Finding all sorting tandem duplication random loss operations

Abstract

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.

Improved systematic tRNA gene annotation allows new insights into the evolution of mitochondrial tRNA structures and into the mechanisms of mitochondrial genome rearrangements

“…While the standard model, i.e. a tandem duplication followed by a complete loss of one of the redundant copies, is well understood from a formal/bioinformatic point of view ( 76 , 77 ), our results motivate also for further studies of the TDRL model. In particular, this includes multiplications, cases with inverse duplications and especially the possibility of partial loss.…”

The highly rearranged mitochondrial genomes of the crabs Maja crispata and Maja squinado (Majidae) and gene order evolution in Brachyura

“…In the CREx analyses, the software was allowed to compute up to ten alternative scenarios (option max. alternatives = 10) in every search 65 . The output for the different GO reconstructions was always a single transformational pathway.…”

Some Enumeration Problems in the Duplication-Loss Model of Genome Rearrangement

“…Another way to think of a TDRL operation on π is as a partition of π into two of its subsequences which are then concatenated. For example, in (1), π id (5) is partitioned into (2,3,5) and (1,4), and the final result is (2,3,5,1,4).…”