Sridhar Hannenhalli
Pavel A. Pevzner
Abstract
Genomes frequently evolve by reversals ρ(i,j) that transform a gene order π1 … πiπi+1 … πj-1πj … πn into π1 … πiπj-1 … πi+1πj … πn. Reversal distance between permutations π and σis the minimum number of reversals to transform π into Α. Analysis of genome rearrangements in molecular biology started in the late 1930's, when Dobzhansky and Sturtevant published a milestone paper presenting a rearrangement scenario with 17 inversions between the species of Drosophilia. Analysis of genomes evolving by inversions leads to a combinatorial problem of sorting by reversals studied in detail recently. We study sorting of signed permutations by reversals, a problem that adequately models rearrangements in a small genomes like chloroplast or mitochondrial DNA. The previously suggested approximation algorithms for sorting signed permutations by reversals compute the reversal distance between permutations with an astonishing accuracy for both simulated and biological data. We prove a duality theorem explaining this intriguing performance and show that there exists a “hidden” parameter that allows one to compute the reversal distance between signed permutations in polynomial time.
- AIGYER, M., AND WEST, D.B. 1987. Sorting by insertion of leading element. J. Combin. Theory 45, 306 -309. Google Scholar
- BAFNA, g., AND PEVZNER, P. 1995. Sorting by reversals: Genome rearrangements in plant organelles and evolutionary history of X chromosome. Mol. Biol. Evol. 12, 239-246.Google Scholar
- BAFNA, g., AND PEVZNER, P. 1996. Genome rearrangements and sorting by reversals. SIAM J. Comput. 25, 272-289. Google Scholar
- BAFNA, g., AND PEVZNER, P. 1998. Sorting by transpositions. SIAM J. Disc. Math. 11, 224-240. Google Scholar
- BERMAN, P., AND HANNENHALLI, S. 1996. Fast sorting by reversals. In Combinatorial Pattern Matching, Proceedings of the 6th Annual Symposium (CPM'96). Lecture Notes in Computer Science. Springer-Verlag, Berlin, Germany, pp. 168-185. Google Scholar
- CAPRARA, A. 1997. Sorting by reversals is difficult. In Proceedings of the 1st Annual International Conference on Computational Molecular Biology (RECOMB97). pp. 75-83. Google Scholar
- COHEN, D., AND BLUM, M. 1993. Improved bounds for sorting pancakes under a conjecture, Manuscript.Google Scholar
- EVEN, S., AND GOLDREICH, O. 1981. The minimum-length generator sequence problem is NP- hard. J. Algorithms 2, 311-313.Google Scholar
- GATES, W. H., AND PAPADIMITRIOU, C.H. 1979. Bounds for sorting by prefix reversals. Disc. Math. 27, 47-57.Google Scholar
- HANNENHALLI, S. 1995. Polynomial algorithm for computing translocation distance between genomes. In Combinatorial Pattern Matching, Proceedings of the 6th Annual Symposium (CPM'95). Lecture Notes in Computer Science. Springer-Verlag, Berlin, Germany, pp. 162-176.Google Scholar
- HANNENHALLI, S., CHAPPEY, C., KOONIN, E., AND PEVZNER, P. 1995. Genome sequence comparison and scenarios for gene rearrangements: A test case. Genomics, 30, 299-311.Google Scholar
- HANNENHALLI, S., AND PEVZNER, P. 1995. Transforming men into mice (polynomial algorithm for genomic distance problem). In Proceedings of the 36th Annual IEEE Symposium on Foundations of Computer Science. IEEE Computer Society Press, Los Alamitos, Calif., pp. 581-592. Google Scholar
- HANNENHALLI, S., AND PEVZNER, P. 1996. To cut .. or not to cut (applications of comparative physical maps in molecular evolution). In Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms (Atlanta, Ga., Jan. 28-30). ACM, New York, pp. 304-313. Google Scholar
- HEYDARI, M., AND SUDBOROUGH, I.H. 1993. On sorting by prefix reversals and the diameter of pancake networks, Manuscript.Google Scholar
- JERRUM, M. 1985. The complexity of finding minimum-length generator sequences. Theoret. Comput. Sci. 36, 265-289. Google Scholar
