Stability of Colicin Plasmids in Continuous Culture: Mathematical Model and Analysis

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Abstract
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.