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Abstract

The Genome Halving Problem is motivated by the whole genome duplication events in molecular evolution that double the gene content of a genome and result in a perfect duplicated genome thatcontains two identical copies of each chromosome. The genome then becomes a subject to rearrangements resulting in some rearranged duplicated genome. The Genome Halving Problem (first introduced and solved by Nadia El-Mabrouk and David Sankoff) is to reconstruct the ancestral pre-duplicated genome from the rearranged duplicated genome. The El-Mabrouk–Sankoff algorithm is rather complex and in this paper we present a simpler algorithm that is based on a generalization of the notion of the breakpoint graph to the case of duplicated genomes. This generalization makes the El-Mabrouk–Sankoff result more transparent and promises to be useful in future studies of genome duplications.

Keywords

Genome Duplication Genome Duplication Event Cycle Decomposition Signed Permutation Black Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bader, D.A., Moret, B.M.E., Yan, M.: A linear-time algorithm for computing inversion distances between signed permutations with an experimental study. J. Comput. Biol. 8, 483–491 (2001)CrossRefGoogle Scholar
  2. 2.
    Bafna, V., Pevzner, P.A.: Genome rearrangement and sorting by reversals. SIAM Journal on Computing 25, 272–289 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bergeron, A.: “A very elementary presentation of the Hannenhalli-Pevzner theory”. In: Amir, A., Landau, G.M. (eds.) CPM 2001. LNCS, vol. 2089, pp. 106–117. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Bergeron, A., Mixtacki, J., Stoye, J., Bergeron, A., Mixtacki, J., Stoye, J.: Reversal distance without hurdles and fortresses. In: Sahinalp, S.C., Muthukrishnan, S.M., Dogrusoz, U. (eds.) CPM 2004. LNCS, vol. 3109, pp. 388–399. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Dietrich, F.S., et al.: The Ashbya gossypii Genome as a Tool for Mapping the Ancient Saccharomyces cerevisiae Genome. Science 304, 304–307 (2004)CrossRefGoogle Scholar
  6. 6.
    El-Mabrouk, N., Nadeau, J.H., Sankoff, D.: “Genome halving”. In: Farach-Colton, M. (ed.) CPM 1998. LNCS, vol. 1448, pp. 235–250. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  7. 7.
    El-Mabrouk, N., Sankoff, D.: “On the reconstruction of ancient doubled circular genomes using minimum reversal”. Genome Informatics 10, 83–93 (1999)Google Scholar
  8. 8.
    El-Mabrouk, N., Bryant, B., Sankoff, D.: Reconstructing the pre-doubling genome. In: Proceedings of the Third Annual International Conference on Computational Molecular Biology RECOMB 1999, pp. 154–163 (1999)Google Scholar
  9. 9.
    El-Mabrouk, N., Sankoff, D.: The Reconstruction of Doubled Genomes. SIAM Journal on Computing 32, 754–792 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Hannenhalli, S., Pevzner, P.: Transforming cabbage into turnip (polynomial algorithm for sorting signed permutations by reversals). In: Proceedings of the Twenty- Seventh Annual ACM Symposium on Theory of Computing (1995), pp. 178–189. ACM Press, New York (1995); Journal of the ACM 46, 1–27 (1999) CrossRefGoogle Scholar
  11. 11.
    Kaplan, H., Shamir, R., Tarjan, R.: Faster and simpler algorithm for sorting signed permutations by reversals. SIAM Journal on Computing 29, 880–892 (1999)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Kellis, M., et al.: Proof and evolutionary analysis of ancient genome duplication in the yeast Saccharomyces cerevisiae. Nature 428, 617–624 (2004)CrossRefGoogle Scholar
  13. 13.
    Ohno, S., Wolf, U., Atkin, N.: Evolution from fish to mammals by gene duplication. Hereditas 59, 169–187 (1968)CrossRefGoogle Scholar
  14. 14.
    Pevzner, P., Tesler, G.: Genome Rearrangements in Mammalian Evolution: Lessons from Human and Mouse Genomes. Genome Research 13, 37–45 (2003)CrossRefGoogle Scholar
  15. 15.
    Skrabanek, L., Wolfe, K.H.: “Eukaryote genome duplication - where’s the evidence?”. Curr. Opin. Genet. Devel. 8, 694–700 (1998)CrossRefGoogle Scholar
  16. 16.
    Tannier, E., Sagot, M.-F.: “Sorting by reversals in subquadratic time”. In: Sahinalp, S.C., Muthukrishnan, S.M., Dogrusoz, U. (eds.) CPM 2004. LNCS, vol. 3109, Springer, Heidelberg (2004)CrossRefGoogle Scholar
  17. 17.
    Wolfe, K.H., Shields, D.C.: Molecular evidence for an ancient duplication of the entire yeast genome. Nature 387, 708–713 (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Max A. Alekseyev
    • 1
  • Pavel A. Pevzner
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity of California at San DiegoLa JollaU.S.A.

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