Abstract
Computing the edit distance between two genomes is a basic problem in the study of genome evolution. The double-cut-and-join (DCJ) model has formed the basis for most algorithmic research on rearrangements over the last few years. The edit distance under the DCJ model can be computed in linear time for genomes without duplicate genes, while the problem becomes NP-hard in the presence of duplicate genes. In this paper, we propose an ILP (integer linear programming) formulation to compute the DCJ distance between two genomes with duplicate genes. We also provide an efficient preprocessing approach to simplify the ILP formulation while preserving optimality. Comparison on simulated genomes demonstrates that our method outperforms MSOAR in computing the edit distance, especially when the genomes contain long duplicated segments. We also apply our method to assign orthologous gene pairs among human, mouse and rat genomes, where once again our method outperforms MSOAR.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Fertin, G., Labarre, A., Rusu, I., Tannier, E., Vialette, S.: Combinatorics of Genome Rearrangements. MIT Press (2009)
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)
Yancopoulos, S., Attie, O., Friedberg, R.: Efficient sorting of genomic permutations by translocation, inversion and block interchange. Bioinformatics 21(16), 3340–3346 (2005)
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(51), 5300–5316 (2009)
Chen, X.: On sorting permutations by double-cut-and-joins. In: Thai, M.T., Sahni, S. (eds.) COCOON 2010. LNCS, vol. 6196, pp. 439–448. Springer, Heidelberg (2010)
Chen, X., Sun, R., Yu, J.: Approximating the double-cut-and-join distance between unsigned genomes. BMC Bioinformatics 12(suppl. 9), S17 (2011)
Yancopoulos, S., Friedberg, R.: Sorting genomes with insertions, deletions and duplications by DCJ. In: Nelson, C.E., Vialette, S. (eds.) RECOMB-CG 2008. LNCS (LNBI), vol. 5267, pp. 170–183. Springer, Heidelberg (2008)
Moret, B.M.E., Lin, Y., Tang, J.: Rearrangements in phylogenetic inference: Compare, model, or encode? In: Chauve, C., El-Mabrouk, N., Tannier, E. (eds.) Models and Algorithms for Genome Evolution. Computational Biology, vol. 19, pp. 147–172. Springer, Berlin (2013)
Hannenhalli, S., Pevzner, P.A.: Transforming cabbage into turnip (polynomial algorithm for sorting signed permutations by reversals). In: Proc. 27th Ann. ACM Symp. Theory of Comput. (STOC 1995), pp. 178–189. ACM Press, New York (1995)
Bader, D.A., Moret, B.M.E., Yan, M.: A fast linear-time algorithm for inversion distance with an experimental comparison. J. Comput. Biol. 8(5), 483–491 (2001)
Jean, G., Nikolski, M.: Genome rearrangements: a correct algorithm for optimal capping. Inf. Proc. Letters 104(1), 14–20 (2007)
Ozery-Flato, M., Shamir, R.: Two notes on genome rearrangement. J. Bioinf. Comp. Bio. 1(1), 71–94 (2003)
Tesler, G.: Efficient algorithms for multichromosomal genome rearrangements. J. Comput. Syst. Sci. 65(3), 587–609 (2002)
Bailey, J.A., Eichler, E.E.: Primate segmental duplications: crucibles of evolution, diversity and disease. Nature Reviews Genetics 7(7), 552–564 (2006)
Lynch, M.: The Origins of Genome Architecture. Sinauer (2007)
Jiang, Z., Tang, H., Ventura, M., Cardone, M.F., Marques-Bonet, T., She, X., Pevzner, P.A., Eichler, E.E.: Ancestral reconstruction of segmental duplications reveals punctuated cores of human genome evolution. Nature Genetics 39(11), 1361–1368 (2007)
Chen, X., Zheng, J., Fu, Z., Nan, P., Zhong, Y., Lonardi, S., Jiang, T.: Assignment of orthologous genes via genome rearrangement. ACM/IEEE Trans. on Comput. Bio. & Bioinf. 2(4), 302–315 (2005)
Suksawatchon, J., Lursinsap, C., Bodén, M.: Computing the reversal distance between genomes in the presence of multi-gene families via binary integer programming. Journal of Bioinformatics and Computational Biology 5(1), 117–133 (2007)
Laohakiat, S., Lursinsap, C., Suksawatchon, J.: Duplicated genes reversal distance under gene deletion constraint by integer programming. Bioinformatics and Biomedical Engineering, 527–530 (2008)
Fu, Z., Chen, X., Vacic, V., Nan, P., Zhong, Y., Jiang, T.: MSOAR: a high-throughput ortholog assignment system based on genome rearrangement. Journal of Computational Biology 14(9), 1160–1175 (2007)
Shi, G., Zhang, L., Jiang, T.: MSOAR 2.0: Incorporating tandem duplications into ortholog assignment based on genome rearrangement. BMC Bioinformatics 11(1), 10 (2010)
Kececioglu, J., Sankoff, D.: Exact and approximation algorithms for sorting by reversals, with application to genome rearrangement. Algorithmica 13(1), 180–210 (1995)
Shao, M., Lin, Y.: Approximating the edit distance for genomes with duplicate genes under DCJ, insertion and deletion. BMC Bioinformatics 13(suppl. 19), S13 (2012)
Gurobi Optimization Inc. Gurobi optimizer reference manual (2013)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Shao, M., Lin, Y., Moret, B. (2014). An Exact Algorithm to Compute the DCJ Distance for Genomes with Duplicate Genes. In: Sharan, R. (eds) Research in Computational Molecular Biology. RECOMB 2014. Lecture Notes in Computer Science(), vol 8394. Springer, Cham. https://doi.org/10.1007/978-3-319-05269-4_22
Download citation
DOI: https://doi.org/10.1007/978-3-319-05269-4_22
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05268-7
Online ISBN: 978-3-319-05269-4
eBook Packages: Computer ScienceComputer Science (R0)