S

where the reaction is going at maximum velocity and is independent of substrate concentration (a zero-order reaction). In measuring the total activity of an enzyme preparation, the substrate concentration used should be large enough to saturate all the active sites of the enzyme molecules during the course of measurements (to follow the zero-order kinetics); whereas if a standard enzyme preparation is used to titrate the concentration of a substrate, substrate concentration should be diluted to make sure that first-order kinetic is followed (v = kS, velocity is a measure of substrate concentration).

Many food materials are composed of live cells (fresh food), many others are made by using the activities of live cells (such as fermentation processes) or by using enzymes (such as glucose from starch), and all food materials are affected by foreign live cells (food spoilage). From a food processing application point of view, two types of enzyme are currently important. These are hydrolytic enzymes (no cofactor required) and oxidoreductases (cofactors required).

The kinetic behavior of an enzyme system is not unique to the system. Other chemical kinetic analyses have found similar phenomena. For example, the concept of station-arity or a steady state is common in enzyme kinetics, in kinetic studies involving free-radical intermediates, and in those involving a stationary activated complex concentration.

The first satisfactory mathematical analysis of the diphasic activity curve was carried out by Michaelis and Menten in 1913. They assumed that the intermediate complex ES was reversibly formed according to the mass action law:

and that the rate of breakdown of ES to form product P was small in relation to the rate of establishment of the equilibrium described by k1 and k2. The constant that they derived is, therefore, the dissociation constant of ES complex. Twelve years later, the concept of steady-state approximation to enzyme kinetics was introduced (1). It was believed that the catalyzed reaction may deplete ES complex at a substantial rate and that the Michaelis constant Km measured experimentally from kinetic curves is in fact (k2 + k3)/kl, which can be derived from the steady-state solution (equation 10) to the rate equations for mechanisms describable by equation 12. In addition to the steady-state assumption, it should be noted that equation 10 has been derived for negligible P, the product concentration. In other words, in using equation 10, initial rate of reaction should be used. A practical definition of the Mi-

chaelis constant is that it is the substrate concentration at half maximum velocity. Under carefully defined conditions of temperature, pH, ionic strength of buffer, and so on, for an enzyme-substrate pair, KM is a constant. It approximates the affinity of an enzyme for its substrate. In general, the affinities of respiratory enzymes (oxidoreduc-tases) for their substrates are higher than those of hydrolytic enzymes for their substrates. As shown in Table 1, the Km values for respiratory enzymes are lower than that of hydrolases. There are a few reports on the KM values of immobilized enzymes (3,4). Because of the possible complications of external and internal diffusional resistance, the true values of KM for immobilized enzymes are difficult to obtain. Experimentally, a high substrate-to-enzyme concentration ratio (zero-order region of Michaelis-Menten kinetics) in a batch reactor with high velocity of flow (high agitation rate in stirred reactor) would minimize the external mass-transfer effect; the use of ultrafine particles (or ultrathin membrane) as enzyme carriers would minimize the internal mass-transfer effect.

The activities of enzymes are affected by temperature and pH. Because of the protein nature of an enzyme, thermal denaturation of the enzyme protein is evident in the high end of the temperature range. Generally speaking, up to perhaps 45°C, the predominant effect will be an increase in reaction rate and have a temperature dependence of the Arrhenius form. Above 45°C, the opposing factor, namely thermal denaturation, becomes increasingly important. Around 55°C, rapid denaturation usually destroys the catalytic function of the enzyme protein.

The effect of pH, as that of temperature, on enzymatic activity is typified by a bell-shaped curve with a relatively narrow plateau. The plateau is usually called the optimal pH, or optimal temperature point. These optimal points are to be maintained if maximum enzymatic activities are desired. After an enzyme is immobilized on a carrier, the pH and temperature optimal points may be different from that of the free-enzyme counterpart. In addition to pH and temperature stabilities, operational stability and storage stability of immobilized enzymes are also important from practical points of view. Storage stability of 50 immobilized enzyme systems were reviewed (5). Of these, 30 exhibited greater storage stability, 8 exhibited less than the freeenzyme counterparts. Operational stability of immobilized enzymes depends on the enzyme itself, method of immobilization, operational conditions, and so on. Table 2 illustrates the half-life of various immobilized-enzyme systems, which range from a few days to more than a year.

The kinetic behavior of enzymes may be modified by the following factors when they are immobilized: (1) change in

Table 1. Michaelis-Menten Constants KM for Various Enzymes

Enzyme

Substrate

Km<

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