Molecular clocks reduce plasmid loss rates: the R1 case.J Mol Biol 2000; 297(1):179-92JM
Plasmids control their replication so that the replication frequency per plasmid copy responds to the number of plasmid copies per cell. High sensitivity amplification in replication response to copy number deviations generally reduces variation in copy numbers between different single cells, thereby reducing the plasmid loss rate in a cell population. However, experiments show that plasmid R1 has a gradual, insensitive replication control predicting considerable copy number variation between single cells. The critical step in R1 copy number control is regulation of synthesis of a rate-limiting cis-acting replication protein, RepA. De novo synthesis of a large number of RepA molecules is required for replication, suggesting that copy number control is exercised at multiple steps. In this theoretical kinetic study we analyse R1 multistep copy number control and show that it results in the insensitive replication response found experimentally but that it at the same time effectively prohibits the existence of only one plasmid copy in a dividing cell. In combination with the partition system of R1, this can lead to very high segregational stability. The R1 control mechanism is compared to the different multistep copy number control of plasmid ColE1 that is based on conventional sensitivity amplification. This implies that while copy number control for ColE1 efficiently corrects for fluctuations that have already occurred, R1 copy number control prevents their emergence in cells that by chance start their cycle with only one plasmid copy. We also discuss how regular, clock-like, behaviour of single plasmid copies becomes hidden in experiments probing collective properties of a population of plasmid copies because the individual copies are out of phase. The model is formulated using master equations, taking a stochastic approach to regulation, but the mathematical formalism is kept to a minimum and the model is simplified to its bare essence. This simplicity makes it possible to extend the analysis to other replicons with similar design principles.