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Alignments with Non-overlapping Moves, Inversions and Tandem Duplications in O(n 4) Time

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Book cover Computing and Combinatorics (COCOON 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4598))

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Abstract

Sequence alignment is a central problem in bioinformatics. The classical dynamic programming algorithm aligns two sequences by optimizing over possible insertions, deletions and substitution. However, other evolutionary events can be observed, such as inversions, tandem duplications or moves (transpositions). It has been established that the extension of the problem to move operations is NP-complete. Previous work has shown that an extension restricted to non-overlapping inversions can be solved in O(n 3) with a restricted scoring scheme. In this paper, we show that the alignment problem extended to non-overlapping moves can be solved in O(n 5) for general scoring schemes, O(n 4logn) for concave scoring schemes and O(n 4) for restricted scoring schemes. Furthermore, we show that the alignment problem extended to non-overlapping moves, inversions and tandem duplications can be solved with the same time complexities. Finally, an example of an alignment with non-overlapping moves is provided.

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References

  1. Needleman, S.B., Wunsch, C.D.: A general method applicable to the search for similarities in the amino acid sequence of two proteins. J. Mol. Biol. 48(3), 443–453 (1970)

    Article  Google Scholar 

  2. Fliess, A., Motro, B., Unger, R.: Swaps in protein sequences. Proteins. 48(2), 377–387 (2002)

    Article  Google Scholar 

  3. Lopresti, D., Tomkins, A.: Block edit models for approximate string matching. Theor. Comput. Sci. 181(1), 159–179 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  4. Shapira, D., Storer, J.A.: Edit distance with move operations. In: Apostolico, A., Takeda, M. (eds.) CPM 2002. LNCS, vol. 2373, pp. 85–98. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  5. Chrobak, M., Kolman, P., Sgall, J.: The greedy algorithm for the minimum common string partition problem. ACM Trans. Algorithms 1(2), 350–366 (2005)

    Article  MathSciNet  Google Scholar 

  6. Cormode, G., Muthukrishnan, S.: The string edit distance matching problem with moves. In: SODA 2002. Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms, Philadelphia, PA. Society for Industrial and Applied Mathematics, pp. 667–676. ACM Press, New York (2002)

    Google Scholar 

  7. Caprara, A.: Sorting by reversals is difficult. In: RECOMB 1997. Proceedings of the first annual international conference on Computational molecular biology, pp. 75–83. ACM Press, New York (1997)

    Chapter  Google Scholar 

  8. Schoeninger, M., Waterman, M.S.: A local algorithm for dna sequence alignment with inversions. Bull. Math. Biol. 54(4), 521–536 (1992)

    Google Scholar 

  9. Chen, Z.Z., Gao, Y., Lin, G., Niewiadomski, R., Wang, Y., Wu, J.: A space-efficient algorithm for sequence alignment with inversions and reversals. Theor. Comput. Sci. 325(3), 361–372 (2004)

    Article  MATH  Google Scholar 

  10. do Lago, A.P., Muchnik, I.: A sparse dynamic programming algorithm for alignment with non-overlapping inversions. Theoret. Informatics Appl. 39(1), 175–189 (2005)

    Article  MATH  Google Scholar 

  11. Alves, C.E.R., do Lago, A.P., Vellozo, A.F.: Alignment with non-overlapping inversions in o(n 3 logn) time. In: Proceedings of GRACO 2005. Electronic Notes in Discrete Mathematics, vol. 19, pp. 365–371. Elsevier, Amsterdam (2005)

    Google Scholar 

  12. Vellozo, A.F., Alves, C.E.R., do Lago, A.P.: Alignment with non-overlapping inversions in o(n 3)-time. In: Bücher, P., Moret, B.M.E. (eds.) WABI 2006. LNCS (LNBI), vol. 4175, pp. 186–196. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  13. Apic, G., Gough, J., Teichmann, S.A.: Domain combinations in archaeal, eubacterial and eukaryotic proteomes. J. Mol. Biol. 310(2), 311–325 (2001)

