Approximate search for known gene clusters in new genomes using PQ-trees

Gene clusters are groups of genes that are co-locally conserved across various genomes, not necessarily in the same order. Their discovery and analysis is valuable in tasks such as gene annotation and prediction of gene interactions, and in the study of genome organization and evolution. The discovery of conserved gene clusters in a given set of genomes is a well studied problem, but with the rapid sequencing of prokaryotic genomes a new problem is inspired. Namely, given an already known gene cluster that was discovered and studied in one genomic dataset, to identify all the instances of the gene cluster in a given new genomic sequence. Thus, we define a new problem in comparative genomics, denoted PQ-TREE SEARCH that takes as input a PQ-tree T representing the known gene orders of a gene cluster of interest, a gene-to-gene substitution scoring function h, integer arguments [Formula: see text] and [Formula: see text], and a new sequence of genes S. The objective is to identify in S approximate new instances of the gene cluster; These instances could vary from the known gene orders by genome rearrangements that are constrained by T, by gene substitutions that are governed by h, and by gene deletions and insertions that are bounded from above by [Formula: see text] and [Formula: see text], respectively. We prove that PQ-TREE SEARCH is NP-hard and propose a parameterized algorithm that solves the optimization variant of PQ-TREE SEARCH in [Formula: see text] time, where [Formula: see text] is the maximum degree of a node in T and [Formula: see text] is used to hide factors polynomial in the input size. The algorithm is implemented as a search tool, denoted PQFinder, and applied to search for instances of chromosomal gene clusters in plasmids, within a dataset of 1,487 prokaryotic genomes. We report on 29 chromosomal gene clusters that are rearranged in plasmids, where the rearrangements are guided by the corresponding PQ-trees. One of these results, coding for a heavy metal efflux pump, is further analysed to exemplify how PQFinder can be harnessed to reveal interesting new structural variants of known gene clusters.