A Modular Mathematical Model of Fermentation in an Industrial-Scale Bioreactor

This paper presents a modular hybrid mathematical model of bacterial fermentation developed by integrating a detailed kinetic model for the central carbon metabolism of Escherichia coli with a simplified four-compartment model of a large stirred bioreactor. The model describes the growth dynamics of E. coli, taking into account the hydrodynamic characteristics of the cultivation environment and spatial concentration gradients. The first module simulates liquid exchange flows between neighboring reactor zones and tracks the spatial distribution of substrate, acetate, dissolved oxygen, and biomass, while the second one, which is a kinetic model, includes main metabolic pathways such as glycolysis, the tricarboxylic acid cycle, and oxidative phosphorylation. Compared to most previous hybrid approaches relying on simplified kinetics, the present model integrates a detailed kinetic representation of E. coli central metabolism and is openly implemented on the BioUML platform, which ensures its reproducibility and extensibility. Numerical simulations reveal how mixing intensity affects concentration gradients and metabolic regimes across the reactor. Additionally, the model was used to identify an optimal mixing regime corresponding to the state where the system first enters the regime of complete aerobic substrate oxidation. The proposed model is applicable for numerical analysis of industrial-scale bioreactors and for predicting metabolic dynamics under various hydrodynamic conditions.