The Gene Family-Free Median of Three

Abstract

Background:The gene family-free framework for comparative genomics aims at providing methods for gene order analysis that do not require prior gene family assignment, but work directly on a sequence similarity graph. We study two problems related to the breakpoint median of three genomes, which asks for the construction of a fourth genome that minimizes the sum of breakpoint distances to the input genomes.Methods: We present a model for constructing a median of three genomes in this family-free setting, based on maximizing an objective function that generalizes the classical breakpoint distance by integrating sequence similarity in the score of a gene adjacency. We study its computational complexity and we describe an integer linear program (ILP) for its exact solution. We further discuss a related problem called family-free adjacencies for k genomes for the special case of k ≤ 3 and present an ILP for its solution. However, for this problem, the computation of exact solutions remains intractable for sufficiently large instances. We then proceed to describe a heuristic method, FFAdj-AM, which performs well in practice. Results:The developed methods compute accurate positional orthologs for genomes comparable in size of bacterial genomes on simulated data and genomic data acquired from the OMA orthology database. In particular, FFAdj-AM performs equally or better when compared to the well-established gene family prediction tool MultiMSOAR. Conclusions: We study the computational complexity of a new family-free model and present algorithms for its solution. With FFAdj-AM, we propose an appealing alternative to established tools for identifying higher confidence positional orthologs.

The Rooted SCJ Median with Single Gene Duplications

“…However, in 2009, Tannier, Zheng and Sankoff proved that computing a median gene order that is allowed to contain an arbitrary mixture of linear and circular chromosomes was tractable in the breakpoint distance model, by using a reduction to the problem of computing a Maximum Weight Matching (MWM) [22]. This tractability result, the first of its kind in genome rearrangements, renewed the interest in gene order median problems, although most of the following work presented intractability results, even on variations of the breakpoint distance [5,9,14]. A notable exception was the Single-Cut-or-Join (SCJ) distance, introduced by Feijão and Meidanis [11], where it was shown that both the SCJ median problem and the SCJ SPP are tractable.…”