The yield equations in the modeling and control of bioprocesses.

Two basic questions in bioprocess modeling are how many rate equations must be specified and which processes (substrate uptake, product formation, etc.) they should describe. The number of rate equations is constrained by the yield equations, which represent the balances of reducing power, energy in the form of ATP, and the various elements involved in microbial metabolism. These balances are derived from a simplified picture that divides metabolism into catabolic, anabolic, respiratory, and product formation pathways. The linear growth equation for aerobic metabolism and the Ludeking-Piret equation for product formation by fermentation are derived from these balances, and the yield coefficients are related to the metabolic parameters, Y(ATP) (P/O), etc. The use of oxygen for purposes other than respiration is included in the analysis and extends the idea of a constant "yield on available electrons" to very reduced substrates. These balances specify the number of degrees of freedom, i.e., the number of pieces of information required to complete the description of the system. This information may be in the form of measurements, knowledge of the biochemical pathways, or rate equations. The number of rate measurements available (usually two, the consumption rates of O(2) and CO(2)) versus the number needed defines the state estimation problem in bioprocess control. Rate equations usually specify the biomass growth rate, but it may be preferable to specify the specific consumption rate of the limiting nutrient. (c) 1993 John Wiley & Sons, Inc.