Determination of experimental and mathematical oscillatory conditions for Zymomonas mobilis with different death rates for viable and VBNC cells

A chemostat inoculated with Zymomonas mobilis shows an oscillatory behavior when the ethanol concentration surpasses a critical value, as a consequence of the ethanol inhibitory effect. This phenomenon has been modeled with the Levenspiel law μmax(1 − P/kp)n, with n = 1. However, it has not been analytically determined whether for n ≠ 1, a super-critical Hopf bifurcation with respect to the dilution rate is responsible of the observed oscillations. In this contribution, it were determined that there is a unique Hopf point and a stability change of the non-trivial steady state, from unstable to stable as the dilution rate increases. Constraints were formulated for the product critical concentrations, the dilution rate and the parameter n. A Z. mobilis culture within a chemostat, under oscillatory conditions, was monitored to collect experimental data, that were compared with the analytical results. To improve the mathematical model, different death rates were proposed for the viable and the viable but not culturable cells. The local analytical results held for the modified model.