Modeling the Effects of Substrate Fluctuations on the Maintenance Rate in Bioreactors with a Probabilistic Approach

A simple interaction by exchange with the mean (IEM) mixing model is implemented to describe the glucose concentration segregations in industrial and laboratory scale bioreactors. This approach is coupled with a population balance model (PBM) for the growth rate adaptation and a metabolic model dependent on the individuals state, both from the literature [1]. The model formulation is validated against different published experiments and it is shown that the IEM model reduces the computational costs when just the segregation of few species is of interest. A model for the maintenance costs of Escherichia coli subject to glucose concentration fluctuation is also presented and implemented in the context of the IEM mixing model. An Eulerian formulation of the effects of the substrate fluctuations on the maintenance rate is proposed and tied to a more intuitive Lagrangian vision. The study of these metabolic changes due to substrate heterogeneities helps the understanding of the relationships between hydrodynamics and cells metabolism and it improves the agreement between numerical and experimental data.