On the Structure of Syntenic Distance

This paper examines some of the rich structure of the syntenic distance model of evolutionary distance, introduced by Ferretti et al. (1996). The syntenic distance between two genomes is the minimum number of fissions, fusions, and translocations required to transform one into the other, ignoring gene order within chromosomes. We prove that the previously unanalyzed algorithm given by Ferretti et al. (1996) is a 2-approximation and no better, and that, further, it always outperforms the algorithm presented by DasGupta et al. (1998). We also prove the same results for an improved version of the Ferretti et al. algorithm. We then prove a number of properties which give insight into the structure of optimal move sequences. We give instances in which any move sequence working solely within connected components is nearly twice optimal and prove a general lower bound based on the spread of genes from each chromosome. We then prove a monotonicity property for the syntenic distance, and bound the difficulty of the hardest instance of any size. We discuss the results of implementing these algorithms and testing them on real and simulated synteny data.