herent dissociation constant of the product from the enzyme, the concentration of enzyme in the matrix, the diffusion coefficient of the substrate, and the apparent Michaelis constant. The derivation of the equation for internal mass transfer limitations in spherical particles assumes that the enzyme is uniformly distributed throughout the particle. Recent evidence indicates that this may not always be the case. It should be noted that the internal mass transfer limitations on the reaction rate are most deleterious at low substrate concentrations. The above equation would seem to indicate that with increasing internal mass transfer limitations the enzyme that has been immobilized is used less and less effectively; that is, to achieve a twofold increase in reaction rate one must increase the enzyme concentration at least fourfold. An effectiveness factor can be derived for the various circumstances limiting enzyme catalysis in each of the forms in which enzymes are used analytically. This is basically the rate observed in the presence of the ratelimiting factor relative to the rate of reaction in the absence of the limitation. The enzyme-loading factor, a, is of fundamental importance in both the response of the analytical system to substrate and the effective use of
the enzyme. An increase in the loading factor results in an increase in the analytical response but may result in a decrease in the efficiency of enzyme use. An increase in the loading factor might also result in a desirable increase in the amount of time the enzyme preparation can be used. It is not uncommon to set the experimental conditions to maximize the loading factor and accept any consequences. Clearly there are commercial implications of this trade-off that will have a significant impact on the design of immobilized-enzyme instrumentation. Effect on stability. One of the advantages cited when immobilized enzymes are discussed is an increase in stability. However, we have observed, as have others, that this so-called advantage is ambiguous. There are a number of reasons for these equivocal findings. First, there are several types of stability that can be measured. Storage stability is simply the ability of the enzyme to retain its activity under a specified set of storage conditions. Thermal stability is a measure of the ability of the enzyme-matrix system to withstand elevations in temperature, frequently in excess of those that would denature the native protein. In principle, an enzyme system capable of withstanding autoclaving and other types of sterilization could
be developed. Finally, operational stability reflects the ability of the enzyme system to function in the analysis system. It is a function not only of the enzyme, but also the carrier durability, the inhibitor concentrations in the analysis stream, the pH, and other physical characteristics of the analyte solution. Unfortunately, the storage stability is most frequently reported, and comparison of the various types of stability is difficult. A second consideration is the manner in which the stability of the enzyme is measured. As noted above, diffusion can have a significant effect on the observed enzyme kinetics. It can also have a substantial influence on the stability measurements. When the enzyme loading is high and the system is diffusion controlled, the rate of reaction is independent of the enzyme concentration. Thus, a significant amount of enzyme could be inactivated before the diffusional limitations were removed and a decrease in "activity" was measured. Although this is an operational increase in stability, no inherent stabilization of the enzyme has occurred. In economic terms, there may have been no cost savings. Inexplicably, systematic study of the experimental factors leading to increased, controlled stabilization has
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