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Continuous cultures of mammalian cells are complex systems displayinghallmark phenomena of nonlinear dynamics, such as multi-stability, hysteresis,as well as sharp transitions between different metabolic states. In thiscontext mathematical models may suggest control strategies to steer the systemtowards desired states. Although even clonal populations are known to exhibitcell-to-cell variability, most of the currently studied models assume that thepopulation is homogeneous. To overcome this limitation, we use the maximumentropy principle to model the phenotypic distribution of cells in a chemostatas a function of the dilution rate. We consider the coupling between cellmetabolism and extracellular variables describing the state of the bioreactorand take into account the impact of toxic byproduct accumulation on cellviability. We present a formal solution for the stationary state of thechemostat and show how to apply it in two examples. First, a simplified modelof cell metabolism where the exact solution is tractable, and then agenome-scale metabolic network of the Chinese hamster ovary (CHO) cell line.Along the way we discuss several consequences of heterogeneity, such as:qualitative changes in the dynamical landscape of the system, increasingconcentrations of byproducts that vanish in the homogeneous case, and largerpopulation sizes.

Maximum entropy and population heterogeneity in continuous cell cultures