Genome Rearrangement in Mitochondria and Its Computational Biology

  • István Miklós
  • Jotun Hein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3388)


In the first part of this paper, we investigate gene orders of closely related mitochondrial genomes for studying the properties of mutations rearranging genes in mitochondria. Our conclusions are that the evolution of mitochondrial genomes is more complicated than it is considered in recent methods, and stochastic modelling is necessary for its deeper understanding and more accurate inferring. The second part is a review on the Markov chain Monte Carlo approaches for the stochastic modelling of genome rearrangement, which seem to be the only computationally tractable way to this problem. We introduce the concept of partial importance sampling, which yields a class of Markov chains being efficient both in terms of mixing and computational time. We also give a list of open algorithmic problems whose solution might help improve the efficiency of partial importance samplers.


Markov Chain Monte Carlo Mitochondrial Genome Genome Rearrangement Exit Rate Target Distribution 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Sturtevant, A.H., Novitski, E.: The homologies of chromosome elements in the genus Drosophila. Genetics 26, 517–541 (1941)Google Scholar
  2. 2.
    Palmer, J.D., Herbon, L.A.: Plant mitochondrial DNA evolves rapidly in structure, but slowly in sequence. J. Mol. Evol. 28, 87–97 (1988)CrossRefGoogle Scholar
  3. 3.
    Bader, D.A., Moret, B.M.E., Yan, M.: A linear-time algorithm for computing inversion distance between signed permutations with an experimental study. J. Comp. Biol. 8(5), 483–491 (2001)CrossRefGoogle Scholar
  4. 4.
    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
  5. 5.
    Hannenhalli, S., Pevzner, P.A.: Transforming Cabbage into Turnip: Polynomial Algorithm for Sorting Signed Permutations by Reversals. Journal of ACM 46(1), 1–27 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Kaplan, H., Shamir, R., Tarjan, R.: A faster and simpler algorithm for sorting signed permutations by reversals. SIAM J. Comput. 29(3), 880–892 (1999)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Siepel, A.: An algorithm to find all sorting reversals. In: Proceedings of RECOMB 2002, pp. 281–290 (2002)Google Scholar
  8. 8.
    Hannenhalli, S.: Polynomial algorithm for computing translocation distance between genomes. In: Proceedings of CPM 1996, pp. 168–185 (1996)Google Scholar
  9. 9.
    Bafna, V., Pevzner, A.: Sorting by transpositions. SIAM J. Disc. Math. 11(2), 224–240 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Berman, P., Hannenhalli, S., Karpinski, M.: 1.375-approximation algorithm for sorting by reversals. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 200–210. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Eriksen, N.: (1+ε)-approximation of sorting by reversals and transpositions. In: Gascuel, O., Moret, B.M.E. (eds.) WABI 2001. LNCS, vol. 2149, pp. 227–237. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Gu, Q.-P., Peng, S., Sudborough, H.I.: A 2-Approximation Algorithm for Genome Rearrangements by Reversals and Transpositions. Theor. Comp. Sci. 210(2), 327–339 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Kececioglu, J.D., Sankoff, D.: Exact and Approximation Algorithms for Sorting by Reversals, with Application to Genome Rearrangement. Algorithmica 13(1/2), 180–210 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Blanchette, M., Kunisawa, T., Sankoff, D.: Parametric genome rearrangement. Gene 172, GC11–GC17 (1996)Google Scholar
  15. 15.
    Felsenstein, J.: Inferring phylogenies. Sinauer Associates (2003) Google Scholar
  16. 16.
    Hein, J., Wiuf, C., Knudsen, B., Moller, M.B., Wibling, G.: Statistical alignment: Computational properties, homology testing and goodness-of-fit. J. Mol. Biol. 203, 265–279 (2000)CrossRefGoogle Scholar
  17. 17.
    Larget, B., Simon, D.L., Kadane, B.J.: Bayesian phylogenetic inference from animal mitochondrial genome arrangements. J. Roy. Stat. Soc. B. 64(4), 681–695Google Scholar
  18. 18.
    York, T.L., Durrett, R., Nielsen, R.: Bayesian estimation of inversions in the history of two chromosomes. J. Comp. Biol. 9, 808–818 (2002)CrossRefGoogle Scholar
  19. 19.
    Durrett, R., Nielsen, R., York, T.L.: Bayesian estimation of genomic distance. Genetics 166, 621–629 (2004)CrossRefGoogle Scholar
  20. 20.
    Miklós, I.: MCMC Genome Rearrangement. Bioinformatics 19, ii130–ii137 (2003)Google Scholar
  21. 21.
    Miklós, I., Ittzés, P., Hein, J.: ParIS genome rearrangement server. Bioinformatics (2004) (advance published) doi:10.1093/bioinformatics/bti060Google Scholar
  22. 22.
    Boore, J.L.: The duplication/random loss model for genome rearrangement exemplified by mitochondrial genomes of deuterostome animals. In: Sankoff, D., Nadau, J.H. (eds.) Comparative Genomics. Computational Biology Series, vol. 1. Kluwer Academic Publishers, Dordrecht (2000)Google Scholar
  23. 23.
    Miklós, I., Lunter, G.A., Holmes, I.: A ’long indel’ model for evolutionary sequence alignment. Mol. Biol. Evol. 21(3), 529–540 (2004)CrossRefGoogle Scholar
  24. 24.
    Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equations of state calculations by fast computing machines. J. Chem. Phys. 21(6), 1087–1091 (1953)CrossRefGoogle Scholar
  25. 25.
    Liu, J.S.: Monte Carlo strategies in scientific computing. Springer Series in Statistics, New-York (2001)Google Scholar
  26. 26.
    Hastings, W.K.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57(1), 97–109 (1970)zbMATHCrossRefGoogle Scholar
  27. 27.
    von Neumann, J.: Various techniques used in connection with random digits. National Bureau of Standards Applied Mathematics Series 12, 36–38 (1951)Google Scholar
  28. 28.
    Nadau, J.H., Taylor, B.A.: Lengths of chromosome segments conserved since divergence of man and mouse. PNAS 81, 814–818 (1984)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • István Miklós
    • 1
  • Jotun Hein
    • 2
  1. 1.Hungarian Academy of Science and Eötvös Loránd University of Science, Theoretical Biology and Ecology GroupBudapestHungary
  2. 2.Oxford Centre for Gene FunctionUniversity of OxfordOxfordUK

Personalised recommendations