  Continuous cultures of mammalian cells are complex systems displaying
hallmark phenomena of nonlinear dynamics, such as multi-stability, hysteresis,
as well as sharp transitions between different metabolic states. In this
context mathematical models may suggest control strategies to steer the system
towards desired states. Although even clonal populations are known to exhibit
cell-to-cell variability, most of the currently studied models assume that the
population is homogeneous. To overcome this limitation, we use the maximum
entropy principle to model the phenotypic distribution of cells in a chemostat
as a function of the dilution rate. We consider the coupling between cell
metabolism and extracellular variables describing the state of the bioreactor
and take into account the impact of toxic byproduct accumulation on cell
viability. We present a formal solution for the stationary state of the
chemostat and show how to apply it in two examples. First, a simplified model
of cell metabolism where the exact solution is tractable, and then a
genome-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, increasing
concentrations of byproducts that vanish in the homogeneous case, and larger
population sizes.
