The present work is aimed at studying the dynamic behaviour of the tryptopnanase (tna) operon, which encodes the proteins necessary to uptake and metabolise tryptophan to use it as a carbon source in the absence of glucose. To this end, we designed a micro-bioreactor capable of driving a bacterial culture to a stationary state. This allowed us to explore (at the single cell level) the tna operon steady-state dynamics under multiple culture conditions. Our experimental results suggest that the tna operon is bistable for a specific range of environmental tryptophan and glucose concentrations, and evidence that both reagents play a role on the activation of the enzyme in charge of metabolising tryptophan: tryptophanase (TnaA). Based on our experimental data and the already known regulatory mechanisms, we developed a mathematical model for the tna operon regulatory pathway. Our modelling results reinforce the claim that the tna operon is bistable, and further suggest that the activity of enzyme TnaA is regulated by the environmental levels of glucose and tryptophan via a common signalling pathway. Possible biological implications of our findings are further discussed.