Are There Rearrangement Hotspots in the Human Genome?

In a landmark paper, Nadeau and Taylor [18] formulated the random breakage model (RBM) of chromosome evolution that postulates that there are no rearrangement hotspots in the human genome. In the next two decades, numerous studies with progressively increasing levels of resolution made RBM the de facto theory of chromosome evolution. Despite the fact that RBM had prophetic prediction power, it was recently refuted by Pevzner and Tesler [4], who introduced the fragile breakage model (FBM), postulating that the human genome is a mosaic of solid regions (with low propensity for rearrangements) and fragile regions (rearrangement hotspots). However, the rebuttal of RBM caused a controversy and led to a split among researchers studying genome evolution. In particular, it remains unclear whether some complex rearrangements (e.g., transpositions) can create an appearance of rearrangement hotspots. We contribute to the ongoing debate by analyzing multi-break rearrangements that break a genome into multiple fragments and further glue them together in a new order. In particular, we demonstrate that (1) even if transpositions were a dominant force in mammalian evolution, the arguments in favor of FBM still stand, and (2) the ‘‘gene deletion’’ argument against FBM is flawed

Transposition Distance Based On The Algebraic Formalism

In computational biology, genome rearrangements is a field in which we study mutational events affecting large portions of a genome. One such event is the transposition, that changes the position of contiguous blocks of genes inside a chromosome. This event generates the problem of transposition distance, that is to find the minimal number of transpositions transforming one chromosome into another. It is not known whether this problem is -hard or has a polynomial time algorithm. Some approximation algorithms have been proposed in the literature, whose proofs are based on exhaustive analysis of graphical properties of suitable cycle graphs. In this paper, we follow a different, more formal approach to the problem, and present a 1.5-approximation algorithm using an algebraic formalism. Besides showing the feasibility of the approach, the presented algorithm exhibits good results, as our experiments show. © 2008 Springer-Verlag Berlin Heidelberg.5167 LNBI115126Bader, D.A., Moret, B.M.E., Yan, M., A linear-time algorithm for computing inversion distance between signed permutations with an experimental study (2001) Journal of Computational Biology, 8 (5), pp. 483-491Bafna, V., Pevzner, P.A., Sorting by transpositions (1995) Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 614-623. , San Francisco, USA, JanuaryBafna, V., Pevzner, P.A., Sorting by transpositions (1998) SIAM Journal on Discrete Mathematics, 11 (2), pp. 224-240Benoît-Gagné, M., Hamel, S.: A new and faster method of sorting by transpositions. In: Ma, B., Zhang, K. (eds.) CPM 2007. LNCS, 4580, pp. 131-141. Springer, Heidelberg (2007)Christie, D.A., Sorting permutations by block-interchanges (1996) Information Processing Letters, 60 (4), pp. 165-169Christie, D.A., (1998) Genome Rearrangement Problems, , PhD thesis, Glasgow UniversityElias, I., Hartman, T.: A 1.375-approximation algorithm for sorting by transpositions. In: Casadio, R., Myers, G. (eds.) WABI 2005. LNCS (LNBI), 3692, pp. 204-215. Springer, Heidelberg (2005)Hannenhalli, S., Pevzner, P.A., Transforming men into mice (polynomial algorithm for genomic distance problem) (1995) Proceedings of the 36th Annual Symposium on Foundations of Computer Science (FOCS, pp. 581-592. , October, IEEE Computer Society Press, Los Alamitos () 1995Hartman, T.: A simpler 1.5-approximation algorithm for sorting by transpositions. In: Baeza-Yates, R., Chávez, E., Crochemore, M. (eds.) CPM 2003. LNCS, 2676, pp. 156-169. Springer, Heidelberg (2003)Hartman, T., Shamir, R.: A simpler and faster 1.5-approximation algorithm for sorting by transpositions. In: Proceedings of CPM 2003, pp. 156-169 (2003) (extended version)Honda, M.I., (2004) Implementation of the algorithm of Hartman for the problem of sorting by transpositions, , Master's thesis, Department of Computer Science, University of Brasilia in portugueseMeidanis, J., Dias, Z., An alternative algebraic formalism for genome rearrangements (2000) Comparative Genomics: Empirical and Analyitical Approaches to Gene Order Dynamics, Map Alignment and Evolution of Gene Families, pp. 213-223. , Sankoff, D, Nadeau, J.H, eds, Kluwer Academic Publishers, Dordrecht NovemberMeidanis, J., Walter, M.E.M.T., Dias, Z., Transposition distance between a permutation and its reverse (1997) Proceedings of the 4th South American Workshop on String Processing (WSP 1997), pp. 70-79. , Baeza-Yates, R, ed, Valparaiso, Chile, pp, Carleton University PressMira, C., Meidanis, J., Algebraic formalism for genome rearrangements (part 1) (2005), Technical Report IC-05-10, Institute of Computing, University of Campinas JuneMira, C.V.G., Meidanis, J., Analysis of sorting by transpositions based on algebraic formalism (2004) The Eighth Annual International Conference on Research in Computational Molecular Biology (RECOMB, , MarchWalter, M.E.M.T., Curado, L.R.A.F., Oliveira, A.G.: Working on the problem of sorting by transpositions on genome rearrangements. In: Baeza-Yates, R., Chávez, E., Crochemore, M. (eds.) CPM 2003. LNCS, 2676, pp. 372-383. Springer, Heidelberg (2003)Walter, M.E.M.T., Dias, Z., Meidanis, J., A new approach for approximating the transposition distance (2000) String Processing and Information Retrieval, pp. 199-208. , SPIREWalter, M.E.M.T., Oliveira, E.T.G., Extending the theory of Bafna and Pevzner for the problem of sorting by transpositions (2002) Tendências em Matemática Aplicada e Computacional - TEMA - SBMAC, 3 (1), pp. 213-222. , in portugueseWalter, M.E.M.T., Soares, L.S.N., Dias, Z., Branch-and-bound algorithms for the problem of sorting by transpositions on genome rearrangements (2006) Proceedings of the 26th Congress of the Brazilian Computer Society, XXXIII Seminário integrado de hardware e software - SEMISH, pp. 69-8