Sigmoidal and growth rate kinetic hysteresis in biochemical systems

Two types of kinetic hysteresis curves are modeled in this paper: hysteresis in batch enzyme kinetic reactions and growth rate hysteresis in open fermentation systems. It is shown that a sigmoidal shape can be developed by including two features in a kinetic model without resorting to allosteric arguments. These are parallel pathways branching from an intermediate to the product, and a bimolecular terminal step. Parallel pathways are needed to cause a localized convexity change and the bimolecular step is required for the quadratic initial product rate rise. The counter-clockwise hysteresis effect in open fermentation vessels can be developed starting from a limiting substrate-lumped cell machinery kinetic model. The formation of an intermediate complex, which in turn leads to more cells, makes the fermentation model analogous to an enzyme-substrate model. Relating the enzyme and fermentation models with a common approach makes it possible to directly extend the extensive theory of enzyme systems to the more complex fermentation process.