Shorter Communication On the existence of oscillatory behavior in unstructured models of bioreactors

Continuous cultures of some microorganisms such as Saccharomyces cerevisiae and Zymomonas mobilis have long been known to exhibit oscillatory behavior under suitable operating conditions (JoK bses, Egberts, Baalen, & Roels, 1985; Parulekar, Semones, Rolf, Lievense, & Lim, 1986). The understanding and the modeling of these oscillations is important for the knowledge of pathway regulationof cell metabolism and also for the optimization and control of the microbial process. Various models with di!erent levels of complexity have been proposed in the literature to describe these spontaneous oscillations (Porro, Martegani, Ranzi, & Alberghina, 1988; StraK ssle, Sonnleitner, & Fiechter, 1988; Cazzador, 1991; Hjortso & Nielsen, 1994). The need for such complex models arises from the fact that the basic unstructured model, inwhich, the metabolic activity is described solely by growth rate and yield coe$cient, does not recognize any internal structure of the cell nor a diversity between cell forms, and thus fails to describe situations where the cell compositionor the morphology of the cell culture are also important variables (Nielsen & Villadsen, 1994). The inadequacy of the unstructured model manifests itself in its failure to predict transient behavior following sudden changes in operating parameters, e.g. dilution rate, and in predicting stable autonomous oscillations occurring under suitable conditions.