Competition of plasmid-bearing and plasmid-free organisms in a chemostat: A study of bifurcation phenomena

The stability of the classical Levin–Stewart model that describes the competition between plasmid-bearing and plasmid-free populations in a chemostat is revisited using a combination of bifurcation theory and continuation techniques. Simple analytical conditions are derived that describe the conditions for the coexistence of the competing cells and for the safe operation of the chemostat. The ability of the model to predict the coexistence of the competing cells in an oscillatory mode is also studied. Analytical results with respect to arbitrary growth kinetics are derived that set the necessary conditions for the existence of Hopf points in the model as well as for the occurrence of a number of Hopf degeneracies. These general conditions are applied to Monod/Haldane substrate inhibition growth models. Practical branch sets in terms of model parameters are readily constructed for Monod–Monod, Monod–inhibition, inhibition–Monod and inhibition–inhibition cases. The dynamic analysis, on the other hand, allows the identification of regions of one and two Hopf points predicted by the model. The combination of results of both static and dynamic bifurcation allows the delineation of a total of 45 qualitatively different regions and helps to construct a useful picture, in the multidimensional parameter space, of the different behaviors predicted by the model. Practical criteria are also set for the comparison between these regions, and for the study of the effects that various limiting substrates can have on recombinant culture stability and as regards the desired rate properties to be looked for in screening media formulations.