The Reversal Median Problem, Common Intervals, and Mitochondrial Gene Orders

  • Matthias Bernt
  • Daniel Merkle
  • Martin Middendorf
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4216)

Abstract

An important problem for phylogenetic investigations that are based on gene orders is to find for three given gene orders a fourth gene order that has a minimum sum of reversal distances to the three given gene orders. This problem is called Reversal Median problem (RMP). The RMP is studied here under the constraint that common (combinatorial) structures are preserved which are modeled as common intervals. An existing branch-and-bound algorithm for RMP is extended here so that it can solve the RMP with common intervals optimally. This algorithm is applied to mitochondrial gene order data for different animal taxa. It is shown that common intervals occur often for most taxa and that many common intervals are destroyed when the RMP is solved optimally with standard methods that do not consider common intervals.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bérard, S., Bergeron, A., Chauve, C.: Conservation of Combinatorial Structures in Evolution Scenarios. In: Lagergren, J. (ed.) RECOMB-WS 2004. LNCS (LNBI), vol. 3388, pp. 1–14. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  2. 2.
    Bergeron, A., Blanchette, M., Chateau, A., Chauve, C.: Reconstructing Ancestral Gene Orders Using Conserved Intervals. In: Jonassen, I., Kim, J. (eds.) WABI 2004. LNCS (LNBI), vol. 3240, pp. 14–25. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Heber, S., Stoye, J.: Algorithms for Finding Gene Clusters. In: Gascuel, O., Moret, B.M.E. (eds.) WABI 2001. LNCS, vol. 2149, pp. 252–263. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Sankoff, D.: Edit distance for genome comparison based on non-local operations. In: Apostolico, A., Galil, Z., Manber, U., Crochemore, M. (eds.) CPM 1992. LNCS, vol. 644, pp. 121–135. Springer, Heidelberg (1992)Google Scholar
  5. 5.
    Caprara, A.: The Reversal Median Problem. INFORMS Journal on Computing 15(1), 93–113 (2003)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Landau, G.M., Parida, L., Weimann, O.: Using PQ Trees for Comparative Genomics. In: Apostolico, A., Crochemore, M., Park, K. (eds.) CPM 2005. LNCS, vol. 3537, pp. 128–143. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Moret, B.M.E., Tang, J., Warnow, T.: Reconstructing phylogenies from gene-content and gene-order data. Mathematics of Evolution and Phylogeny. In: Gascuel, O. (ed.), pp. 321–352. Oxford University Press, Oxford (2004)Google Scholar
  8. 8.
    Bourque, G., Pevzner, P.A.: Genome-Scale Evolution: Reconstructing Gene Orders in the Ancestral Species. Genome Res. 12(1), 26–36 (2002)Google Scholar
  9. 9.
    Blanchette, M., Bourque, G., Sankoff, D.: Breakpoint phylogenies. Genome Informatics, 25–34 (1997)Google Scholar
  10. 10.
    Siepel, A.C., Moret, B.M.E.: Finding an Optimal Inversion Median: Experimental Results. In: Gascuel, O., Moret, B.M.E. (eds.) WABI 2001. LNCS, vol. 2149, pp. 189–203. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  11. 11.
    Bernt, M., Merkle, D., Middendorf, M.: Genome Rearrangement Based on Reversals that Preserve Conserved Intervals. IEEE/ACM Transactions on Computational Biology and Bioinformatics (to appear)Google Scholar
  12. 12.
    Bergeron, A., Stoye, J.: On the Similarity of Sets of Permutations and Its Applications to Genome Comparison. In: Warnow, T.J., Zhu, B. (eds.) COCOON 2003. LNCS, vol. 2697. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Figeac, M., Varré, J.: Sorting by Reversals with Common Intervals. In: Jonassen, I., Kim, J. (eds.) WABI 2004. LNCS (LNBI), vol. 3240, pp. 26–37. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  14. 14.
    Bérard, S., Bergeron, A., Chauve, C., Paul, C.: Perfect sorting by reversals is not always difficult. In: Casadio, R., Myers, G. (eds.) WABI 2005. LNCS (LNBI), vol. 3692, pp. 228–238. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    Hannenhalli, S., Pevzner, P.: Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals. In: Proc. 27th Ann. ACM Symp. on Theory of Comput., pp. 178–189 (1995)Google Scholar
  16. 16.
    Boore, J.L.: Mitochondrial database (2005), http://evogen.jgi.doe.gov/

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Matthias Bernt
    • 1
  • Daniel Merkle
    • 1
  • Martin Middendorf
    • 1
  1. 1.Parallel Computing and Complex Systems Group, Department of Computer ScienceUniversity of LeipzigGermany

Personalised recommendations