Abstract
BackgroundGenome median and genome halving are combinatorial optimization problems that aim at reconstruction of ancestral genomes by minimizing the number of evolutionary events between them and genomes of the extant species. While these problems have been widely studied in past decades, their solutions are often either not efficient or not biologically adequate. These shortcomings have been recently addressed by restricting the problems solution space.ResultsWe show that the restricted variants of genome median and halving problems are, in fact, closely related. We demonstrate that these problems have a neat topological interpretation in terms of embedded graphs and polygon gluings. We illustrate how such interpretation can lead to solutions to these problems in particular cases.ConclusionsThis study provides an unexpected link between comparative genomics and topology, and demonstrates advantages of solving genome median and halving problems within the topological framework.
Highlights
One of the key computational problems in comparative genomics is the reconstruction of ancestral genomes based on gene1 orders in the extant species [1,2,3,4]
Since most dramatic changes in genomic architectures are caused by genome rearrangements, this problem is often posed as minimization of the total distance between extant and ancestral genomes along the branches of the evolutionary tree
In the simplest form, it is known as the genome halving problem (GHP), which asks for an ordinary genome for a given all-duplicated genome such that the distance between them is minimized
Summary
One of the key computational problems in comparative genomics is the reconstruction of ancestral genomes based on gene orders in the extant species [1,2,3,4]. WGD events are known to happen in evolution of yeasts [5], fishes [6], plants [7], and even mammalian species [8], which inspires the problem of reconstruction of doubled genomes, i.e., genomes immediately resulted from a WGD in the course of evolution This problem is often posed for input genomes that have all genes present either in a single copy (ordinary genomes) or in two copies (allduplicated genomes). Genome median and genome halving are combinatorial optimization problems that aim at reconstruction of ancestral genomes by minimizing the number of evolutionary events between them and genomes of the extant species While these problems have been widely studied in past decades, their solutions are often either not efficient or not biologically adequate. A DCJ in genome P corresponds in G(P) to the replacement of a pair of P-edges with a different pair of P-edges on the same set of four vertices
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