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We revisit the modeling of the diauxic growth of a pure microorganism on twodistinct sugars which was first described by Monod. Most available models aredeterministic and make the assumption that all cells of the microbial ecosystembehave homogeneously with respect to both sugars, all consuming the first oneand then switching to the second when the first is exhausted. We propose here astochastic model which describes what is called "metabolic heterogeneity". Itallows to consider small populations as in microfluidics as well as largepopulations where billions of individuals coexist in the medium in a batch orchemostat. We highlight the link between the stochastic model and thedeterministic behavior in real large cultures using a large populationapproximation. Then the influence of model parameter values on model dynamicsis studied, notably with respect to the lag-phase observed in real systemsdepending on the sugars on which the microorganism grows. It is shown that bothmetabolic parameters as well as initial conditions play a crucial role onsystem dynamics.

Bacterial Metabolic Heterogeneity: from Stochastic to Deterministic Models