Genome Rearrangements with Partially Ordered Chromosomes

Genomic maps often do not specify the order within some groups of two or more markers. The synthesis of a master map from several sources introduces additional order ambiguity due to markers missing from some sources. We represent each chromosome as a partial order, summarized by a directed acyclic graph (DAG), to account for poor resolution and of missing data. The genome rearrangement problem is then to infer a minimum number of translocations and reversals for transforming a set of linearizations, one for each chromosomal DAG in the genome of one species, to linearizations of the DAGs of another species. We augment each DAG to a directed graph (DG) in which all possible linearizations are embedded. The chromosomal DGs representing two genomes are combined to produce a single bicoloured graph. From this we extract a maximal decomposition into alternating coloured cycles, determining an optimal sequence of rearrangements. We test this approach on simulated partially ordered genomes.