Finding All Sorting Tandem Duplication Random Loss Operations
A tandem duplication random loss (TDRL) operation duplicates a contiguous segment of genes, followed by the loss of one copy of each of the duplicated genes. Although the importance of this operation is founded by several recent biological studies, it has been investigated only rarely from a theoretical point of view. Of particular interest are sorting TDRLs which are TDRLs that, when applied to a permutation representing a genome, reduce the distance towards another given permutation. The identification of sorting genome rearrangement operations in general is a key ingredient of many algorithms for reconstructing the evolutionary history of a set of species. In this paper we present methods to compute all sorting TDRLs for two given gene orders. In addition, a closed formula for the number of sorting TDRLs is derived and further properties of sorting TDRLs are investigated. It is also shown that the theoretical findings are useful for identifying unique sorting TDRL scenarios for mitochondrial gene orders.
KeywordsGene Order Tandem Duplication Binary String Closed Formula Restricted Case
Unable to display preview. Download preview PDF.
- 1.Ajana, Y., Lefebvre, J.-F., Tillier, E.R.M., El-Mabrouk, N.: Exploring the set of all minimal sequences of reversals an application to test the replication-directed reversal hypothesis. In: Guigó, R., Gusfield, D. (eds.) WABI 2002. LNCS, vol. 2452, pp. 300–315. Springer, Heidelberg (2002)CrossRefGoogle Scholar
- 7.Chaudhuri, K., Chen, K., Mihaescu, R., Rao, S.: On the tandem duplication-random loss model of genome rearrangement. In: SODA, pp. 564–570 (2006)Google Scholar
- 9.Hannenhalli, S., Pevzner, P.A.: Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals. In: ACM Symposium on Theory of Computing, pp. 178–189 (1995)Google Scholar
- 15.Swenson, K.M., Marron, M., Earnest-DeYoung, J.V., Moret, B.M.E.: Approximating the true evolutionary distance between two genomes. ACM Journal on Experimental Algorithmics 12(3.5) (2008)Google Scholar
- 16.Tang, J., Moret, B.M.E., Cui, L., de Pamphilis, C.W.: Phylogenetic reconstruction from arbitrary gene-order data. In: Proc. 4th IEEE Conf. on Bioinformatics and Bioengineering BIBE 2004, pp. 592–599 (2004)Google Scholar