Repetitive Short-Term Stimuli Imposed in Poor Mixing Zones Induce Long-Term Adaptation of E. coli Cultures in Large-Scale Bioreactors: Experimental Evidence and Mathematical Model

Rapidly changing concentrations of substrates frequently occur during large-scale microbial cultivations. These changing conditions, caused by large mixing times, result in a heterogeneous population distribution. Here, we present a powerful and efficient modeling approach to predict the influence of varying substrate levels on the transcriptional and translational response of the cell. This approach consists of two parts, a single-cell model to describe transcription and translation for an exemplary operon (trp operon) and a second part to characterize cell distribution during the experimental setup. Combination of both models enables prediction of transcriptional patterns for the whole population. In summary, the resulting model is not only able to anticipate the experimentally observed short-term and long-term transcriptional response, it further allows envision of altered protein levels. Our model shows that locally induced stress responses propagate throughout the bioreactor, resulting in temporal, and spatial population heterogeneity. Stress induced transcriptional response leads to a new population steady-state shortly after imposing fluctuating substrate conditions. In contrast, the protein levels take more than 10 h to achieve steady-state conditions.