Fundamentals of Biochemical Engineering, Part 1 - Bailey, J., Ollis, D. 1989

Application of Enzyme-Catalyzed Reactions
Kinetics of Reactions Catalyzed by Immobilized Enzymes

To design reactors with immobilized enzyme catalysts, a thorough understanding of the kinetic properties of immobilized Enzymes is essential. The observed catalytic properties of an individual immobilized enzyme catalyst particle, or of a Reactor where enzymes are retained by a semipermeable membrane, are governed by the interplay of two coupled processes: substrate transport and the catalytic enzymatic reaction. This section focuses On the Relationship between mass transfer and the catalytic reaction, and how this interaction affects the catalytic activity of an individual immobilized enzyme particle.

We begin our examination of how mass transfer and chemical processes interact to determine the overall activity, inactivation, and other parameters of an immobilized enzyme catalyst by referring to the diagram in Fig. 4.16. This figure illustrates a cross-section of a thin layer of immobilized enzyme in contact on both sides with a substrate solution. Far from the catalyst, the Substrate Concentration and other parameters, such as pH, maintain the same values as those in the bulk reaction medium—parameters that are readily determined using standard analytical chemistry Methods.

Because the substrate is transformed within the immobilized enzyme and the reaction product is formed concurrently, concentration gradients arise between the bulk solution and the active sites of the immobilized enzyme. Specifically, the substrate must be transported from the solution to the outer surface of the catalyst. In the absence of agitation, this process relies on molecular diffusion. Typically, The rate of substrate transport to the catalyst surface is enhanced through stirring or by establishing a fluid flow of the solution. If the active enzyme resides exclusively On the surface of the immobilized particle, or if the substrate cannot penetrate the interior of the catalyst particle, only this external mass transfer needs to be considered. Frequently, however, the enzyme is distributed uniformly throughout a substrate-permeable matrix. In such cases, catalytic activity is largely concentrated and distributed within the catalyst pellet, meaning the substrate must diffuse into the pellet to reach an Active Site where the reaction takes place. The reaction products must then travel the reverse path. Under these circumstances, both external mass transfer and intraparticle diffusion processes must be taken into account.

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FIG. 4.16. Schematic representation of mass transfer and chemical transformations in a bilateral immobilized enzyme layer. The phenomena indicated at the top of the figure give rise to the specific concentration profiles of the substrate and reaction product shown in the middle. These profiles can be quantified using the parameters listed at the bottom of the diagram.

As illustrated in Fig. 4.16, the reaction within the immobilized enzyme layer proceeds at a rate determined by the local concentrations within that layer. Due to the aforementioned concentration gradients, local reaction rates vary depending on the spatial Location OF THE reaction site, while the overall rate of substrate conversion represents the sum of all local transformation rates throughout the permeable catalyst. Under steady-state conditions, this overall rate equals the rate of substrate transport to the catalyst. Clearly, the rate of the overall process generally depends on both the transport rate and the intrinsic rate of the catalytic reaction.

Deriving the mathematical expressions to describe these coupled processes, along with the criteria used to evaluate their relative significance, represents a major milestone in chemical engineering. These interconnected processes play a critical role in Reactions Catalyzed by immobilized enzymes and Cells; yet, their impact has often been overlooked in both theoretical research and the practical development of immobilized biocatalysts. Therefore, we will examine the fundamental principles and methods of mathematical modeling for immobilized enzyme systems, as well as its outcomes, in considerable detail. This topic is covered even more comprehensively in chemical engineering textbooks and specialized monographs.