Finding all sorting tandem duplication random loss operations

A tandem duplication random loss (TDRL) operation duplicates a contiguous segment of genes, followed by the random 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.

[1]  Walther Janous,et al.  Elementary Problems: E3141-E3146 , 1986 .

[2]  Matthias Bernt,et al.  Finding all sorting tandem duplication random loss operations , 2009, J. Discrete Algorithms.

[3]  Mathilde Bouvel,et al.  A variant of the tandem duplication - random loss model of genome rearrangement , 2008, Theor. Comput. Sci..

[4]  Matthias Bernt,et al.  Using median sets for inferring phylogenetic trees , 2007, Bioinform..

[5]  J. Boore The duplication/random loss model for gene rearrangement exemplified by mitochondrial genomes of deu , 2000 .

[6]  Satish Rao,et al.  On the tandem duplication-random loss model of genome rearrangement , 2006, SODA '06.

[7]  M. Bernt,et al.  Gene order rearrangement methods for the reconstruction of phylogeny , 2009 .

[8]  Jijun Tang,et al.  Phylogenetic reconstruction from arbitrary gene-order data , 2004, Proceedings. Fourth IEEE Symposium on Bioinformatics and Bioengineering.

[9]  R. Zardoya,et al.  A hotspot of gene order rearrangement by tandem duplication and random loss in the vertebrate mitochondrial genome. , 2005, Molecular biology and evolution.

[10]  Pavel A. Pevzner,et al.  Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals , 1995, JACM.

[11]  Anne Bergeron,et al.  Parking Functions, Labeled Trees and DCJ Sorting Scenarios , 2009, RECOMB-CG.

[12]  Nadia El-Mabrouk,et al.  Exploring the Set of All Minimal Sequences of Reversals - An Application to Test the Replication-Directed Reversal Hypothesis , 2002, WABI.

[13]  J. Inoue,et al.  Evolution of the deep-sea gulper eel mitochondrial genomes: large-scale gene rearrangements originated within the eels. , 2003, Molecular biology and evolution.

[14]  J. Boore,et al.  Complete mtDNA sequences of two millipedes suggest a new model for mitochondrial gene rearrangements: duplication and nonrandom loss. , 2002, Molecular biology and evolution.

[15]  M. Miya,et al.  The phylogenetic position of toadfishes (order Batrachoidiformes) in the higher ray-finned fish as inferred from partitioned Bayesian analysis of 102 whole mitochondrial genome sequences , 2005 .

[16]  D. Sankoff,et al.  Duplication, Rearrangement, and Reconciliation , 2000 .

[17]  Marie-France Sagot,et al.  Exploring the Solution Space of Sorting by Reversals, with Experiments and an Application to Evolution , 2008, TCBB.

[18]  Vineet Bafna,et al.  Sorting by Transpositions , 1998, SIAM J. Discret. Math..

[19]  P. Diaconis,et al.  Trailing the Dovetail Shuffle to its Lair , 1992 .

[20]  Adam C. Siepel An Algorithm to Enumerate Sorting Reversals for Signed Permutations , 2003, J. Comput. Biol..

[21]  Nadia El-Mabrouk,et al.  Genome Rearrangement by Reversals and Insertions/Deletions of Contiguous Segments , 2000, CPM.

[22]  Krister M. Swenson,et al.  Approximating the true evolutionary distance between two genomes , 2008, JEAL.

[23]  Vineet Bafna,et al.  Sorting permutations by tanspositions , 1995, SODA '95.

[24]  P. Diaconis,et al.  SHUFFLING CARDS AND STOPPING-TIMES , 1986 .

[25]  D. Sankoff,et al.  Comparative Genomics: "Empirical And Analytical Approaches To Gene Order Dynamics, Map Alignment And The Evolution Of Gene Families" , 2000 .

[26]  John N. Tsitsiklis,et al.  Introduction to Probability , 2002 .