Trade-off between segregational stability and metabolic burden: a mathematical model of plasmid ColE1 replication control.

A model of ColE1 copy number control has been developed where molecular details of replication are connected both to segregational stability and metabolic burden. Efficient replication control reduces copy number variation and increases segregational stability for a given average copy number. Copy number variation is predicted to depend on the type of inhibition mechanism as well as RNA I and RNA II turnover rate constants. It is shown that when both RNA I and RNA II transcription frequencies and the rate constant for degradation of free RNA I are very large, a hyperbolic inhibition mechanism must compensate with a 1.4 times greater average copy number to obtain the same segregational stability as an exponential inhibition mechanism. How sensitively the replication frequency responds to changes in RNA I concentration depends on the type of inhibition mechanism and the number of attempts to form an RNA II replication primer per plasmid and cell cycle. If RNA I is too stable, it will not follow changes in plasmid concentration closely, and when the transcription frequency for RNA I is only slightly higher than for RNA II, RNA I concentration becomes randomized. In both these cases, the proportionality between the single cell RNA I and plasmid concentrations is lost and this impairs copy number control. Thresholds in the rate for degradation of free RNA I as well as in RNA I and RNA II transcription frequencies have been computed, where an increase in these rate constants has a negligible effect on segregational stability but a corresponding decrease leads to segregational disaster. This indicates that there exists a well defined optimal set of rate constants where the regulation system works well without excessive metabolic load. A number of new experiments are suggested to address features of particular importance for the evolution of ColE1 copy number control.