On the Distribution of Synteny Block Lengths in Prokaryote Genomes under a Neutral Model of Genome Dynamics

In bacterial and archaeal genomes, functionally linked genes often cluster in operons that enable coregulation of expression of these genes and production of their protein products in stoichiometric amounts. Many operons are shared by genomes of distantly related bacteria and archaea due in part to evolutionary conservation and in part to horizontal gene transfer (HGT). In contrast, similarity between species in their gene order along the chromosome can be merely a result of evolutionary closeness such that synteny has not yet been disrupted by genome dynamic events occurring during evolution. In general, however, accurate differentiation of operons from spurious gene clusters is a non-trivial task that depends on an underlying model of neutral genome evolution. Here, we employ a recently developed stochastic model of genome rearrangement (“jump model”) that accounts for HGT across prokaryote species evolving along a phylogenetic tree to infer the size distribution of shared gene strings (synteny blocks) under neutral evolution. Analytic expressions are derived for the expected number of synteny blocks of a given size (or of maximal size) depending on the evolutionary distance between the genomes and the rates of different types of evolutionary events. This analysis is related to the well-studied family of stick-breaking problems, but the discrete structure and stochastic nature of the evolutionary process provide for the development of a simple, independent model. We demonstrate the predictive power of this model by computer simulations of synthetic data as well as by simulating genomes on real trees obtained from the Alignable Tight Genome Clusters database.