Analysis and Mathematical Modeling of Autonomously Oscillating Yeast Cultures.

The conditions that precede the onset of autonomous oscillations in continuous yeast cultures were studied in three different types of experiments. It was found that the final state of the culture depends on the protocol used to start-up the reactor. Reaching the desired operating point by slow dilution rate changes gave rise to different final states, two oscillatory states and one steady state, depending on the rate of change in dilution rate. The multiplicity of stable states at a single operating point is not explained by current distributed models and points towards a segregated mechanism of these oscillations. The ability of an age population balance model to capture experimentally observed oscillatory dynamics of continuous cultures of budding yeast was investigated. Consistent with experimental evidence, numerical simulations of the model revealed the existence of several, stable periodic solutions. However, each occurred over a different range of dilution rates. Experiments have shown that the steady state in continuous yeast cultures appears to be stable, even under conditions that allow oscillatory dynamics. The stability of the steady state of the age population balance model under conditions that allow oscillatory dynamics was not resolved. Another population balance model in terms of mass distribution of unbudded cells and age distribution of budded cells was also proposed. The model was based on a more detailed cell cycle than that used in the development of the age distribution model. Therefore, the hybrid mass-age model was superior to the age model in its ability to simulate situations in which the yeast culture is starved. In agreement with experimental evidence, the model predicts the auto-synchronization of batch yeast cultures during their batch growth with a final bimodal cell mass distribution. Furthermore, the oscillations occur spontaneously as the simulated batch culture is switched to continuous operation. The model also predicts multiple oscillatory states at separate regions of the dilution rate and predicts the existence of an oscillatory state and an extended unstable steady state at the same operating conditions