Identifying Orthologs: Cycle Splitting on the Breakpoint Graph

Gene rearrangements have successfully been used in phylogenetic reconstruction and comparative genomics (see the survey of [4] and the monograph of [6]), but usually under the assumption that all genomes have the same gene content and that no gene is duplicated. While these assumptions allow one to work with organellar genomes, they are too restrictive when comparing nuclear genomes [1], where themain challenge is how to deal with gene families, specifically, how to identify orthologs. While searching for orthologies is a common task in computational biology, it is usually done using sequence data. We approach that problem using gene rearrangement data. Sankoff [5] first addressed this problem with his introduction of exemplars, in which he suggested identifying a single gene within each family (the exemplar) on the basis of a parsimonious criterion (using the fewest rearrangements) and discarding all others. Our group provided an alternate approach in which a correspondence is established between gene families on the basis of conserved segments [3, 8]; our results suggested that considering all members of a gene family yields better results than keeping only exemplars, but were limited in that the assignment of orthologs did not take into account any rearrangement structure beyond conserved segments. Here we take steps to remedy this problem by providing an optimization framework derived from the breakpoint graph (the basic structure behind the last decade of work in gene rearrangements [2]) in which to phrase the problem; we give preliminary theoretical results in support of our framework.