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Tandem Duplications, Segmental Duplications and Deletions, and Their Applications

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Computer Science – Theory and Applications (CSR 2020)

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Abstract

We review two streams of recent research results in this paper. The first is on converting a sequence A to another sequence B using the minimum number of tandem duplications. This research originates from the copying systems in computer science in the early 1980s, and also from biology more than 40 years ago. We review our recent NP-hardness result on this paper, together with several open problems along the line. Segmental duplications and deletions are more discussed recently on cancer research where besides genomes (sequences), the so-called copy number profile (a vector where the ith component represents the number of the ith segment appearing in the genome, regardless of their orders) are also used. We again review some of our recent hardness results and preliminary positive results, together with some open problems. This paper is mostly self-contained.

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References

  1. Alon, N., Bruck, J., Hassanzadeh, F.F., Jain, S.: Duplication distance to the root for binary sequences. IEEE Trans. Inf. Theory 63(12), 7793–7803 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  2. Angibaud, S., Fertin, G., Rusu, I., Thevenin, A., Vialette, S.: On the approximability of comparing genomes with duplicates. J. Graph Algorithms Appl. 13(1), 19–53 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Benson, G., Dong, L.: Reconstructing the duplication history of a tandem repeat. In: Proceedings of ISMB 1999, pp. 44–53 (1999)

    Google Scholar 

  4. Bovet, D.P., Varricchio, S.: On the regularity of languages on a binary alphabet generated by copying systems. Inf. Process. Lett. 44(3), 119–123 (1992)

    Google Scholar 

  5. Bulteau, L., Fertin, G., Rusu, I.: Sorting by transposition is difficult. SIAM J. Discrete Math. 26(3), 1148–1180 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  6. The Cancer Genome Atlas Research Network: Integrated genomic analyses of ovarian carcinoma. Nature 474, 609–615 (2011)

    Article  Google Scholar 

  7. Charlesworth, B., Sniegowski, P., Stephan, W.: The evolutionary dynamics of repetitive DNA in eukaryotes. Nature 371(6494), 215–220 (1994)

    Article  Google Scholar 

  8. Chaudhuri, K., Chen, K., Mihaescu, R., Rao, S.: On the tandem duplication-random loss model of genome rearrangement. In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2006), pp. 564–570 (2006)

    Google Scholar 

  9. Chen, Z., Wang, L., Wang, Z.: Approximation algorithms for reconstructing the duplication history of tandem repeats. Algorithmica 54(4), 501–529 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Cho, D.-J., Han, Y.-S., Kim, H.: Bound-decreasing duplication system. Theoret. Comput. Sci. 793, 152–168 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  11. Chowdhury, S., Shackney, S., Heselmeyer-Haddad, K., Ried, T., Schaeffer, A., Schwartz, R.: Algorithms to model single gene, single chromosome, and whole genome copy number changes jointly in tumor phylogenetics. Plos Comput. Biol. 10(7), e1003740 (2014)

    Article  Google Scholar 

  12. Ciriello, G., Killer, M., Aksoy, B., Senbabaoglu, Y., Schultz, N., Sanders, C.: Emerging landscape of oncogenic signatures across human cancers. Nat. Genet. 45, 1127–1133 (2013)

    Article  Google Scholar 

  13. Cooke, S., et al.: Intra-tumour genetic heterogeneity and poor chemoradiotherapy response in cervical cancer. Br. J. Cancer 104(2), 361–368 (2011)

    Article  Google Scholar 

  14. Cooke, S., Brenton, J.: Evolution of platinum resistance in high-grade serous ovarian cancer. Lancet Oncol. 12(12), 1169–1174 (2011)

    Article  Google Scholar 

  15. Cowin, P., et al.: LRP1B deletion in high-grade serous ovarian cancers is associated with acquired chemotherapy resistance to liposomal doxorubicin. Cancer Res. 72(16), 4060–4073 (2012)

    Article  Google Scholar 

  16. Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Introduction to Algorithms, Second edn. MIT Press, Cambridge (2001)

    Google Scholar 

  17. Dassow, J., Mitrana, V., Paun, G.: On the regularity of the duplication closure. Bull. EATCS 69, 133–136 (1999)

    MathSciNet  MATH  Google Scholar 

  18. Downey, R., Fellows, M.: Parameterized Complexity. Springer, Heidelberg (1999). https://doi.org/10.1007/978-1-4612-0515-9

