Deterministic models to decipher the lag phase duration during diauxie

The deterministic model developed by Graham et al. [2020], which is the approximation in large population of a stochastic model, allowed the authors to propose a ‘macroscopic description’ of metabolic heterogeneity of Escherichia coli growing on glucose and xylose. However, these models did not include any mechanistic model to explain the variations of the duration of the ‘lag-phase’ observed when the glucose is exhausted and before the xylose is being consumed. Here, we propose a deterministic mechanistic model to explain how E. coli switches its consumption of a sugar to another one depending on the dynamic of intracellular XylR molecules. The model is developed and investigated numerically. It reveals some important observability issues.