Simulation of the rate of transfer of antibiotic resistance between Escherichia coli strains cultured under well controlled environmental conditions

It was demonstrated that the tetracycline resistance plasmid in Escherichia coli resembling K-12 23:06 containing the E. coli plasmid DM0133 could be transferred to tetracycline sensitive E. coli K-12 MG1655 YFP. The sensitive recipient strain has a slight metabolic advantage in continuous fermentation in absence of tetracycline pressure and as a result the numbers of the resistant recipient strain increase during fermentation. In presence of tetracycline pressure the sensitive strain is eliminated, but when it acquires tetracycline resistance the strain has still the same metabolic advantage as its sensitive parent strain in absence of tetracycline. Here a model will be shown that could explain the rate of transformation of a sensitive into a resistant recipient strain and its subsequent growth during continuous fermentation. According to the model the probability of formation of mutants would be much higher at the dilution rate of 0.09 compared to 0.28, whereas the growth of mutants would be much faster at high dilution rate. The growth model shows how the recipient mutants and the donor cells behave in relation to the dilution rate and the number of mutants. Apart from a deterministic model describing the growth rate of both the donor strain and the resistant recipient strain a stochastic model was developed that is particularly useful when low numbers of mutants are formed.