Conditions for the evolution of gene clusters in bacterial genomes

Abstract

Genes encoding proteins in a common pathway are often found near each other along bacterial chromosomes. Several explanations have been proposed to account for the evolution of these structures. For instance, natural selection may directly favour gene clusters through a variety of mechanisms, such as increased efficiency of coregulation. An alternative and controversial hypothesis is the selfish operon model, which asserts that clustered arrangements of genes are more easily transferred to other species, thus improving the prospects for survival of the cluster. According to another hypothesis (the persistence model), genes that are in close proximity are less likely to be disrupted by deletions. Here we develop computational models to study the conditions under which gene clusters can evolve and persist. First, we examine the selfish operon model by re-implementing the simulation and running it under a wide range of conditions. Second, we introduce and study a Moran process in which there is natural selection for gene clustering and rearrangement occurs by genome inversion events. Finally, we develop and study a model that includes selection and inversion, which tracks the occurrence and fixation of rearrangements. Surprisingly, gene clusters fail to evolve under a wide range of conditions. Factors that promote the evolution of gene clusters include a low number of genes in the pathway, a high population size, and in the case of the selfish operon model, a high horizontal transfer rate. The computational analysis here has shown that the evolution of gene clusters can occur under both direct and indirect selection as long as certain conditions hold. Under these conditions the selfish operon model is still viable as an explanation for the evolution of gene clusters.

Figure 1. Gene clustering under the original selfish operon model.

The plots show A) the average minimum arc distance between genes, B) the proportion of genes clustered under 3 minutes and C) the total population size over time, for three realisations of the process using three values of the rearrangement probability , indicated in solid (), dashed () and dotted curves (). Unless indicated otherwise, there are three genes in the pathway and the parameter values are , and . Only the first 15,000 steps of the simulations are shown here.

Figure 2. Gene clustering under the selfish operon model.

The average minimum arc distance between genes at equilibrium as a function of various parameters: A) the probability of rearrangement under the original uncorrected translocation process, B) rearrangement probability with the translocation process corrected so that the probability of choosing the genes in question is included, C) the maximum transfer probability ; D) the parameter , which describes the decay in the horizontal transfer rate over distance. Each point indicates the mean of 100 runs and error bars show the central 90% of simulations. Each simulation was run for 50,000 time steps. Unless indicated otherwise, there are three genes in the pathway and the parameter values are , , and .

Figure 3. A sensitivity analysis for the selfish operon model with inversion rather than translocation.

Each panel plots the average minimum arc distance between the genes. Simulations were run for 50,000 steps. In the top three panels (A–C) one parameter is varied at a time while keeping the others constant. Each point represents the mean of 100 simulations and error bars indicate the central 90% of simulations. The responses are shown for three different values of the number of genes, . The plots show distances over the probability of rearrangement, which occurs here through inversion (panels A and D), the maximum probability of transfer (B and E) and the decay in transfer probability over distance (C and F). The default parameter values for these simulations are , and The bottom three panels (D–F) show the results of simulations for in which the parameters were set randomly according to latin hypercube sampling with 150 points and 40 simulations per point.

Figure 4. Gene clustering under a Moran model.

The average minimum arc distance between genes over time for four sample runs of the simulation using rearrangement rates (A and D), (B) and (C). The other parameters are and genes. In panel D) a run of the simulation is shown in which we model selection for distance using a sigmoidal instead of exponential function. In this case, fitness decreases markedly between distances of 5 and 20kb. The final distance after 200 generations was 176 kb. Observe that in panel B) it took more than 10 times as long for the genes to approach a clustered state (distance 284 kb) than in panel A) (distance 77 kb), and that in panel C) the genes are still far apart at around 850 kb after 20,000 generations.

Figure 5. Rearrangement substitution model, varying one parameter at a time.

The panels show the average minimum arc distance between the genes plotted over A) the inversion probability , B) the population size , C) the decay in fitness over distance and D) the number of genes in the pathway in question. The default parameter values are , , and . Simulations were run for 50,000 generations. Each point represents the mean from 100 simulations and the error bars indicate the central 90% of simulated values.

Figure 6. Rearrangement substitution model, varying the parameters of the model using latin hypercube sampling with 200 points.

The panels show the average minimum arc distance between the genes plotted over A) the inversion probability , B) the population size , C) the decay in fitness over distance and D) the number of genes in the pathway in question. Simulations were run for 50,000 generations. Each point represents the mean from 100 simulations.