Restricted DCJ-Indel Model Revisited
The Double Cut and Join (DCJ) is a generic operation representing many rearrangements that can change the organization of a genome, but not its content. For comparing two genomes with unequal contents, in addition to DCJ operations, we have to allow insertions and deletions of DNA segments. The distance in the so-called general DCJ-indel model can be exactly computed, but 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 the restricted DCJ-indel model, in which the reincorporation of a circular chromosome has to be done immediately after its creation. This model was studied recently by da Silva et al. (BMC Bioinformatics 13, Suppl. 19, S14), but only an upper bound for the restricted DCJ-indel distance was provided. Here we solve an open problem posed in that paper and present a very simple proof showing that the distance, that can be computed in linear time, is always the same for both the general and the restricted DCJ-indel models. We also present a simpler algorithm for computing an optimal restricted DCJ-indel sorting scenario in O(n logn) time.
KeywordsTriangular Inequality Circular Chromosome Genomic Distance Linear Genome Duplicate Marker
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- 1.Hannenhalli, S., Pevzner, P.: Transforming men into mice (polynomial algorithm for genomic distance problem). In: Proc. of FOCS 1995, pp. 581–592 (1995)Google Scholar
- 9.Adam, Z., Sankoff, D.: The ABCs of MGR with DCJ. Evol. Bioinform. Online 4, 69–74 (2008)Google Scholar
- 12.Thomas, A., Varré, J.S., Ouangraoua, A.: Genome dedoubling by DCJ and reversal. BMC Bioinformatics 12(suppl. 19), S20 (2012)Google Scholar
- 16.da Silva, P.H., Machado, R., Dantas, S., Braga, M.D.V.: Restricted DCJ-indel model: sorting linear genomes with DCJ and indels. BMC Bioinformatics 13(suppl. 19), S14 (2012)Google Scholar
- 19.Swenson, K.M., Arndt, W., Tang, J., Moret, B.: Phylogenetic reconstruction from complete gene orders of whole genomes. In: Proc. of Asia-Pacific Bioinformatics Conf. Advances in Bioinformatics and Comp. Biology, vol. 6, pp. 241–250 (2008)Google Scholar
- 21.Braga, M.D.V., Machado, R., Ribeiro, L.C., Stoye, J.: On the weight of indels in genomic distances. BMC Bioinformatics 12(suppl. 9), S13 (2011)Google Scholar
- 23.Willing, E., Zaccaria, S., Braga, M.D.V., Stoye, J.: On the inversion-indel distance. BMC Bioinformatics 14(suppl. 11), S3 (2013)Google Scholar
- 24.Braga, M.D.V., Machado, R., Ribeiro, L.C., Stoye, J.: Genomic distance under gene substitutions. BMC Bioinformatics 12(suppl. 9), S8 (2011)Google Scholar