This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Genome Rearrangement Based on Reversals that Preserve Conserved Intervals
July-September 2006 (vol. 3 no. 3)
pp. 275-288
The order of genes in the genomes of species can change during evolution and can provide information about their phylogenetic relationship. An interesting method to infer the phylogenetic relationship from the gene orders is to use different types of rearrangement operations and to find possible rearrangement scenarios using these operations. One of the most common rearrangement operations is reversals, which reverse the order of a subset of neighbored genes. In this paper, we study the problem to find the ancestral gene order for three species represented by their gene orders. The rearrangement scenario should use a minimal number of reversals and no other rearrangement operations. This problem is called the Median problem and is known to be NP--complete. In this paper, we describe a heuristic algorithm for finding solutions to the Median problem that searches for rearrangement scenarios with the additional property that gene groups should not be destroyed by reversal operations. The concept of conserved intervals for signed permutations is used to describe such gene groups. We show experimentally, for different types of test problems, that the proposed algorithm produces very good results compared to other algorithms for the Median problem. We also integrate our reversal selection procedure into the well-known MGR and GRAPPA algorithms and show that they achieve a significant speedup while obtaining solutions of the same quality as the original algorithms on the test problems.

[1] D. Sankoff, “Edit Distance for Genome Comparison Based on Non-Local Operations,” Proc. Third Ann. Symp. Combinatorial Pattern Matching, pp. 121-135, 1992.
[2] S. Hannenhalli and P.A. Pevzner, “Transforming Cabbage into Turnip: Polynomial Algorithm for Sorting Signed Permutations by Reversals,” Proc. 27th Ann. ACM Symp. Theory of Computing, pp. 178-189, 1995.
[3] A. Bergeron, J. Mixtacki, and J. Stoye, “Reversal Distance without Hurdles and Fortresses,” Proc. 15th Ann. Symp. Combinatorial Pattern Matching (CPM 2004), pp. 388-399, 2004.
[4] A. Caprara, “The Reversal Median Problem,” INFORMS J. Computing, vol. 15, no. 1, pp. 93-113, 2003.
[5] B.M.E. Moret, J. Tang, and T. Warnow, “Reconstructing Phylogenies from Gene-Content and Gene-Order Data,” Math. Evolution and Phylogeny, O. Gascuel, ed., pp. 321-352, Oxford Univ. Press, 2005.
[6] A.C. Siepel and B.M.E. Moret, “Finding an Optimal Inversion Median: Experimental Results,” Proc. First Int'l Workshop Algorithms in Bioinformatics (WABI 2001), pp. 189-203, 2001.
[7] G. Bourque and P.A. Pevzner, “Genome-Scale Evolution: Reconstructing Gene Orders in the Ancestral Species,” Genome Research, vol. 12, no. 1, pp. 26-36, 2002.
[8] M. Blanchette, G. Bourque, and D. Sankoff, “Breakpoint Phylogenies,” Genome Informatics, pp. 25-34, 1997.
[9] M. Blanchette, T. Kunisawa, and D. Sankoff, “Gene Order Breakpoint Evidence in Animal Mitochondrial Phylogeny,” J. Molecular Evolution, vol. 49, no. 2, pp. 193-203, 1999.
[10] A.C. Siepel, “Exact Algorithms for the Reversal Median Problem,” master's thesis, Univ. of New Mexico, 2001.
[11] A. Bergeron and J. Stoye, “On the Similarity of Sets of Permutations and Its Applications to Genome Comparison,” Proc. COCOON: Ann. Int'l Conf. Computing and Combinatorics, 2003.
[12] A. Bergeron, M. Blanchette, A. Chateau, and C. Chauve, “Reconstructing Ancestral Gene Orders Using Conserved Intervals,” Proc. Fourth Int'l Workshop Algorithms in Bioinformatics (WABI 2004), pp. 14-45, 2004.
[13] A. Bergeron, S. Heber, and J. Stoye, “Common Intervals and Sorting by Reversals: A Marriage of Necessity,” Proc. European Conf. Computational Biology (ECCB 2002), pp. 54-63, 2002.
[14] J. Setubal and J. Meidanis, Introduction to Computational Molecular Biology. PWS Publishing, 1997.
[15] A.C. Siepel, “An Algorithm to Enumerate All Sorting Reversals,” Proc. Sixth Ann. Int'l Conf. Computational Biology, pp. 281-290, 2002.
[16] J.L. Boore, “Animal Mitochondrial Genomes,” Nucleic Acids Research, vol. 27, no. 8, pp. 1767-1780, 1999.
[17] J.L. Boore, “Mitochondrial Gene Arrangement Guide,” 2001, http://evogen.jgi.doe.gov/second_levels/ mitochondriaMGA_ Guide.html.
[18] B.M.E. Moret, L. Wang, T. Warnow, and S. Wyman, “New Approaches for Reconstructing Phylogenies from Gene Order,” Bioinformatics, vol. 17, pp. 165-173, 2001.

Index Terms:
Median problem, genome rearrangement, reversal operations, conserved intervals.
Citation:
Matthias Bernt, Daniel Merkle, Martin Middendorf, "Genome Rearrangement Based on Reversals that Preserve Conserved Intervals," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 3, no. 3, pp. 275-288, July-Sept. 2006, doi:10.1109/TCBB.2006.38
Usage of this product signifies your acceptance of the Terms of Use.