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enzyme conformation, (2) steric effects, (3) microenviron-mental effects, and (4) external and internal diffusional effects. Theoretically, the change in enzyme conformation would cause a change in innate activity of the enzyme, that is, the Km value. Factors 2 to 4 are ineffective in modifying the true catalytic reaction per se, but nevertheless, obscure the kinetics of the reaction. If enzymes are bound to non-porous systems, the reaction rate can be controlled by one of the following steps: (2) diffusion of substrate from the bulk solution to the surface of the immobilized enzyme, (2) enzymatic reaction at the surface, or (3) diffusion of the reaction products back into the bulk solution. Assuming a linear gradient of substrate concentration across a Nernst diffusion layer, a near-stagnant layer of fluid around the immobilized enzyme particle surface, it has been suggested that the approximate behavior of such systems can be represented by:

dt SB+ Km+ i^jAx where Ns is the molar flux of substrate at the boundary layer, VM is the maximum activity of the enzyme, SB is the bulk concentration of substrate, Ax is the thickness of the Nernst layer, and Ds is the substrate diffusivity (12).

The values of KM and VM from a Lineweaver-Burk plot (1/v vs 1/s) of data obtained using immobilized enzymes are usually dependent on flow conditions and particle size (or membrane thickness) of the immobilized enzyme used. If existing mass-transfer resistances are neglected in immobilized enzymes experiments, the apparent .K^ obtained is usually higher in value than that of the free enzyme counterpart, unless the enzyme carriers have high affinity for the substrate. Because the thickness of the diffusion layer is inversely proportional to agitation rate, the apparent Km value can be expected to decrease with increased substrate flow over the solid catalysts, provided bulk diffusional resistance is the principal factor affecting the kinetics of the process. As indicated before, an apparent Km value close to the true KM of the immobilized enzyme can be obtained by experiments where possible bulk diffusional effect is limited by using a high substrate-to-enzyme concentration ratio and by maintaining high substrate flow over the catalyst surface, and internal diffusional effect is minimized by using fine particles or thin membranes. True KM values of immobilized enzymes are important parameters for the purpose of reactor scale-up and control for commercial purposes. On the other hand, because apparent KM is dependent on mass-transfer effects and thus on reactor size, throughput and configuration, it is of little use in this connection. Thus the determination of true Km is an important task. Basically there are three groups of experimental methods for evaluating the intrinsic kinetic parameters, such as KM and VM, in heterogeneous catalysis. These are as follows (13,14):

1. A certain type of immobilized-enzyme reactor configuration of a single size and a single loading of enzymes are used; the variable is substrate-surface concentration.

Table 2. Operational Stability of Some Immobilized Enzymes

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