A two-dimensional population balance model for cell growth including multiple uptake systems
Résumé
Cell growth in a chemostat is a well-documented research topic. How cells uptake the avail-able substrate to gain weight and engage cell division is not generally taken into account inthe modelling bioreactors. In fact, the growth rate is related to a population doubling timewhereas the microorganisms’ growth in mass is due to the mass transfer of substrates fromthe liquid phase to the biotic phase. Clearly, growth in mass precedes growth in number.Similarly, the transport of substrates down to the cell scale precedes the mass transfer. Thisarticle’s main feature is a two-dimensional population balance model that allows to uncou-ple growth in mass and growth in number when the equilibrium between a cell populationand its environment is disrupted. The cell length and the rate of anabolism are chosen asinternal variables. It is proved that the hypothesis “growth in number = growth in mass” isvalid at steady-state or in exponential growth only. The glucose uptake is assumed drivenby two transport systems with a different affinity constant for the substrate. This combina-tion of two regulated uptake systems operating in parallel explains a 3-fold increase in theuptake following a glucose pulse, but can also predict substrate uptake rates higher thanthe maximal batch value as observed in some experiments. These features are obtainedby considering carbon fluxes in the formulation of regulation principles for uptake dynam-ics. The population balance’s implementation in a multi-compartment reactor is a naturalprospective work and allows extensions to industrial processes.
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