Quantitative model of ColE1 plasmid copy number control

Initiation of replication of the Escherichia coli plasmid ColE1 is inhibited by formation of a complex between a small plasmid RNA (RNA I) and the pre-primer for DNA synthesis (RNA II). Complex formation (and inhibition of replication) is enhanced by the plasmid-encoded Rom protein. The in vitro kinetics of complex formation were previously studied both experimentally and theoretically. The in vivo concentrations and half-lives of RNA I, RNA II and Rom protein have been measured recently. We present a dynamic model for the in vivo replication control mechanism that accounts for the measured concentration values. From the model we deduce a simple formula for the steady-state plasmid concentration. Our results agree with a previous simple steady-state analysis done by Brenner and Tomizawa, in that plasmid copy number is most strongly dependent on the per plasmid rate of RNA I synthesis. However, our model predicts other parameter dependencies that are not evident from or at variance with the previous analysis. Accordingly, we predict that plasmid copy number is greatly influenced by changes in the rate constant describing the formation of an initial unstable RNA I-RNA II complex, but is only slightly influenced by changes in the dissociation rate of this complex. Plasmid copy number per average cell volume is predicted to increase linearly with increases in the RNA II synthesis rate and with increases in the generation time of the host culture. Rom protein, which promotes conversion of the unstable RNA I-RNA II complex to a stable complex, serves to decrease copy number; however, its presence or absence does not seem to qualitatively alter the copy number control mechanism. Our model predicts the quantitative increase of plasmid copy number in rom- mutants. Several experiments are suggested to investigate the predictions of the model.