A generic model for changes in microbial kinetic coefficients

Abstract

Acclimation patterns in kinetic coefficients clearly demonstrate the limits of Monod's theory for the mathematical description of microbial growth. Focusing on E. coli grown under variable glucose levels, these patterns turn out to be highly diverse and sometimes even contradictory. Here, a new model based on an optimisation assumption is applied to a spectrum of adaptation phenomena, which are observed at steady-state as well as during transient situations. On the level of apparent kinetic coefficients, rates of adaptation are calculated depending on differential growth benefits. The resulting dynamics is bounded since maximum growth rate and substrate affinity are related by a non-linear trade-off. Long-term effects of phenotypic and genotypic changes under glucose limitation are robustly predicted by the model and explained in terms of their adaptive significance. Equivocal short-term recovery patterns occurring after sudden substrate excess are traced back to differences in the internal physiological state of the cells which in turn can be calculated in dependence on the inoculum history. Metabolic stress is a second determinant of short-term variations in kinetic coefficients which is here quantified in relation to external conditions as well as the internal state of cells. We demonstrate that lag phenomena and oscillations in anabolic activity exercised by E. coli under continuous growth acceleration can be reproduced without formulations being explicit in lag periods, metabolite concentrations or the timing of experimental changes. The overall predictive power of the simple approach indicates that slow as well as fast adjustments in apparent kinetic characteristics are strongly related to a dynamic optimisation strategy.