Abstract
In this chapter we investigate the DCJ and algebraic distances and how they are found. We introduce a new graphical method to determine the permutation cycles which embody the composition permutation for the genome transformation in the algebraic method. This graphical method helps tie the two approaches together. In the usual approaches, the two methods differ only in the distance component due to the even paths in the adjacency graph of Bergeron, Mixtacki, and Stoye involving operations changing type and number of chromosomes, such as fission, fusion, altering chromosome type from circular to linear, and vice versa. Discussing each distance individually, we compare their underlying assumptions. Both methods resort to cycles to determine the distance, but the basic DCJ uses “caps” to close paths. Without caps the algebraic distance differs from the standard DCJ for even paths. However, if caps and null chromosomes are added, the weighting schemes agree. A convention which can be done in multiple ways is the method of path closure. We discuss implementation of the original closure rule to arrive at the usual weighting scheme for the DCJ. Instead, by a new alternative closure rule which we introduce, the distance diverts to the algebraic distance. Finally, we note that although the Bergeron, Mixtacki, and Stoye DCJ approach via the adjacency graph does away with “fictitious” caps and nulls, vestiges of fictitious operations may remain, as the resulting weighting scheme is equivalent to that of the basic DCJ.
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References
Bader, M., Ohlebusch, E.: Sorting by weighted reversals, transpositions, and inverted transpositions. J. Comput. Biol. 14, 615–636 (2007)
Bafna, V., Pevzner, P.: Sorting by transpositions. SIAM J. Discrete Math. 224–240 (1998)
Bafna, V., Pevzner, P.A.: Genome rearrangements and sorting by reversals. In: Proceedings of the 34th Annual IEEE Symposium on Foundations of Computer Science, vol. 46, pp. 148–157. IEEE Press, New York (1993)
Bergeron, A., Mixtacki, J., Stoye, J.: A unifying view of genome rearrangements. In: Moret, B. (ed.) Algorithms in Bioinformatics Proceedings of WABI 2006 (2006)
Blanchette, M., Kunisawa, T., Sankoff, D.: Parametric analysis of genome rearrangement. Gene 172, 11–17 (1996)
Christie, D.: Sorting permutations by block interchanges. Inf. Process. Lett. 60, 165–169 (1996)
Dobzhansky, T., Sturtevant, A.H.: Inversions in the chromosomes of Drosophila pseudoobscura. Genetics 23, 28–64 (1984)
Feijao, P., Meidanis, J.: SCJ: a breakpoint-like distance that simplifies several rearrangement problems. IEEE/ACM Trans. Comput. Biol. Bioinform. 8(5), 1318–1329 (2011). doi:10.1109/TCBB.2011.34.
Feijao, P., Meidanis, J.: Extending the algebraic formalism for genome rearrangements to include linear chromosomes. IEEE/ACM Trans. Comput. Biol. Bioinform. 99(PrePrints), 1 (2012). doi:10.1109/TCBB.2012.161
Friedberg, R., Darling, A.E., Yancopoulos, S.: Genome rearrangement by the double cut and join operation. In: Keith, J.M. (ed.) Bioinformatics, Methods in Molecular Biology, vol. 452, pp. 385–416. Humana Press, Clifton (2008)
Hannenhalli, S., Pevzner, P.A.: Transforming cabbage into turnip (polynomial algorithm for sorting signed permutations by reversals). J. ACM 46(1), 1–27 (1999). Previously appeared at Proc. of the 27th Annual Symposium on the Theory of Computing (STOC 95), Las Vegas, Nevada, pp. 178–189 (1995)
Hannenhalli, S., Pevzner, P.A.: Transforming mice into men (polynomial algorithm for genomic distance problem). In: Proc. of the 36 Annual Symposium on Foundations of Computer Science (FOCS 95), Milwaukee, Wisconsin, pp. 581–592 (1995)
Meidanis, J., Dias, Z.: An alternative algebraic formalism for genome rearrangements. In: Sankoff, D., Nadeau, J. (eds.) Comparative Genomics, pp. 213–223. Kluwer Academic, Dordrecht (2000)
Nadeau, J.H., Taylor, B.A.: Lengths of chromosomal segments conserved since divergence of man and mouse. Proc. Natl. Acad. Sci. USA 81, 814–818 (1984)
Sankoff, D.: Edit distance for genome comparison based on non-local operations. In: Combinatorial Pattern Matching, Third Annual Symposium. Lecture Notes in Computer Science, vol. 644, pp. 121–135. Springer, Berlin (1992)
Sankoff, D., Goldstein, M.: Probabilistic models for genome shuffling. Bull. Math. Biol. 51, 117–124 (1989)
Sankoff, D., Cedergren, R., Abel, Y.: Genome divergence through gene rearrangement. Methods Enzymol. 183, 428–438 (1990)
Sankoff, D., Leduc, G., Antoine, N., Paquin, B., Lang, B.F., Gene, C.R.: Order comparisons for phylogenetic inference: evolution of the mitochondrial genome. Proc. Natl. Acad. Sci. USA 89, 6575–6579 (1992)
Tesler, G.: Efficient algorithms for multichromosomal genome rearrangements. J. Comput. Syst. Sci. 65, 587–609 (2002)
Yancopoulos, S., Attie, O., Friedberg, R.: Efficient sorting of genomic permutations by translocation, in version and block interchange. Bioinformatics 21(16), 3340–3346 (2005)
Acknowledgements
We would like to thank Richard Friedberg for a long, inspiring conversation over dinner at an Indian restaurant in New York, on February 24th, 2013. We thank Pedro Feijao and Marilia Braga for shorter, but also inspiring, conversations. S.Y. thanks Nick Chiorazzi for his tolerance and support, David Sankoff for introducing Joao to me, and Judith Ficksman for her heartfelt encouragement. Finally, we thank our reviewer for meticulous and insightful comments.
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Meidanis, J., Yancopoulos, S. (2013). The Emperor Has No Caps! A Comparison of DCJ and Algebraic Distances. In: Chauve, C., El-Mabrouk, N., Tannier, E. (eds) Models and Algorithms for Genome Evolution. Computational Biology, vol 19. Springer, London. https://doi.org/10.1007/978-1-4471-5298-9_10
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DOI: https://doi.org/10.1007/978-1-4471-5298-9_10
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