Abstract
In genome rearrangements, the double cut and join (DCJ) operation, introduced by Yancopoulos et al., allows to represent most rearrangement events that could happen in multichromosomal genomes, such as inversions, translocations, fusions and fissions. No restriction on the genome structure considering linear and circular chromosomes is imposed. An advantage of this general model is that it leads to considerable algorithmic simplifications. Recently several works concerning the DCJ operation have been published, and in particular an algorithm was proposed to find an optimal DCJ sequence for sorting one genome into another one. Here we study the solution space of this problem and give an easy to compute formula that corresponds to the exact number of optimal DCJ sorting sequences to a particular subset of instances of the problem. In addition, this formula is also a lower bound to the number of sorting sequences to any instance of the problem.
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References
Alekseyev, M.A., Pevzner, P.A.: Breakpoint graphs and ancestral genome reconstructions. Genome Res. 19, 943–957 (2009)
Bergeron, A., Chauve, C., Hartmann, T., St-Onge, K.: On the properties of sequences of reversals that sort a signed permutation. In: Proceedings of JOBIM 2002, pp. 99–108 (2002)
Bergeron, A., Mixtacki, J., Stoye, J.: A unifying view of genome rearrangements. In: Bücher, P., Moret, B.M.E. (eds.) WABI 2006. LNCS (LNBI), vol. 4175, pp. 163–173. Springer, Heidelberg (2006)
Braga, M.D.V., Sagot, M.-F., Scornavacca, C., Tannier, E.: Exploring the solution space of sorting by reversals with experiments and an application to evolution. IEEE/ACM Trans. Comput. Biol. Bioinf. 5(3), 348–356 (2008); Preliminary version in Proceedings of ISBRA 2007. LNCS (LNBI), vol. 4463, pp. 293–304 (2007)
Hannenhalli, S., Pevzner, P.: Transforming men into mice (polynomial algorithm for genomic distance problem). In: Proceedings of FOCS 1995, pp. 581–592 (1995)
Ouangraoua, A., Bergeron, A.: Parking functions, labeled trees and DCJ sorting scenarios. In: Ciccarelli, F.D., Miklós, I. (eds.) RECOMB-CG 2009. LNCS (LNBI), vol. 5817, pp. 24–35. Springer, Heidelberg (2009)
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)
Siepel, A.: An algorithm to enumerate sorting reversals for signed permutations. J. Comput. Biol. 10, 575–597 (2003)
Yancopoulos, S., Attie, O., Friedberg, R.: Efficient sorting of genomic permutations by translocation, inversion and block interchange. Bioinformatics 21, 3340–3346 (2005)
Zeilberger, D.: Yet another proof of Cayley’s formula for the number of labelled trees, http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimPDF/cayley.pdf
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Braga, M.D.V., Stoye, J. (2009). Counting All DCJ Sorting Scenarios. In: Ciccarelli, F.D., Miklós, I. (eds) Comparative Genomics. RECOMB-CG 2009. Lecture Notes in Computer Science(), vol 5817. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04744-2_4
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DOI: https://doi.org/10.1007/978-3-642-04744-2_4
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