Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Hannenhalli, S., Pevzner, P.: Transforming men into mice (polynomial algorithm for genomic distance problem). In: Proc. of FOCS 1995, pp. 581–592 (1995)
Tesler, G.: Efficient algorithms for multichromosomal genome rearrangements. J. Comput. Syst. Sci. 65, 587–609 (2002)
Ozery-Flato, M., Shamir, R.: Two notes on genome rearrangement. J. Bioinf. Comput. Biol. 1, 71–94 (2003)
Jean, G., Nikolski, M.: Genome rearrangements: A correct algorithm for optimal capping. Inf. Process. Lett. 104, 14–20 (2007)
Bergeron, A., Mixtacki, J., Stoye, J.: A new linear time algorithm to compute the genomic distance via the double cut and join distance. Theor. Comput. Sci. 410, 5300–5316 (2009)
Erdős, P.L., Soukup, L., Stoye, J.: Balanced vertices in trees and a simpler algorithm to compute the genomic distance. Appl. Math. Lett. 24, 82–86 (2011)
Yancopoulos, S., Attie, O., Friedberg, R.: Efficient sorting of genomic permutations by translocation, inversion and block interchange. Bioinformatics 21, 3340–3346 (2005)
Bergeron, A., Mixtacki, J., Stoye, J.: A unifying view of genome rearrangements. In: Bücher, P., Moret, B.M.E. (eds.) WABI 2006. LNCS (LNBI), vol. 4175, pp. 163–173. Springer, Heidelberg (2006)
Adam, Z., Sankoff, D.: The ABCs of MGR with DCJ. Evol. Bioinform. Online 4, 69–74 (2008)
Mixtacki, J.: Genome halving under DCJ revisited. In: Hu, X., Wang, J. (eds.) COCOON 2008. LNCS, vol. 5092, pp. 276–286. Springer, Heidelberg (2008)
Tannier, E., Zheng, C., Sankoff, D.: Multichromosomal median and halving problems under different genomic distances. BMC Bioinformatics 10, 120 (2009)
Thomas, A., Varré, J.S., Ouangraoua, A.: Genome dedoubling by DCJ and reversal. BMC Bioinformatics 12(suppl. 19), S20 (2012)
Kováč, J., Warren, R., Braga, M.D.V., Stoye, J.: Restricted DCJ model (the problem of chromosome reincorporation). J. Comput. Biol. 18, 1231–1241 (2011)
Yancopoulos, S., Friedberg, R.: DCJ path formulation for genome transformations which include Insertions, Deletions, and Duplications. J. Comput. Biol. 16, 1311–1338 (2009)
Braga, M.D.V., Willing, E., Stoye, J.: Double cut and join with insertions and deletions. J. Comput. Biol. 18, 1167–1184 (2011)
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)
Braga, M.D.V.: An overview of genomic distances modeled with indels. In: Bonizzoni, P., Brattka, V., Löwe, B. (eds.) CiE 2013. LNCS, vol. 7921, pp. 22–31. Springer, Heidelberg (2013)
El-Mabrouk, N.: Sorting signed permutations by reversals and insertions/deletions of contiguous segments. J. Discr. Alg. 1, 105–122 (2001)
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)
da Silva, P.H., Machado, R., Dantas, S., Braga, M.D.V.: DCJ-indel and DCJ-substitution distances with distinct operation costs. Alg. for Mol. Biol. 8, 21 (2013)
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)
Hilker, R., Sickinger, C., Pedersen, C., Stoye, J.: UniMoG - a unifying framework for genomic distance calculation and sorting based on DCJ. Bioinformatics 28, 2509–2511 (2012)
Willing, E., Zaccaria, S., Braga, M.D.V., Stoye, J.: On the inversion-indel distance. BMC Bioinformatics 14(suppl. 11), S3 (2013)
Braga, M.D.V., Machado, R., Ribeiro, L.C., Stoye, J.: Genomic distance under gene substitutions. BMC Bioinformatics 12(suppl. 9), S8 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Braga, M.D.V., Stoye, J. (2013). Restricted DCJ-Indel Model Revisited. In: Setubal, J.C., Almeida, N.F. (eds) Advances in Bioinformatics and Computational Biology. BSB 2013. Lecture Notes in Computer Science(), vol 8213. Springer, Cham. https://doi.org/10.1007/978-3-319-02624-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-02624-4_4
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02623-7
Online ISBN: 978-3-319-02624-4
eBook Packages: Computer ScienceComputer Science (R0)