Mass action models describing extant horizontal transfer of plasmids: inferences and parameter sensitivities

Predicting the fate of horizontally transmissible elements in extant microbial communities might be facilitated by the availability of suitable mathematical models. Since the mid-1970s, mass action models have been introduced to describe the transfer of conjugal and mobilizable genetic elements. This chapter will summarize and explain the assumptions behind spatially homogenous models, and show the predictions by these models under typical scenarios, such as evaluating existence conditions of conjugal plasmids under chemostat or seasonal growth conditions. Special attention is given to the sensitivity of the outcomes to the various plasmid dynamic parameters. For our analysis, we developed a set of user-friendly MatLab routines, which are deposited in the public domain. We hope that the availability of these routines will encourage the computationally untrained microbiologist to make use of these mathematical models. Finally, further permutations, as well as limitations of these mass action models in view of the structured complexity of most microbial systems are addressed.