Model for the dynamics of colicin plasmids in continuous culture

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 that often lead to displacement by plasmid-free cells. In order to determine the conditions under which bacteriocin plasmids can prevent instability, we have developed and analyzed 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. Dependence of the system dynamic behavior on key parameters has been elucidated and a simple parameter criterion for prevention of plasmid instability has been derived. The possibility of instability prevention was found to be extremely sensitive to dilution rate.