Stability of colicin plasmids in continuous culture: mathematical model and analysis

Bacteriocin plasmids may be useful in preventing plasmid instability because the bacteriocin they produce selectively kills otherwise identical bacterial cells lacking the plasmid. This capability may allow plasmid-bearing cells to persist despite the problems of growth rate depression and segregational plasmid loss which often lead to displacement by plasmid-free cells.In order to determine the conditions under which bacteriocin plasmids can prevent instability, we develop and analyze a mathematical model for the growth of colicin plasmid-bearing E. coli in continuous culture. Model behavior compares successfully with experimental results of Adams et al. (1979) [1]. Dependence of the system dynamic behavior on key parameters is elucidated and a simple parameter criterion for prevention of plasmid instability is derived. The possibility of instability prevention is found to be extremely sensitive to dilution rate.