    Article  Google Scholar 

  14. Kaessmann, H., Zöllner, S., Nekrutenko, A., Li, W.H.: Signatures of domain shuffling in the human genome. Genome Res. 12(11), 1642–1650 (2002)

    Article  Google Scholar 

  15. Liu, M., Walch, H., Wu, S., Grigoriev, A.: Significant expansion of exon-bordering protein domains during animal proteome evolution. Nucleic Acids Res. 33(1), 95–105 (2005)

    Article  Google Scholar 

  16. Vibranovski, M.D., Sakabe, N.J., de Oliveira, R.S., de Souza, S.J.: Signs of ancient and modern exon-shuffling are correlated to the distribution of ancient and modern domains along proteins. J. Mol. Evol. 61(3), 341–350 (2005)

    Article  Google Scholar 

  17. Bashton, M., Chothia, C.: The geometry of domain combination in proteins. J. Mol. Biol. 315(4), 927–939 (2002)

    Article  Google Scholar 

  18. Shandala, T., Gregory, S.L., Dalton, H.E., Smallhorn, M., Saint, R.: Citron kinase is an essential effector of the pbl-activated rho signalling pathway in drosophila melanogaster. Development 131(20), 5053–5063 (2004)

    Article  Google Scholar 

  19. Andrade, M.A., Perez-Iratxeta, C., Ponting, C.P.: Protein repeats: structures, functions, and evolution. J. Struct. Biol. 134(2-3), 117–131 (2001)

    Article  Google Scholar 

  20. Marcotte, E.M., Pellegrini, M., Yeates, T.O., Eisenberg, D.: A census of protein repeats. J. Mol. Biol. 293(1), 151–160 (1999)

    Article  Google Scholar 

  21. Maes, M.: On a cyclic string-to-string correction problem. Inf. Process. Lett. 35(2), 73–78 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  22. Myers, E.W.: An overview of sequence comparison algorithms in molecular biology. Technical Report 91-29, Univ. of Arizona, Dept. of Computer Science (1991)

    Google Scholar 

  23. Gusfield, D.: Algorithms on Strings, Trees, and Sequences: computer science and computational biology. Press Syndicate of the University of Cambridge, Cambridge (1997/1999)

    Google Scholar 

  24. Landau, G.M., Ziv-Ukelson, M.: On the common substring alignment problem. J. Algorithms 41(2), 338–354 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  25. Schmidt, J.P.: All highest scoring paths in weighted grid graphs and their application to finding all approximate repeats in strings. SIAM J. Comput. 27(4), 972–992 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  26. Aggarwal, A., Klawe, M.M., Moran, S., Shor, P., Wilber, R.: Geometric applications of a matrix-searching algorithm. Algorithmica 2(1), 195–208 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  27. Gonnet, G.H., Hallett, M.T., Korostensky, C., Bernardin, L.: Darwin v. 2.0: An interpreted computer language for the biosciences. Bioinformatics 16(2), 101–103 (2000)

    Article  Google Scholar 

  28. Monge, G.: Déblai et remblai. Mémoires de l’Académie Royale des Sciences (1781)

    Google Scholar 

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Authors and Affiliations

  1. ETH Zurich, Institute of Computational Science, Switzerland

    Christian Ledergerber & Christophe Dessimoz

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  1. Christian Ledergerber
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  2. Christophe Dessimoz
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Guohui Lin

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Ledergerber, C., Dessimoz, C. (2007). Alignments with Non-overlapping Moves, Inversions and Tandem Duplications in O(n 4) Time. In: Lin, G. (eds) Computing and Combinatorics. COCOON 2007. Lecture Notes in Computer Science, vol 4598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73545-8_17

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  • DOI: https://doi.org/10.1007/978-3-540-73545-8_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73544-1

  • Online ISBN: 978-3-540-73545-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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