On Computing the Breakpoint Reuse Rate in Rearrangement Scenarios

In the past years, many combinatorial arguments have been made to support the theory that mammalian genome rearrangement scenarios rely heavily on breakpoint reuse. Different models of genome rearrangements have been suggested, from the classical set of operations that include inversions, translocations, fusions and fissions, to more elaborate models that include transpositions. Here we show that the current definition of breakpoint reuse rateis based on assumptions that are seldom true for mammalian genomes, and propose a new approach to compute this parameter. We explore the formal properties of this new measure and apply these results to the human-mouse genome comparison. We show that the reuse rate is intimately linked to a particular rearrangement scenario, and that the reuse rate can vary from 0.89 to 1.51 for scenarios of the same length that transform the mouse genome into the human genome, where a rate of 1 indicates no reuse at all.