On the Distribution of Synteny Blocks Under a Neutral Model of Genome Dynamics

Prokaryotes are a rich source of versatile molecular functional systems that typically consist of multiple, interacting proteins. The study of such systems leads to fundamental biological discoveries, for example, understanding of the origins of innate and adaptive immunity in animals and also provides for the development of various biotechnology applications. The discovery of functional systems by microbial genome mining is facilitated by the fact that functionally coupled genes in bacterial and archaeal genomes often cluster in operons that are conserved across long evolutionary spans. However, accurate differentiation of operons from spurious gene clusters by genome comparison is a non-trivial task that depends on an underlying model of neutral genomes evolution. Here, we investigate the predictions of a gene clustering based on a recently developed stochastic model of genome rearrangement arising from horizontal gene transfer between evolving species along a phylogenetic tree. We focus on synteny blocks, that is, strings of genes conserved across genomes and derive analytic expressions for the expected number of synteny blocks of a given size (or of maximal size) in terms of the temporal separation between the genomes and the rates of evolutionary events. Our setting is similar to the heavily studied stick breaking problem family, but its discrete structure and the stochastic nature of the underlying process suggest a simple, independent model. We demonstrate the predictive power of this model both in simulations and on real data from the ATGC data base.