Abstract
In the median problem, we are given a distance or dissimilarity measure d, three genomes G 1,G 2, and G 3, and we want to find a genome G (a median) such that the sum ∑\(_{i=1}^{\rm 3}\) d(G,G i ) is minimized. The median problem is a special case of the multiple genome rearrangement problem, where one wants to find a phylogenetic tree describing the most “plausible” rearrangement scenario for multiple species. The median problem is NP-hard for both the breakpoint and the reversal distance [5,14]. To the best of our knowledge, there is no approach yet that takes biological constraints on genome rearrangements into account. In this paper, we make use of the fact that in circular bacterial genomes the predominant mechanism of rearrangement are inversions that are centered around the origin or the terminus of replication [8,10,18]. This constraint simplifies the median problem significantly. More precisely, we show that the median problem for the reversal distance can be solved in linear time for circular bacterial genomes.
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References
Bader, D.A., Moret, B.M.E., Yan, M.: A linear-time algorithm for computing inversion distance between signed permutations with an experimental study. Journal of Computational Biology 8, 483–491 (2001)
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)
Blanchette, M., Bourque, G., Sankoff, D.: Breakpoint phylogenies. In: Proc. Genome Informatics Workshop, pp. 25–34. Univ. Academy Press, Tokyo (1997)
Bourque, B., Pevzner, P.A.: Genome-scale evolution: Reconstructing gene orders in the ancestral species. Genome Research 12(1), 26–36 (2002)
Caprara, A.: Formulations and hardness of multiple sorting by reversals. In: Proc. 3rd Annual International Conference on Research in Computational Molecular Biology, pp. 84–94. ACM Press, New York (1999)
Caprara, A.: On the practical solution of the reversal median problem. In: Gascuel, O., Moret, B.M.E. (eds.) WABI 2001. LNCS, vol. 2149, pp. 238–251. Springer, Heidelberg (2001)
Dobzhansky, T., Sturtevant, A.H.: Inversions in the chromosomes of Drosophila pseudoobscura. Genetics 23, 28–64 (1938)
Eisen, J.A., Heidelberg, J.F., White, O., Salzberg, S.L.: Evidence for symmetric chromosomal inversions around the replication origin in bacteria. Genome Biology 1(6), 1–9 (2000)
Hannenhalli, S., Pevzner, P.A.: Transforming cabbage into turnip (polynomial algorithm for sorting signed permutations by reversals). Journal of the ACM 48, 1–27 (1999)
Hughes, D.: Evaluating genome dynamics: The constraints on rearrangements within bacterial genomes. Genome Biology 1(6), 1–8 (2000)
Kaplan, H., Shamir, R., Tarjan, R.E.: A faster and simpler algorithm for sorting signed permutations by reversals. SIAM J. Comput. 29(3), 880–892 (1999)
Moret, B.M.E., Siepel, A.C., Tang, J., Liu, T.: Inversion medians outperform breakpoint medians in phylogeny reconstruction from gene-order data. In: Guigó, R., Gusfield, D. (eds.) WABI 2002. LNCS, vol. 2452, pp. 521–536. Springer, Heidelberg (2002)
Nadeau, J.H., Taylor, B.A.: Lengths of chromosomal segments conserved since divergence of man and mouse. Proceedings of the National Academy of Sciences of the United States of America 81(3), 814–818 (1984)
Pe’er, I., Shamir, R.: The median problems for breakpoints are NP-complete. Technical Report TR98-071, Electronic Colloquium on Computational Complexity (1998)
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)
Sankoff, D., Blanchette, M.: Multiple genome rearrangement and breakpoint phylogeny. Journal of Computational Biology 5(3), 555–570 (1998)
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)
Tiller, E.R.M., Collins, R.: Genome rearrangement by replication-directed translocation. Nature Genetics 26, 195–197 (2000)
Watterson, G.A., Ewens, W.J., Hall, T.E., Morgan, A.: The chromosome inversion problem. Journal of Theoretical Biology 99, 1–7 (1982)
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Ohlebusch, E., Abouelhoda, M.I., Hockel, K., Stallkamp, J. (2005). The Median Problem for the Reversal Distance in Circular Bacterial Genomes. In: Apostolico, A., Crochemore, M., Park, K. (eds) Combinatorial Pattern Matching. CPM 2005. Lecture Notes in Computer Science, vol 3537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496656_11
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DOI: https://doi.org/10.1007/11496656_11
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