A Pseudo-Boolean Framework for Computing Rearrangement Distances between Genomes with Duplicates

Abstract

Computing genomic distances between whole genomes is a fundamental problem in comparative genomics. Recent researches have resulted in different genomic distance definitions, for example, number of breakpoints, number of common intervals, number of conserved intervals, and Maximum Adjacency Disruption number. Unfortunately, it turns out that, in presence of duplications, most problems are NP-hard, and hence several heuristics have been recently proposed. However, while it is relatively easy to compare heuristics between them, until now very little is known about the absolute accuracy of these heuristics. Therefore, there is a great need for algorithmic approaches that compute exact solutions for these genomic distances. In this paper, we present a novel generic pseudo-boolean approach for computing the exact genomic distance between two whole genomes in presence of duplications, and put strong emphasis on common intervals under the maximum matching model. Of particular importance, we show three heuristics which provide very good results on a well-known public dataset of gamma-Proteobacteria.

Analysis of Gene Order Evolution Beyond Single-Copy Genes

“…The exemplar approach [95] selects exactly one representative of each gene family in each genome, in a way that minimizes the number of breakpoints or inversions. Other approaches maximize the number of genes matched in each family [29,3]. A more general method allowing all gene copies to be kept, and accounting for reversals, translocations, fusions and fissions, has been developed and implemented in the MSOAR software [46,68,104].…”

“…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). We review the rearrangement phylogeny problem in Section 5 emphasizing the case of multiple gene copies.…”

On the Approximability of Comparing Genomes with Duplicates

“…Usually, the above mentioned matching is chosen in order to optimize the studied measure, following the parsimony principle. Three models achieving this correspondence have been proposed : the exemplar model [23], the intermediate model [3] and the maximum matching model [25]. Before defining precisely the measures and models studied in this paper, we need to introduce some notation.…”

“…Let G 2 be the genome G 2 = +2 − 1 + 6 + 3 − 5 − 4 + 2 − 1 − 2. Then the pair (G 1 , G 2 ) is balanced and is of type (3,3). Let d 1 = (G 1 [4], G 1 [5]) be the duo (+4, +5) and d 2 be the duo (G 2 [5], G 2 [6]).…”

“…Otherwise, we say that (a, b) induces an adjacency of (G 1 , G 2 ). For example, when G 1 = +1 + 2 + 3 + 4 + 5 and G 2 = +5 − 4 − 3 + 2 + 1, the duo (2,3) in G 1 induces a breakpoint of (G 1 , G 2 ) while (3,4) in G 1 induces an adjacency of (G 1 , G 2 ). We note by B(G 1 , G 2 ) (resp.…”