  19. Ehrenfeucht, A., Rozenberg, G.: On regularity of languages generated by copying systems. Discrete Appl. Math. 8(3), 313–317 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  20. El-Kebir, M., et al.: Copy-number evolution problems: complexity and algorithms. In: Frith, M., Storm Pedersen, C.N. (eds.) WABI 2016. LNCS, vol. 9838, pp. 137–149. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-43681-4_11

    Chapter  Google Scholar 

  21. Fellows, M., Hermelin, D., Rosamond, F., Vialette, S.: On the parameterized complexity of multiple-interval graph problems. Theoret. Comput. Sci. 410(1), 53–61 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006). https://doi.org/10.1007/3-540-29953-X

  23. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman W. H., New York (1979)

    MATH  Google Scholar 

  24. Gascuel, O., Hendy, M.D., Jean-Marie, A., McLachlan, R.: The combinatorics of tandem duplication trees. Syst. Biol. 52(1), 110–118 (2003)

    Google Scholar 

  25. Gusfield, D.: Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology. Cambridge University Press, Cambridge (1997)

    Google Scholar 

  26. Gusfield, D., Stoye, J.: Linear time algorithms for finding and representing all the tandem repeats in a string. J. Comput. Syst. Sci. 69(4), 525–546 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  27. Hannenhalli, S., Pevzner, P.: Transforming men into mice (polynomial algorithm for genomic distance problem). In: Proceedings of FOCS 1995, pp. 581–592 (1995)

    Google Scholar 

  28. Hassanzadeh, F., Schwartz, M., Bruck, J.: The capacity of string-duplication systems. IEEE Trans. Inf. Theory 62(2), 811–824 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  29. Ito, M., Leupold, P., Shikishima-Tsuji, K.: Closure of language classes under bounded duplication. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 238–247. Springer, Heidelberg (2006). https://doi.org/10.1007/11779148_22

    Chapter  MATH  Google Scholar 

  30. Jain, S., Hassanzadeh, F., Bruck, J.: Capacity and expressiveness of genomic tandem duplication. IEEE Trans. Inf. Theory 63(10), 6129–6138 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  31. Jiang, H., Zheng, C., Sankoff, D., Zhu, B.: Scaffold filling under the breakpoint and related distances. IEEE/ACM Trans. Comput. Biol. Bioinform. 9(4), 1220–1229 (2012)

    Google Scholar 

  32. Landau, G., Schmidt, J., Sokol, D.: An algorithm for approximate tandem repeats. J. Comput. Biol. 8(1), 1–18 (2001)

    Article  Google Scholar 

  33. Lander, E.S., et al.: Initial sequencing and analysis of the human genome. Nature 409(6822), 860–921 (2001)

    Article  Google Scholar 

  34. Lafond, M., Zhu, B., Zou, P.: The tandem duplication distance is NP-hard. CoRR abs/1906.05266, June 2019

    Google Scholar 

  35. Lafond, M., Zhu, B., Zou, P.: The tandem duplication distance is NP-hard. In: Proceedings of STACS 2020. LiPIcs, vol. 154, pp. 15:1–15:15 (2020)

    Google Scholar 

  36. Lafond, M., Zhu, B., Zou, P.: Genomic problems involving copy number profiles: complexity and algorithms. CoRR abs/2002.04778, February 2020

    Google Scholar 

  37. Lafond, M., Zhu, B., Zou, P.: Genomic problems involving copy number profiles: complexity and algorithms. In: Proceedings of CPM 2020. LiPIcs, vol. 161, pp. 22:1–22:25 (2020)

    Google Scholar 

  38. Letunic, I., Copley, R., Bork, P.: Common exon duplication in animals and its role in alternative splicing. Hum. Mol. Genet. 11(13), 1561–1567 (2002)

    Article  Google Scholar 

  39. Leupold, P., Mitrana, V., Sempere, J.M.: Formal languages arising from gene repeated duplication. In: Jonoska, N., Paun, G., Rozenberg, G. (eds.) Aspects of Molecular Computing. LNCS, vol. 2950, pp. 297–308. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-24635-0_22

    Chapter  Google Scholar 

  40. Leupold, P., Carlos, M.V., Mitrana, V.: Uniformly bounded duplication languages. Discrete Appl. Math. 146(3), 301–310 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  41. Li, S., Dou, X., Ge, R., Qian, M., Wan, L.: A remark on copy number variation detection. Plos One 13(4), e0196226 (2018)

    Article  Google Scholar 

  42. Li, W., Olivier, M.: Current analysis platforms and methods for detecting copy number variation. Physiol. Genomics 45(1), 1–16 (2013)

