Analysis of a model for minichromosome segregation in Escherichia coli

The present article contains a theoretical, quantitative analysis of the implications of the Helmstetter-Leonard model (1987, J. molec. Biol. 197, 195-204.) for the segregation of chromosomal DNA in Escherichia coli, on the expected copy-number distribution of minichromosomes in a culture in steady-state exponential growth. According to the model, two determinants are involved in the mechanism of chromosome segregation: a partition system that assures the equal allotment of chromosomes between daughter cells at cell division, and a locus within the minimal oriC region that specifies the attachment site of the chromosomes to the cell envelope at initiation of replication. There are many parameters that must be taken into account in such a study, and since some of them are probabilistic in nature, a strictly analytical approach is not feasible and we had to resort to computer simulation. A wide range of parameter values was tested, in all combinations. The minichromosome copy-number distributions obtained all had a prominent mode equal to the number of oriC binding sites and their main features were determined essentially by that and very little by any of the other parameters of the model. In order to avoid the unrealistic situation in which this one feature completely dominates the results, the original model was modified so that each individual minichromosome is no longer required to replicate during every cell generation, by introducing a limit to the number of unsuccessful attempts to locate a suitable binding site. The copy-number distributions predicted by this version of the model are quantitatively and qualitatively very different and depend on all the components of the model. The simulation results are sufficiently well-behaved to allow consideration as to whether a particular empirical minichromosome copy-number distribution--when such data become available--could in fact be governed by the proposed model; it may even be possible to get a rough estimate for the different parameters involved.