Variation and modeling of the probability of plasmid loss as a function of growth rate of plasmid-bearing cells of Escherichia coli during continuous cultures.

A large number of models concerning cultures of genetically engineered bacteria have been described. Among them, some are specifically adapted to continuous cultures and lead to the determination of two variables: (i) the difference in the specific growth rates between plasmid-carrying cell and plasmid-free cells (deltamicro) and (ii) the frequency of plasmid loss by plasmid-containing cells (p(r)micro(+)). Until now, studies have been performed on the global expression p(r)micro(+) and deltamicro, whose value during continuous assays have been supposed approximately constant (mean value) and not on separate values of both terms p(r) and micro(+), respectively, probability of plasmid loss and specific growth rate of the plasmid-carrying cells. So far these studies do not allow examination of the relationship between these two last parameters. Experimental results were obtained with Escherichia coli C600 galk (GAPDH), a genetically engineered strain that synthetizes an elevated quantity of glyceraldehyde-3-phosphate dehydrogenase (GAPDH). From data obtained during continuous cultures, it is shown that during an assay, deltamicro, and p(r)micro(+) do not remain constant. An appropriate mathematical analysis of the expression of micro(-) (specific growth rate of the plasmid-free cells) and micro(+) has been built up. This allows the evaluation of the values of micro(+) and micro(-) during the continuous cultures carried out at different dilution rates. Values of p(r) have been calculated from these data. Indeed our results show that p(r) increases with micro(+). A modeling approach which allows correct simulation of this variation is also proposed. This model is derived from the Hill equation regarding cooperative binding of enzymic type reaction.