Abstract
BackgroundA classical problem in studying genome rearrangements is understanding the series of rearrangement events involved in transforming one genome into another in accordance with the parsimonious principle when two genomes with the same set of genes differ in gene order. The most studied event is the reversal, but an increasing number of reports have considered reversals along with other genome rearrangement events. Some recent studies have investigated the use of reversals and block-interchanges simultaneously with a weight proportion of 1:2. However, there has been less progress towards exploring additional combinations of weights.ResultsIn this paper, we present several approaches to examine genome rearrangement problems by considering reversals and block-interchanges together using various weight assignments. An exact algorithm for the weight proportion of 1:2 is developed, and then, its idea is extended to design approximation algorithms for other weight assignments. The results of our simulations suggest that the performance of our approximation algorithm is superior to its theoretical expectation.ConclusionIf the weight of reversals is no more than that of block-interchanges, our algorithm provides an acceptable solution for the transformation of two permutations. Nevertheless whether there are more tractable results for studying the two events remains open.
Highlights
A classical problem in studying genome rearrangements is understanding the series of rearrangement events involved in transforming one genome into another in accordance with the parsimonious principle when two genomes with the same set of genes differ in gene order
The most widely studied type of global mutations is the reversal which inverts a segment in the permutation and changes the sign of each integer in that segment
If we only consider reversals, the so-called problem of sorting by reversals (SBR) is to find the shortest series composed of reversals that transforms the given per
Summary
A classical problem in studying genome rearrangements is understanding the series of rearrangement events involved in transforming one genome into another in accordance with the parsimonious principle when two genomes with the same set of genes differ in gene order. The study of genome rearrangements has been one of the most promising methods for tracing the evolutionary history using gene order comparisons between organisms. The mathematical model treats a chromosome in the genome as a permutation of integers, where each integer represents a gene. These integers are associated with signs, + or -, to indicate the corresponding orientation (strandedness) of the gene. A basic task in genome rearrangement studies is to economically transform one permutation into another using restricted types of global mutations. The most widely studied type of global mutations is the reversal ( called inversion) which inverts a segment in the permutation and changes the sign of each integer in that segment. If we only consider reversals, the so-called problem of sorting by reversals (SBR) is to find the shortest series composed of reversals that transforms the given per-
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