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"Half-lives are estimated as the time required for the loss of 50% of the initial activity during operation, assuming an unimolecular decay kinetics.

"Half-lives are estimated as the time required for the loss of 50% of the initial activity during operation, assuming an unimolecular decay kinetics.

2. The variable is the loading of the enzyme or different-size enzyme particles.

3. An enzymatic membrane is inserted between two reservoirs with different substrate concentrations.

To understand the effects and the control of the live cells, kinetics studies of the enzyme-catalyzed reaction, namely, the functioning unit of metabolic machinery, are necessary as starters. Such studies are usually performed in vitro. The extrapolations of the results of in vitro studies to the in vivo situations are sometimes useful, yet are limited in most cases. Structural factors bearing on the relation of the organization of the cell to enzymatic action should be considered if such extrapolations are to be on the safe side. Most enzymes are quite soluble in water. The in vitro studies on such enzymes can be considered to be in a homogeneous catalytic environment. However, within cells, enzymes are not totally free to move, especially the so-called membrane-bound enzymes. Due to such considerations, sometimes the actual effect of an enzyme-catalyzed reaction in a cell cannot be explained by the chemical reaction studied in vitro alone. The coupling of mass-transfer effect to chemical reaction is necessary to explain the global effect of a reaction on a system with heterogeneous nature. While the advantages of immobilized enzymes in food manufacturing (eg, high fructose syrup production) are evident from an economical point of view, the research on immobilized enzymes will also help the food manufacturers in general, through better understanding of the regulatory machinery in the cells.

A typical microbial growth curve involves a lag phase, an exponential phase, a stationary phase, and a decline phase. In most industrial microbial processes, cells or products accumulated by cells are harvested in the late exponential phase or early stationary phase. During the exponential phase of growth for unicellular organisms undergoing binary fission, the growth rate dx/dt can be expressed in terms of a growth rate constant (or specific growth rate) (and the cell concentration x [equation 11]).

Most microorganisms, if grown properly, follow this first-order, exponential growth. There are exceptions. A linear growth model, namely, dx/dt = constant, was found in some hydrocarbon cultures where limitation is caused by the rate of diffusion of substrate from the surface of oil droplets that have essentially a constant surface area during cultivation. The growth of yeast and filamentous or ganisms do not follow the first-order kinetics of growth in some cases. In these organisms, growth occurs from the tip, but nutrients diffuse throughout the cellular tissue; sometimes fractional reaction orders are obtained in kinetic analyses.

The specific growth rate (i is essentially a first-order reaction rate constant with a dimension of reciprocal of time, that is, h-1. The constancy of ¡i is limited. It is a constant under specified conditions of temperature, pH, type of substrate, substrate concentration, and so on. When different ¡x values are obtained by changing substrate concentration in the experiments, an expression for ju, the so-called Mo-nod equation, is obtained (equation 11).

The form of this equation is exactly the same as that of the Michaelis-Menten equation for enzyme-catalyzed reactions. However, this equation is entirely empirical, whereas that of Michaelis-Menten is mechanistic. This equation usually fits experimental data when cell growth is limited only by a single limiting substrate in a pure culture situation. When there are inhibitors or mixed substrates in the medium, a modified Monod equation can be used to fit the data.

In addition to cell tissue, there are three types of product that can be produced by industrial fermentation processes. These are primary metabolites (eg, monosodium glutamate and food acidulants such as citric acid), secondary metabolites (eg, antibiotics), and enzymes. For primary metabolites and some enzymes, the rate of product formation is proportional to the rate of cell growth. The following equation has been proposed for organic acid fermentations (15):

The production model expressed by equation 14 is called a growth-associated model. The kinetics for the production of secondary metabolites and enzymes (when gratuitous inducer is used) are such that they are accumulated or induced after the cells have advanced into late exponential phase or early stationary phase of growth where cell growth rate has started to decline. A nongrowth-associated model is appropriate in these cases:

The following growth-associated model has been proposed for the kinetics of enzyme induction (16):

f where M0 is the initial amount of unconverted starch; Mf, the final amount of unconverted starch; and M„ the amount of unconverted starch at time t. Thus the rate of the disappearance of native (unconverted) starch during a process can be written in the following form:

xj dt

where the term kE on the right-hand side of equation 16 represents the monomolecular (first-order) decay of the enzyme synthesized in vivo. A more complete model on the kinetics of enzyme induction includes the effects of inducer and repressor concentrations on the kinetics, and the mechanism of protein synthesis can be used as basis for the construction of the model.

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