    Article  Google Scholar 

  43. Macdonald, M., et al.: A novel gene containing a trinucleotide repeat that is expanded and unstable on Huntington’s disease. Cell 72(6), 971–983 (1993)

    Article  Google Scholar 

  44. Maley, C., et al.: Genetic clonal diversity predicts progression to esophageal adenocarcinoma. Nat. Genet. 38(4), 468–473 (2006)

    Google Scholar 

  45. Marusyk, A., Almendro, V., Polyak, K.: Intra-tumour heterogeneity: a looking glass for cancer. Nat. Rev. 13, 323–334 (2012)

    Article  Google Scholar 

  46. Navin, N., et al.: Inferring tumor progression from genomic heterogeneity. Genome Res. 20, 68–80 (2010)

    Article  Google Scholar 

  47. Oesper, L., Ritz, A., Aerni, S., Drebin, R., Raphael, B.: Reconstructing cancer genomes from paired-end sequencing data. BMC Bioinform. 13(Suppl 6), S10 (2012)

    Article  Google Scholar 

  48. Qingge, L., He, X., Liu, Z., Zhu, B.: On the minimum copy number generation problem in cancer genomics. In: Proceedings of ACM BCB 2018, pp. 260–269. ACM (2018)

    Google Scholar 

  49. Schwarz, R., Trinh, A., Sipos, B., Brenton, J., Goldman, N., Markowetz, F.: Phylogenetic quantification of intra-tumour heterogeneity. Plos Comput. Biol. 10(4), e1003535 (2014)

    Article  Google Scholar 

  50. Shah, S., et al.: Mutational evolution in a lobular breast tumor profiled at single nucleotide resolution. Nature 461(7265), 809–813 (2009)

    Article  Google Scholar 

  51. Shamir, R., Zehavi, M., Zeira, R.: A linear-time algorithm for the copy number transformation problem. In: Proceedings of CPM 2016. LiPIcs, vol. 54, pp. 16:1–16:13 (2016)

    Google Scholar 

  52. Sharp, A., et al.: Segmental duplications and copy-number variation in the human genome. Am. J. Hum. Genet. 77(1), 78–88 (2005)

    Article  Google Scholar 

  53. Szostak, J.W., Wu, R.: Unequal crossing over in the ribosomal DNA of Saccharomyces cerevisiae. Nature 284(5755), 426–430 (1980)

    Article  Google Scholar 

  54. Thue, A.: Über unendliche Zeichenreihen (Mathematisk-Naturvidenskabelig Klasse). Videnskabsselskabet, Freetown Christiania, Denmark (1906)

    MATH  Google Scholar 

  55. Tremblay-Savard, O., Bertrand, D., El-Mabrouk, N.: Evolution of orthologous tandemly arrayed gene clusters. BMC Bioinform. 12(S-9), S2 (2011)

    Google Scholar 

  56. Trevisan, L.: Non-approximability results for optimization problems on bounded degree instances. In: Proceedings of 33rd ACM Symposium on Theory of Computing (STOC 2001), pp. 453–461. ACM (2001)

    Google Scholar 

  57. Wang, M.W.: On the irregularity of the duplication closure. Bull. EATCS 70, 162–163 (2000)

    MathSciNet  MATH  Google Scholar 

  58. Watterson, G.A., Ewens, W.J., Hall, T.E., Morgan, A.: The chromosome inversion problem. J. Theoret. Biol. 99(1), 1–7 (1982)

    Article  Google Scholar 

  59. Zhu, B.: A retrospective on genomic preprocessing for comparative genomics. In: Chauve, C., El-Mabrouk, N., Tannier, E. (eds.) Models and Algorithms for Genome Evolution, vol. 19, pp. 183–206. Springer, Heidelberg (2013). https://doi.org/10.1007/978-1-4471-5298-9_9

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Acknowledgments

I would like to thank my collaborators for these research: Manuel Lafond, Letu Qingge and Peng Zou. I also thank Prof. Henning Fernau and the organizers of CSR’2020 to give me the chance to survey these research.

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Correspondence to Binhai Zhu .

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Zhu, B. (2020). Tandem Duplications, Segmental Duplications and Deletions, and Their Applications. In: Fernau, H. (eds) Computer Science – Theory and Applications. CSR 2020. Lecture Notes in Computer Science(), vol 12159. Springer, Cham. https://doi.org/10.1007/978-3-030-50026-9_6

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  • DOI: https://doi.org/10.1007/978-3-030-50026-9_6

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