A Pseudo-boolean Programming Approach for Computing the Breakpoint Distance Between Two Genomes with Duplicate Genes

A fundamental problem in comparative genomics is to compute the distance between two genomes. For two genomes without duplicate genes, we can easily compute a variety of distance measures in linear time, but the problem is NP-hard under most models when genomes contain duplicate genes. Sankoff proposed the use of exemplars to tackle the problem of duplicate genes and gene families: each gene family is represented by a single gene (the exemplar for that family), chosen so as to optimize some metric. Unfortunately, choosing exemplars is itself an NP-hard problem. In this article, we propose a very fast and exact algorithm to compute the exemplar breakpoint distance, based on new insights in the underlying structure of genome rearrangements and exemplars. We evaluate the performance of our algorithm on simulation data and compare its performance to the best effort to date (a divide-and-conquer approach), showing that our algorithm runs much faster and scales much better. We also devise a new algorithm for the intermediate breakpoint distance problem, which can then be applied to assign orthologs. We compare our algorithm with the state-of-the-art method MSOAR by assigning orthologs among five well annotated mammalian genomes, showing that our algorithm runs much faster and is slightly more accurate than MSOAR.

Section: Ilp Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Fast and Exact Algorithm for the Exemplar Breakpoint Distance

Shao

Moret

2016

“…Several years later, Blin et al [8] proposed the maximum matching model (M-model): use as many matched pairs as possible-until all genes in the genome with the smaller number of copies in each gene family are matched. Finally, Angibaud et al [9] proposed what we shall term the intermediate model (I-model): the matching must contain at least one matched pair per gene family-so that the focus is clearly on minimizing the distance, not on meeting constraints on the matching. Figure 1 illustrates these three formulations.…”

Section: Introductionmentioning

confidence: 99%

“…For E-BDP, Sankoff gave a first branchand-bound algorithm in his original paper [7]. Nguyen et al gave a much faster divide-and-conquer approach [11], while Angibaud et al [9] gave an exact algorithm by formulating it as an integer linear program (ILP). In [12], we gave an exact solution through combining ILP and novel preprocessing algorithms and constraint-generating algorithms, which runs very fast (in a few seconds) and scales up to the largest genomes analyzed on both simulations and biological datasets.…”

Section: Introductionmentioning

confidence: 99%

On Computing Breakpoint Distances for Genomes with Duplicate Genes

Shao

Moret

2017

A fundamental problem in comparative genomics is to compute the distance between two genomes in terms of its higher level organization (given by genes or syntenic blocks). For two genomes without duplicate genes, we can easily define (and almost always efficiently compute) a variety of distance measures, but the problem is NP-hard under most models when genomes contain duplicate genes. To tackle duplicate genes, three formulations (exemplar, maximum matching, and any matching) have been proposed, all of which aim to build a matching between homologous genes so as to minimize some distance measure. Of the many distance measures, the breakpoint distance (the number of nonconserved adjacencies) was the first one to be studied and remains of significant interest because of its simplicity and model-free property. The three breakpoint distance problems corresponding to the three formulations have been widely studied. Although we provided last year a solution for the exemplar problem that runs very fast on full genomes, computing optimal solutions for the other two problems has remained challenging. In this article, we describe very fast, exact algorithms for these two problems. Our algorithms rely on a compact integer-linear program that we further simplify by developing an algorithm to remove variables, based on new results on the structure of adjacencies and matchings. Through extensive experiments using both simulations and biological data sets, we show that our algorithms run very fast (in seconds) on mammalian genomes and scale well beyond. We also apply these algorithms (as well as the classic orthology tool MSOAR) to create orthology assignment, then compare their quality in terms of both accuracy and coverage. We find that our algorithm for the "any matching" formulation significantly outperforms other methods in terms of accuracy while achieving nearly maximum coverage.

“…Aiming at precise evaluations of heuristics, we develop in this section an exact generic approach as initiated in (Angibaud et al, 2007a). More precisely, our approach relies on expressing the different problems as 0-1 linear programs (Schrijver, 1998) and using powerful solvers to obtain optimal solutions.…”

Section: Introductionmentioning

confidence: 99%

Efficient Tools for Computing the Number of Breakpoints and the Number of Adjacencies between Two Genomes with Duplicate Genes

Angibaud

Fertin

Rusu

et al. 2008

Self Cite

Comparing genomes of different species is a fundamental problem in comparative genomics. Recent research has resulted in the introduction of different measures between pairs of genomes: reversal distance, number of breakpoints, number of common or conserved intervals, etc. However, classical methods used for computing such mea- 1 scattered across them. Most approaches to overcome this difficulty are based either on the exemplar model, which keeps exactly one copy in each genome of each duplicated gene, or on the maximum matching model, which keeps as many copies as possible of each duplicated gene. The goal is to find an exemplar matching, respectively a maximum matching, that optimizes the studied measure. Unfortunately, it turns out that, in presence of duplications, this problem for each above-mentioned measure is NP-hard.In this paper, we propose to compute the minimum number of breakpoints and the maximum number of adjacencies between two genomes in presence of duplications using two different approaches. The first one is a (exact) generic 0-1 linear programming approach, while the second is a collection of three heuristics. Each of these approaches is applied on each problem and for each of the following models: exemplar, maximum matching and intermediate model, that we introduce here. All these programs are run on a well-known public benchmark dataset of γ-Proteobacteria, and their performances are discussed.