An Extensible Compartment Based Ordinary Differential Equation Model to Provide Spatial Heterogeneity of Vertical Bioreactors to Whole Cell Metabolic Models - mauriceling/mauriceling.github.io GitHub Wiki

Citation: Ling, MHT. 2026 An Extensible Compartment-Based Ordinary Differential Equation Model to Provide Spatial Heterogeneity of Vertical Bioreactors to Whole Cell Metabolic Models. Scholastic Microbiology 1(1): 01-05.

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Large-scale aerobic bioreactors exhibit spatial gradients in dissolved oxygen and substrate from incomplete mixing and transport limitations, leading to heterogeneous microenvironments that influence cellular metabolism and complicate scale-up. Classical well-mixed models cannot capture these gradients, limiting their predictive power for industrial processes and their integration with whole-cell metabolic models. In this study, we present a simple and extensible multi-vertical compartment model for an aerobic bioreactor, formulated as a system of coupled ordinary differential equations derived from finite-volume discretization of the one-dimensional advection–dispersion–reaction framework. The reactor volume is divided into vertically stacked compartments, each assumed well mixed locally while connected through axial advection and axial dispersion. Biomass growth is described using dual-substrate Monod kinetics with substrate and oxygen limitation, and stoichiometric consistency is maintained through yield-based uptake relations. Substrate feed is introduced at the top compartment, while oxygen transfer is modelled via a volumetric mass transfer term, enabling counter-current gradients to emerge. The model is implemented in Python and solved using a stiff ODE integrator, allowing flexible configuration of compartment number, operating parameters, and feed strategies. Simulation results demonstrate the emergence of spatial gradients and their impact on biomass distribution under different operating conditions. This framework provides a computationally efficient bridge between reactor-scale heterogeneity and whole-cell metabolic modelling.