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

Silva, Poly H. da; Machado, Raphael C. S.; Dantas, Simone; Braga, Marília D. V.

doi:10.1186/1471-2105-13-s19-s14

Cited by 7 publications

(7 citation statements)

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“…Although in an arbitrary scenario the order of these operations may vary, from [17] we know that insertions can always be moved ahead of the DCJ operations, s.t. they occur in the first steps, and analogously the deletions can be moved aback to occur after the DCJ operations in the last steps.…”

Section: Resultsmentioning

confidence: 99%

On the inversion-indel distance

et al. 2013

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BackgroundThe inversion distance, that is the distance between two unichromosomal genomes with the same content allowing only inversions of DNA segments, can be computed thanks to a pioneering approach of Hannenhalli and Pevzner in 1995. In 2000, El-Mabrouk extended the inversion model to allow the comparison of unichromosomal genomes with unequal contents, thus insertions and deletions of DNA segments besides inversions. However, an exact algorithm was presented only for the case in which we have insertions alone and no deletion (or vice versa), while a heuristic was provided for the symmetric case, that allows both insertions and deletions and is called the inversion-indel distance. In 2005, Yancopoulos, Attie and Friedberg started a new branch of research by introducing the generic double cut and join (DCJ) operation, that can represent several genome rearrangements (including inversions). Among others, the DCJ model gave rise to two important results. First, it has been shown that the inversion distance can be computed in a simpler way with the help of the DCJ operation. Second, the DCJ operation originated the DCJ-indel distance, that allows the comparison of genomes with unequal contents, considering DCJ, insertions and deletions, and can be computed in linear time.ResultsIn the present work we put these two results together to solve an open problem, showing that, when the graph that represents the relation between the two compared genomes has no bad components, the inversion-indel distance is equal to the DCJ-indel distance. We also give a lower and an upper bound for the inversion-indel distance in the presence of bad components.

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Section: Resultsmentioning

confidence: 99%

On the inversion-indel distance

et al. 2013

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“…In this section we first solve an open problem from [16], before we present a simple algorithm to compute an optimal rearrangement scenario under the restricted DCJ-indel model.…”

Section: Restricted Dcj-indel Modelmentioning

confidence: 99%

“…As shown in [16], the scenario S 1 can be transformed into another optimal scenario S 2 of the same cost, so that S 2 starts with n ins insertions, followed by n DCJ DCJ operations, followed by n del deletions. We can represent S 2 as follows: .…”

Section: Computing the Distancementioning

confidence: 99%

“…A restricted version of the DCJ-indel model has also been considered [16], but the question whether both the unrestricted and the restricted DCJ-indel distances were the same was not so easy to answer as it was for the basic DCJ model. In fact, the paper by da Silva et al [16] gives only an upper bound for the restricted DCJ-indel distance and an algorithm that achieves this bound.…”

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confidence: 99%

“…In fact, the paper by da Silva et al [16] gives only an upper bound for the restricted DCJ-indel distance and an algorithm that achieves this bound. Deriving an exact distance formula and an optimal sorting algorithm were left as open problems.…”

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Sorting Linear Genomes with Rearrangements and Indels

Braga

Stoye

2015

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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Rearrangements are mutations that can change the organization of a genome, but not its content. Examples are inversions of DNA segments, translocations of chromosome ends, fusions and fissions of chromosomes. All mentioned rearrangements can be represented by the generic Double Cut and Join (DCJ) operation. However, the DCJ operation also allows circular chromosomes to be created at intermediate steps, even if the compared genomes are linear. In this case it is more plausible to consider a restriction in which the reincorporation of a circular chromosome has to be done immediately after its creation. We call these two consecutive operations an ER composition. It has been shown that an ER composition mimics either an internal block interchange (when two segments in the same chromosome exchange their positions), or an internal transposition (the special case of a block interchange when the two segments are adjacent). The DCJ distance of two genomes is the same, regardless of this restriction, and can be computed in linear time. For comparing two genomes with unequal contents, in addition to rearrangements we have to allow insertions and deletions of DNA segments-named indels. It is already known that the distance in the model combining DCJ and indel operations can be exactly computed. Again, for linear genomes it would be more plausible to adopt a restricted version with ER compositions. This model was studied recently by da Silva et al. (BMC Bioinformatics 13, Suppl. 19, S14, 2012), but only an upper bound for the restricted DCJ-indel distance was provided. Here we first solve an open problem posed in that paper and present a very simple proof showing that the distance, which can be computed in linear time, is the same for both the unrestricted and the restricted DCJ-indel models. We then give a simpler algorithm for computing an optimal restricted DCJ-indel sorting scenario in O(n log n) time. We also relate the DCJ-indel distance to the restricted DCJ-substitution distance, which instead of indels considers a more powerful operation that allows the substitution of a DNA segment by another DNA segment. We show that the DCJ-indel distance is a 2-approximation for the restricted DCJ-substitution distance.

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Genome Rearrangement Problems with Single and Multiple Gene Copies: A Review

Zeira

Shamir

2019

Computational Biology

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

Cited by 7 publications

References 8 publications

On the inversion-indel distance

On the inversion-indel distance

Sorting Linear Genomes with Rearrangements and Indels

Genome Rearrangement Problems with Single and Multiple Gene Copies: A Review

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