Requirements for rapid plasmid ColE1 copy number adjustments:: A mathematical model of inhibition modes and RNA turnover rates

The random distribution of ColE1 plasmids between the daughter cells at sell division introduces large copy number variations. Statistic variation associated with limited copy number in single cells also causes fluctuations to emerge spontaneously during the cell cycle. Efficient replication control out of steady state is therefore important to tame such stochastic effects of small numbers. In the present model, the dynamic features of copy number control are divided into two parts: first, how sharply the replication frequency per plasmid responds to changes in the concentration of the plasmid-coded inhibitor, RNA I, and second, how tightly RNA I and plasmid concentrations are coupled. Single (hyperbolic)- and multiple (exponential)-step inhibition mechanisms are compared out of steady state and it is shown how the response in replication frequency depends on the mode of inhibition. For both mechanisms, sensitivity of inhibition is "bought" at the expense of a rapid turnover of a replication preprimer, RNA II. Conventional, single-step, inhibition kinetics gives a sloppy replication control even at high RNA II turnover rates, whereas multiple-step inhibition has the potential of working with unlimited precision. When plasmid concentration changes rapidly, RNA I must be degraded rapidly to be "up to date" with the change. Adjustment to steady state is drastically impaired when the turnover rate constants of RNA I decrease below certain thresholds, but is basically unaffected for a corresponding increase. Several features of copy number control that are shown to be crucial for the understanding of ColE1-type plasmids still remain to be experimentally characterized. It is shown how steady-state properties reflect dynamics at the heart of regulation and therefore can be used to discriminate between fundamentally different copy number control mechanisms. The experimental tests of the predictions made require carefully planned assays, and some suggestions for suitable experiments arise naturally from the present work. It is also discussed how the presence of the Rom protein may affect dynamic dualities of copy number control. (C) 1998 Academic Press.