Modeling the dynamics of E. coli populations in the three-dimensional turbulent field of a stirred-tank bioreactor—A structured–segregated approach

In the present work, an Euler–Lagrange approach has been applied to characterize the behavior of a heterogeneous cell population in a stirred-tank bioreactor with non-ideal mixing. It allows one to describe population behavior as the outcome of the interaction between the intracellular state of its individual cell and the turbulent flow field in the reactor. The modeling approach and the numerical method employed are based on an Euler–Lagrange formulation of the system combined with a fractional-step method to allow for a stable, accurate, and numerically efficient solution of the underlying equations. This strategy permits one to account for the heterogeneity present in real reactors in both the abiotic and biotic phases. The example of sugar uptake (phosphotransferase system, PTS) of E. coli cells growing in a fed-batch culture is used to illustrate the application of the approach. The activity of the uptake system depends on the local concentration of glucose as well as the ratio of the intracellular concentrations of phosphoenolpyruvate and pyruvate, which in turn is a function of the history of the individual cell. The simulation results point to distinct differences in the viability of the cells at different scale of operation.