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Restricted DCJ-indel model: sorting linear genomes with DCJ and indels.

da Silva PH, Machado R, Dantas S, Braga MD - BMC Bioinformatics (2012)

Bottom Line: However, when the compared genomes are linear, it is more plausible to use the so-called restricted DCJ model, in which we proceed the reincorporation of a circular chromosome immediately after its creation.When the compared genomes have the same content, it is known that the genomic distance for the restricted DCJ model is the same as the distance for the general model.The question whether this bound can be reduced so that both the general and the restricted DCJ-indel distances are equal remains open.

View Article: PubMed Central - HTML - PubMed

Affiliation: IME, Universidade Federal Fluminense, Niterói, Brazil. poly.hannah@gmail.com

ABSTRACT

Background: The double-cut-and-join (DCJ) is a model that is able to efficiently sort a genome into another, generalizing the typical mutations (inversions, fusions, fissions, translocations) to which genomes are subject, but allowing the existence of circular chromosomes at the intermediate steps. In the general model many circular chromosomes can coexist in some intermediate step. However, when the compared genomes are linear, it is more plausible to use the so-called restricted DCJ model, in which we proceed the reincorporation of a circular chromosome immediately after its creation. These two consecutive DCJ operations, which create and reincorporate a circular chromosome, mimic a transposition or a block-interchange. When the compared genomes have the same content, it is known that the genomic distance for the restricted DCJ model is the same as the distance for the general model. If the genomes have unequal contents, in addition to DCJ it is necessary to consider indels, which are insertions and deletions of DNA segments. Linear time algorithms were proposed to compute the distance and to find a sorting scenario in a general, unrestricted DCJ-indel model that considers DCJ and indels.

Results: In the present work we consider the restricted DCJ-indel model for sorting linear genomes with unequal contents. We allow DCJ operations and indels with the following constraint: if a circular chromosome is created by a DCJ, it has to be reincorporated in the next step (no other DCJ or indel can be applied between the creation and the reincorporation of a circular chromosome). We then develop a sorting algorithm and give a tight upper bound for the restricted DCJ-indel distance.

Conclusions: We have given a tight upper bound for the restricted DCJ-indel distance. The question whether this bound can be reduced so that both the general and the restricted DCJ-indel distances are equal remains open.

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This recombination is a neutral DCJ that has Δλ = -2 (we represent only the labels of the adjacencies, the cuts of the recombination are represented by "/"and "\").
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Figure 6: This recombination is a neutral DCJ that has Δλ = -2 (we represent only the labels of the adjacencies, the cuts of the recombination are represented by "/"and "\").

Mentions: Until this point, we have explored the possible effects of any DCJ that is applied to two adjacencies belonging to a single component of the graph. However, there is another type of DCJ that must be considered. A DCJ operation ρ applied to adjacencies belonging to two different components is called a recombination and can have Δλ(ρ) < 0 [5]. Thus, depending on the value of w and on whether the recombination is an optimal, a neutral or a counter-optimal DCJ, a recombination with Δλ(ρ) < 0 can lead to a sorting sequence with lower cost. As an example, a neutral recombination with Δλ = -2 is represented in Figure 6.


Restricted DCJ-indel model: sorting linear genomes with DCJ and indels.

da Silva PH, Machado R, Dantas S, Braga MD - BMC Bioinformatics (2012)

This recombination is a neutral DCJ that has Δλ = -2 (we represent only the labels of the adjacencies, the cuts of the recombination are represented by "/"and "\").
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3526439&req=5

Figure 6: This recombination is a neutral DCJ that has Δλ = -2 (we represent only the labels of the adjacencies, the cuts of the recombination are represented by "/"and "\").
Mentions: Until this point, we have explored the possible effects of any DCJ that is applied to two adjacencies belonging to a single component of the graph. However, there is another type of DCJ that must be considered. A DCJ operation ρ applied to adjacencies belonging to two different components is called a recombination and can have Δλ(ρ) < 0 [5]. Thus, depending on the value of w and on whether the recombination is an optimal, a neutral or a counter-optimal DCJ, a recombination with Δλ(ρ) < 0 can lead to a sorting sequence with lower cost. As an example, a neutral recombination with Δλ = -2 is represented in Figure 6.

Bottom Line: However, when the compared genomes are linear, it is more plausible to use the so-called restricted DCJ model, in which we proceed the reincorporation of a circular chromosome immediately after its creation.When the compared genomes have the same content, it is known that the genomic distance for the restricted DCJ model is the same as the distance for the general model.The question whether this bound can be reduced so that both the general and the restricted DCJ-indel distances are equal remains open.

View Article: PubMed Central - HTML - PubMed

Affiliation: IME, Universidade Federal Fluminense, Niterói, Brazil. poly.hannah@gmail.com

ABSTRACT

Background: The double-cut-and-join (DCJ) is a model that is able to efficiently sort a genome into another, generalizing the typical mutations (inversions, fusions, fissions, translocations) to which genomes are subject, but allowing the existence of circular chromosomes at the intermediate steps. In the general model many circular chromosomes can coexist in some intermediate step. However, when the compared genomes are linear, it is more plausible to use the so-called restricted DCJ model, in which we proceed the reincorporation of a circular chromosome immediately after its creation. These two consecutive DCJ operations, which create and reincorporate a circular chromosome, mimic a transposition or a block-interchange. When the compared genomes have the same content, it is known that the genomic distance for the restricted DCJ model is the same as the distance for the general model. If the genomes have unequal contents, in addition to DCJ it is necessary to consider indels, which are insertions and deletions of DNA segments. Linear time algorithms were proposed to compute the distance and to find a sorting scenario in a general, unrestricted DCJ-indel model that considers DCJ and indels.

Results: In the present work we consider the restricted DCJ-indel model for sorting linear genomes with unequal contents. We allow DCJ operations and indels with the following constraint: if a circular chromosome is created by a DCJ, it has to be reincorporated in the next step (no other DCJ or indel can be applied between the creation and the reincorporation of a circular chromosome). We then develop a sorting algorithm and give a tight upper bound for the restricted DCJ-indel distance.

Conclusions: We have given a tight upper bound for the restricted DCJ-indel distance. The question whether this bound can be reduced so that both the general and the restricted DCJ-indel distances are equal remains open.

Show MeSH
Related in: MedlinePlus