Natural family-free genomic distance

Abstract

Background A classical problem in comparative genomics is to compute the rearrangement distance, that is the minimum number of large-scale rearrangements required to transform a given genome into another given genome. The traditional approaches in this area are family-based, i.e., require the classification of DNA fragments of both genomes into families. Furthermore, the most elementary family-based models, which are able to compute distances in polynomial time, restrict the families to occur at most once in each genome. In contrast, the distance computation in models that allow multifamilies (i.e., families with multiple occurrences) is NP-hard. Very recently, Bohnenkämper et al. (J Comput Biol 28:410–431, 2021) proposed an ILP formulation for computing the genomic distance of genomes with multifamilies, allowing structural rearrangements, represented by the generic double cut and join (DCJ) operation, and content-modifying insertions and deletions of DNA segments. This ILP is very efficient, but must maximize a matching of the genes in each multifamily, in order to prevent the free lunch artifact that would otherwise let empty or almost empty matchings give smaller distances. Results In this paper, we adopt the alternative family-free setting that, instead of family classification, simply uses the pairwise similarities between DNA fragments of both genomes to compute their rearrangement distance. We adapted the ILP mentioned above and developed a model in which pairwise similarities are used to assign weights to both matched and unmatched genes, so that an optimal solution does not necessarily maximize the matching. Our model then results in a natural family-free genomic distance, that takes into consideration all given genes, without prior classification into families, and has a search space composed of matchings of any size. In spite of its bigger search space, our ILP seems to be boosted by a reduction of the number of co-optimal solutions due to the weights. Indeed, it converged faster than the original one by Bohnenkämper et al. for instances with the same number of multiple connections. We can handle not only bacterial genomes, but also fungi and insects, or sets of chromosomes of mammals and plants. In a comparison study of six fruit fly genomes, we obtained accurate results.

Gene orthology inference via large-scale rearrangements for partially assembled genomes

“…The DCJ-indel distance d id dcj (A, B, O) is the minimum number of DCJ and indel operations required to transform A into B assuming the orthologs given by O and allowing only the genes belonging to the complement O to be inserted or deleted. It can be computed using an approach relying on the cycles and paths of a graph that represents the structural relation between genomes A and B according to the ortholog-set O [3,12] (this graph is equivalent to a consistent decomposition of the family-free relational graph, described in the next subsection and represented in Figure 1 (bottom)). Together with the weights of edges and vertices of S(A, B), the DCJ-indel distance d id dcj allows the computation of the weighted rearrangement distance wd id dcj [12]:…”

“…Denote by OrthoFF(A, B, S) an optimal ortholog-set in S(A, B), which is an orthologset whose rearrangement distance equals GenDiFF(A, B, S). Computing the rearrangement distance GenDiFF(A, B, S) and finding an optimal orthologset OrthoFF(A, B, S) are NP-hard problems [12].…”

“…The family-free relational graph FFR(A, B, S), shown in Figure 1 (bottom), represents all possible weighted distances corresponding to all candidate ortholog-sets in S(A, B) [12]. Given a gene m, denote the extremities of m by m h (head ) and m t (tail ).…”

“…The structure of D[L] has all necessary information for computing the value wd id dcj (A, B, S, O L ), therefore we can say that wd id dcj (A, B, S, O L ) = wd id dcj (D[L]) [12]. Given that S is the set of all possible sibling-sets in FFR(A, B, S), we can modify our optimization problem to…”

“…This model is able to infer pairwise orthologs between two genomes directly, simultaneously based on gene similarities and rearrangements. In practice, its optimization function can be solved exactly due to an ILP formulation [12] that is called FF-DCJ-Indel and also reports an optimal matching of orthologs between the two analyzed genomes. (The ILP FF-DCJ-Indel is itself based on the previous formulations for family-based approaches [7,8].…”