Nonlinear analysis of the effect of maintenance in continuous cell cultures

The effect of maintenance on steady-state behavior in continuous cell cultures is studied theoretically with particular emphasis on stability and multiplicity characteristics. Bifurcation theory and stability analysis is applied to determine how the number and stability of steady-states depend on dilution rate and feed composition for Klebsiella pneumoniae feeding on mixed glucose–xylose substrates. The biological system is analyzed using a cybernetic modeling approach. We propose a numerical strategy which enables us to determine all possible steady-states for a given set of operating conditions. The algorithm exploits the polynomial nature of the equations. Results for a model without maintenance are compared to the predictions of a model with maintenance. It is shown that the model without maintenance effects and constitutive enzyme synthesis rate admits spurious steady-state solutions, which disappear when these effects are taken into account. In both cases multiple steady-states are observed over a range of dilution rates. In addition, the model with maintenance also predicts dynamic instability in the form of self-sustained oscillations. We have also investigated the effect of various parameters on the region of multiplicity to determine operating conditions which would enable experimental verification of our predictions.