To sort a permutation π a into π b means to transform π a into π b through a sequence of allowed operations (in this case the DCJ operation).  ... 
arXiv:1409.7146v1 fatcat:ofwu2mpjd5ggpeov26le2cfg6i

Algebraic double cut and join

Sangeeta Bhatia, Attila Egri-Nagy, Andrew R. Francis
2014 Journal of Mathematical Biology  
In this paper, we realize the DCJ operator as a group action on the space of multichromosomal genomes.  ...  We study this group action, deriving some properties of the group and finding group-theoretic analogues for the key results in the DCJ theory.  ...  Counting the optimal sorting scenarios To sort a permutation π a into π b means to transform π a into π b through a sequence of allowed operations (in this case the DCJ operation).  ... 
doi:10.1007/s00285-014-0852-1 pmid:25502846 fatcat:jpwbv7ac5fbepoe4fwg36jlaai

Bayesian sampling of genomic rearrangement scenarios via double cut and join

I. Miklos, E. Tannier
2010 Bioinformatics  
Indeed, in some special cases, the total number of DCJ sorting scenarios can be analytically calculated, and uniformly distributed random DCJ scenarios can be drawn in polynomial running time, while the  ...  Results: We use the computational facilities of the DCJ model to draw a sampling of HP scenarios. It is based on a parallel MCMC method that cools down DCJ scenarios to HP scenarios.  ...  distribution of all possible scenarios is also hard.  ... 
doi:10.1093/bioinformatics/btq574 pmid:21037244 fatcat:lpijw5nkmfgk3pih44i7awm2mm

Parking Functions, Labeled Trees and DCJ Sorting Scenarios [chapter]

Aïda Ouangraoua, Anne Bergeron
2009 Lecture Notes in Computer Science  
Here we give an exact formula for the number of double-cut-and-join (DCJ) rearrangement scenarios of co-tailed genomes.  ...  We also construct effective bijections between the set of scenarios that sort a cycle and well studied combinatorial objects such as parking functions and labeled trees.  ...  Since each cycle is sorted independently, the number of global scenarios is enumerated by counting the number of sequences that contains ℓ m occurrences of the symbol S m , for 1 ≤ m ≤ C, which is counted  ... 
doi:10.1007/978-3-642-04744-2_3 fatcat:drh2dphvm5cftp5737d66achje

Combinatorial Structure of Genome Rearrangements Scenarios

Aïda Ouangraoua, Anne Bergeron
2010 Journal of Computational Biology  
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 scenarios that sort a component as well studied combinatorial objects such as parking functions, labeled trees and prüfer codes.  ...  In the sequel, parsimonious sorting scenarios are simply referred to as sorting scenarios. Sorting cycle and paths independently A DCJ operation is sorting if it lowers the distance by 1.  ... 
doi:10.1089/cmb.2010.0126 pmid:20874400 fatcat:lc6mxfoerbc25njdctjrqzglka

DCJ-RNA - double cut and join for RNA secondary structures

Ghada H. Badr, Haifa A. Al-aqel
2017 BMC Bioinformatics  
The results, which are based on real datasets, show that the algorithm is able to count the minimum number of rearrangement operations, as well as to report an optimum scenario that can increase the similarity  ...  Sequences can be different, but they all share the same structure and, therefore, the same functionality.  ...  Sorting scenario One related issue is identifying a sorting scenario for the given distance, which provides the operations themselves.  ... 
doi:10.1186/s12859-017-1830-6 pmid:29072145 pmcid:PMC5657034 fatcat:yn6jvykgknhjlliyqgdo43ynzm

Rearrangement Models and Single-Cut Operations [chapter]

Paul Medvedev, Jens Stoye
2009 Lecture Notes in Computer Science  
We show that for any optimal SCJ uni sorting scenario that creates a circular chromosome in an intermediate step, there exists a sorting scenario of equal length without a circular chromosome.  ...  The DCJ model is a superset of all the other models in the cube, and is thus the most general.  ... 
doi:10.1007/978-3-642-04744-2_8 fatcat:v2negq2yjjespmwaifthtifmxq

Rearrangement Models and Single-Cut Operations

Anne Bergeron, Paul Medvedev, Jens Stoye
2010 Journal of Computational Biology  
Among our results is that sorting in the HP model is equivalent to sorting in the reversal model when the initial and final genomes are linear unichromosomal.  ...  The dcj model is a superset of all the other models in the cube, and is thus the most general.  ...  Let A and B be two circular genomes, and let R be a dcj-sorting event on A. Then R 2 dcj circ . Proof.  ... 
doi:10.1089/cmb.2010.0091 pmid:20874405 fatcat:2isezqge4jb67o5cqn2tbnkybe

Sampling and counting genome rearrangement scenarios

István Miklós, Heather Smith
2015 BMC Bioinformatics  
Contribution: In this paper, we give a mini-review about the state-of-the-art of sampling and counting rearrangement scenarios, focusing on the reversal, DCJ and SCJ models.  ...  Even for moderate size inputs, there are a tremendous number of optimal rearrangement scenarios, regardless what the model is and which specific question is to be answered.  ...  to calculate the number of most parsimonious sorting scenarios between G 1 and G 2 .  ... 
doi:10.1186/1471-2105-16-s14-s6 pmid:26452124 pmcid:PMC4603625 fatcat:prugvnwdyffvtojt5l3m5lwwfm
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