Time Dependent Differential Yield as a Scale-up Parameter in Enzyme and Fermentation Reactors

The yield function, for an enzyme-substrate kinetic model of the system, is investigated. Considering Y to be a function of the substrate concentration S, its value as S --> O(+) is investigated.In the "pseudo-steady-state domain," this differential yield function is shown to be bounded above and below by yield functions that are obtained by using the Michaelis-Menten and Briggs-Haldane functions to relate the enzyme-substrate concentration C to S. It is also shown that the yield constant, which is commonly used for enzyme and fermentation systems, is an integral average of the differential yield function. The average yield constant can be used to show consistency of data by relating the area above and below the average yield line when the yield function is plotted against the substrate concentration. The role of the dimensionless parameter, epsilon = k(m)/E*, on the asymptotic yield, is also investigated. The mathematical results are demonstrated on experimental data for a horseradish-peroxidase enzyme system and a gluconic acid fermentation process.