Finding All Sorting Tandem Duplication Random Loss Operations

Authors:
Matthias Bernt;Ming-Chiang Chen;Daniel Merkle;Hung-Lung Wang;Kun-Mao Chao;Martin Middendorf
Affiliations:
Parallel Computing and Complex Systems Group, Department of Computer Science, University of Leipzig, Germany;Department of Computer Science and Information Engineering, National Taiwan University, Taiwan;Department of Mathematics and Computer Science, University of Southern Denmark, Odense, Denmark;Department of Computer Science and Information Engineering, National Taiwan University, Taiwan;Department of Computer Science and Information Engineering, National Taiwan University, Taiwan;Parallel Computing and Complex Systems Group, Department of Computer Science, University of Leipzig, Germany
Venue:
CPM '09 Proceedings of the 20th Annual Symposium on Combinatorial Pattern Matching
Year:
2009

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Abstract

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.