The steady states of microbial growth on mixtures of substitutable substrates in a chemostat

Microbes growing on mixtures of substrates in a chemostat exhibit different substrate utilization patterns, depending on the dilution rate and feed concentrations. For instance, when supplied with high feed concentrations of a binary mixture, both substrates are consumed at low dilution rates, but only one of the substrates is consumed at high dilution rates. The goal of this work is to explain the onset of such transitions, which play a very significant role in ecology and bioengineering. In previous work, we formulated a mathematical model of mixed-substrate growth in batch cultures. We use the extension of this model to continuous cultures as the framework for understanding substrate utilization patterns in continuous cultures. Our explanation rests upon the existence of two special types of dilution rates predicted by the model. The first is the so-called critical dilution rate at which the growth rate becomes zero, leading to cell washout. The existence of the critical dilution rate obtains from the simplest models of microbial growth, and is rooted in the fact that growth is inherently autocatalytic. The second type of special dilution rate, a unique feature of our model, stems from the recognition that synthesis of the enzymes catalysing the uptake of substrates is also autocatalytic. Hence, associated with each substrate is a transition dilution rate at which the synthesis rate of the transport enzyme becomes zero. We show that: (1) the substrate utilization patterns in continuous cultures are completely determined by the relative magnitudes of the critical and transition dilution rates; and (2) the critical and transition dilution rates are in turn determined by the feed concentrations. This allows us to construct an operating diagram, which yields the substrate utilization pattern for any given dilution rate and feed concentrations. The theory explains most of the mixed-substrate phenomena summarized in a recent review article by Egli (1995, Adv. Microbiol. Ecol. 14, 305-386).