A Unifying View of Genome Rearrangements

Analysis of Gene Order Evolution Beyond Single-Copy Genes

“…A related distance that has been extensively studied in the last years is the DCJ distance [11,12,124]. Given a genome G, a Double-Cut-and-Join (DCJ) is an operation that "cuts" two adjacencies ab and cd in a genome, and replaces them by either ac and bd, or ad and bc.…”

“…The DCJ distance is interesting from a theoretical point of view as it leads to a unifying formula including all previously studied rearrangement events, as well as transpositions, for which no polynomial-time exact method is known. Computing the DCJ distance between two signed permutations is a linear-time problem [11,124].…”

“…In the case of two genomes G and H with no gene duplicates and the same gene content, a key result in the field of genome rearrangement is the 1995 Hannenhalli and Pevzner (HP) formula [61,112] for computing the minimum number of inversions and translocations (including chromosomal fusions and fissions) required to transform G into H, leading to a polynomial-time algorithm. More recently, another distance that has been extensively studied is the Double-Cut-and-Join (DCJ) distance which represents a greater repertoire of rearrangement events while giving rise to simpler formal results [11,12,124]. For the purpose of genome rearrangement, handling duplicated genes leads to hard problems (see [3,18,29] for the computation of genomic distances for example).…”

Issues in the Reconstruction of Gene Order Evolution

“…The classical genetics notions of inversion, transposition and reciprocal translocation of chromosome segments, as well as chromosomal fission and fusion, are formalized in such papers as those by Tesler [13] , Yancopoulos et al [25] , and Bergeron et al [26] Briefly, using the string representation of a chromosome, e.g., h 1 · · · h l , where a pair of successive genes h u h u+1 are loosely termed an adjacency if their gene ends constitute an adjacency, we can illustrate:…”

“…The DCJ operation is thus a very general framework. It was introduced by Yancopoulos et al [25] and was simplified by Bergeron et al [26] The minimum number of DCJ operations needed to transform one genome into another (on the same set of genes) is the DCJ distance d DCJ . It can be quickly calculated by defining a bipartite graph where the adjacencies and telomeres of one genome constitute the vertices on one side of the graph and the adjacencies and telomeres of the other genome are the opposing set of vertices.…”