Accounting for mating pair formation in plasmid population dynamics

Plasmids are important vehicles for horizontal gene transfer and rapid adaptation in bacteria, including the spread of antibiotic resistance genes. Conjugative transfer of a plasmid from a plasmid-bearing to a plasmid-free bacterial cell requires contact and attachment of the cells followed by plasmid DNA transfer prior to detachment. We introduce a system of differential equations for plasmid transfer in well-mixed populations that accounts for attachment, DNA transfer, and detachment dynamics. These equations offer advantages over classical mass-action models that combine these three processes into a single "bulk" conjugation rate. By decomposing the process of plasmid transfer into its constituent parts, this new model provides a framework that facilitates meaningful comparisons of plasmid transfer rates in surface and liquid environments. The model also allows one to account for experimental and environmental effects such as mixing intensity. To test the adequacy of the model and further explore the effects of mixing on plasmid transfer, we performed batch culture experiments using three different plasmids and a range of different mixing intensities. The results show that plasmid transfer is optimized at low to moderate shaking speeds and that vigorous shaking negatively affects plasmid transfer. Using reasonable assumptions on attachment and detachment rates, the mathematical model predicts the same behavior.