- KECECIOGLU, J., AND GUSFIELD, D. 1994. Reconstructing a history of recombinations from a set of sequences. In Proceedings of the 5th Annual ACM-SIAM Symposium on Discrete Algorithms, ACM, New York, pp. 471-480. Google Scholar
- KECECIOGLU, J., AND RAVI, R. 1995. Of mice and men: Algorithms for evolutionary distances between genomes with translocation. In Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms (San Francisco, Calif., Jan. 22-24). ACM, New York, pp. 604-613. Google Scholar
- KECECIOGLU, J., AND SANKOFF, D. 1995. Exact and approximation algorithms for the inversion distance between two permutations. Algorithmica 13, 180-210.Google Scholar
- KECECIOGLU, J., AND SANKOFF, D. 1994. Efficient bounds for oriented chromosome inversion distance. In Combinatorial Pattern Matching, Proceedings of the 5th Annual Symposium (CPM'94). Lecture Notes in Computer Science, vol. 807. Springer-Verlag, Berlin, Germany, pp. 307-325. Google Scholar
- MAKAROFF, C. A., AND PALMER, J.D. 1988. Mitochondrial DNA rearrangements and transcrip-tional alterations in the male sterile cytoplasm of Ogura radish. Mol. Cell. Biol. 8, 1474-1480.Google Scholar
- NADEAU, J. H., AND TAYLOR, B. A. 1984. Lengths of chromosomal segments conserved since divergence of man and mouse. Proc. Natl. Acad. Sci. USA 81, 814-818.Google Scholar
- PALMER, J. D., AND HERBON, L.A. 1988. Plant mitochondrial DNA evolves rapidly in structure, but slowly in sequence. J. Mol. Evolut. 27, 87-97.Google Scholar
- PEVZNER, P. A., AND WATERMAN, M. S. 1995. Open combinatorial problems in computational molecular biology. In Proceedings of the 3rd Israel Symposium on Theory of Computing and Systems. IEEE Computer Society Press, Los Alamitos, Calif., pp. 158-163. Google Scholar
- SANKOFF, D. 1992. Edit distance for genome comparison based on non-local operations. In Combinatorial Pattern Matching, Proceedings of the 3rd Annual Symposium (CPM'92). Lecture Notes in Computer Science, vol. 644. Springer-Verlag, Berlin, Germany, pp. 121-135. Google Scholar
- SANKOFF, D., CEDERGREN, R., AND ABEL, Y. 1990. Genomic divergence through gene rearrangement. In Molecular Evolution: Computer Analysis of Protein and Nucleic Acid Sequences, Chap. 26. Academic Press, Orlando, Fla., pp. 428-438.Google Scholar
- SANKOFF, D., LEDUC, G., ANTOINE, N., PAQUIN, B., LANG, B. F., AND CEDERGREN, R. 1992. Gene order comparisons for phylogenetic inference: Evolution of the mitochondrial genome. Proc. Natl. Acad. Sci. USA 89, 6575-6579.Google Scholar
- STURTEVANT, A. H., AND DOBZHANSKY, f. 1936. Inversions in the third chromosome of wild races of drosophila pseudoobscura, and their use in the study of the history of the species. Proc. Nat. Acad. Sci. 22, 448-450.Google Scholar
- TARJAN, R., KAPLAN, H., AND SHAMIR, R. 1997. Faster and simpler algorithm for sorting by reversals. In Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms. ACM, New York, pp. 614-623. Google Scholar
- WATTERSON, G. A., EWENS, W. J., HALL, f. E., AND MORGAN, A. 1982. The chromosome inversion problem. J. Theoret. Biol. 99, 1-7.Google Scholar
Index Terms
- Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
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Antony Peter Stevens
One of the wonders that may be contemplated in the world of genetics is the fact that, although related organisms have very similar genes, these genes are not arranged in the same order along the chromosomes. The differences in order are the result of “crossing over,” which reverses the order of the genes along the genome. We then have what the authors call a “combinatorial puzzle to find a shortest series of reversals to transform one genome into another.” Combinatorial puzzles are liable to combinatorial explosion. An approximation algorithm with a defined bound was already known. The remarkable regularity in performance displayed by this algorithm led to the authors' discovery of a new bound and, with it, the “first polynomial algorithm for a realistic model of genome rearrangements.”
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