Modeling threshold phenomena, metabolic pathways switches and signals in chemostat-cultivated cells: the Crabtree effect in Saccharomyces cerevisiae

Abstract

The long-term Crabtree effect in Saccharomyces cerevisiae cultivated in aerobic chemostat at steady state has been studied for three different substrate concentrations in the feed of the bioreactor (data: J. Gen. Microbiol., 129 (1983) 653). We have shown that a model using two ways of transport/metabolization ( T/ M) of hyperbolic form, with high and low affinity for the substrate, allowed to represent correctly the main characteristics of the phenomenon. The model is based on an explicit form of the T/ M kinetics when the bioreactor is considered as a polyphasic dispersed system (PDS). Mass balances analysis also allows to quantify the critical dilution rate value (threshold), D c , of the transition between respiratory and respirofermentative mode, for which ethanol is produced. A good approximation for the threshold is D c = V S 0 Y X c , S where Y X c , S is the average yield coefficient before transition and V S 0, the maximum specific rate of high affinity T/ M pathway. The theoretical value is 0.3 h −1, and is equal to the experimental value. We thus show in a quantitative way that the transition depends both on culture conditions (global characteristic of the system) and on strain properties (intrinsic characteristic of the microorganism as well). Using two different methods to calculate the residual substrate has carried out the comparison between the simulations end the experimental data. This allowed showing that the latter is not well represented by Monod's model and has confirmed that the affinity for the substrate varies according to the biomass. We have then shown how to calculate the most important specific rates (or metabolic flux) related to biomass, ethanol, oxygen, hydrogen, respiratory and fermentative CO 2 and H 2O within the cellular phase. It has appeared that the oxygen uptake rate directly depends on high-affinity T/ M pathway. This let us think that the regulation of the Crabtree effect in S. cerevisiae depends on the saturation of some glucose metabolization and transport pathways rather than on saturation of the respiratory chains. The specific rates analysis has also allowed us to show, at least in this case, that the metabolization rate (biosynthesis+fueling) had its maximum value on the whole dilution rates interval; metabolites excretion (ethanol and fermentative CO 2) only intervenes to drain a “surplus” glucose flux. As a consequence, the transport capacity must be higher than the one of metabolization. Maximization of the metabolization specific rate could then be used as an optimization criterion in the stoichiometric calculation of metabolic flux (and not the specific growth rate maximization because growth is limited in a chemostat ( μ= D)). We have also shown that the mass balances based on the T/ M processes are in agreement with molar and elementary balances of the general stoichiometric equation for glucose respiration and fermentation under aerobic conditions. Thanks to the specific rates calculating the stoichiometric coefficients has done this. The total mass balance difference does not exceed 4%, which is compatible with the experimental carbon balance. Finally, we have emphasized that the ratio of biosynthesis flux and metabolization flux is constant before and after transition. This observation could be applied as soon as the free substrate concentration in the cellular phase is low. The paper succinctly describes the former theoretical results on which the model is built and sufficiently explains the algorithm for straightforward implementation.