External diffusional restrictions

1 Enzyme Kinetics Under Externai Diffusional Restrictions Effectiveness Factor 

To analyze this case, let us assume that the enzyme is homogeneously distributed over the surface of an impervious support as shown in Fig. 4.6. Substrate conversion into product occurs in three consecutive steps substrate transportation from the bulk medium to the surface of the biocatalyst, enzymatic conversion into product at that surface and product transportation back from the surface to the bulk medium. As shown, substrate and product profiles will develop across the stagnant layer as long as substrate and or product diffusion limits the catalytic potential of the enzyme. Any of these steps can be rate-limiting. 

Substrate transportation through the stagnant layer occurs by molecular diffusion, so  

Two limit situations can be envisaged. One (Case I) in which r is solely determined by substrate transport rate (diffusion limited) and another (case II) in which r is solely determined by the catalytic potential of the enzyme (kinetically limited). In Case I, reaction rate is so fast with respect to substrate transport rate that substrate profile is steep, ss being negligible with respect to so, while in Case II substrate transport rate across the stagnant layer is fast enough with respect to reaction rate so that no substrate profile develops and ss is equal to so. Eq. 4.10 and 4.11 become Eqs. 4.12 and 4.13 respectively  

Ifom Eqs. 4.9 to 4.11, Eq. 4.14 is obtained that represents the enzyme behavior under EDR. 

---

A reduced reaction rate may result from external diffusional restrictions on the surface of carrier materials. In stirred tanks external diffusion plays a minor role as long as the reaction liquid is stirred sufficiently. Further, partition effects can lead to different solubilities inside and outside the carriers. Partition has to be taken into account when ionic or adsorptive forces of low concentrated solutes interact with carrier materials [81 - 83]. The most crucial effects are observed in porous particles due to internal or porous diffusion as outlined below. 

Interplay Between External Diffusional Restrictions and Inhibition... 

As an example, the case of a batch reactor with Michaelis-Menten kinetics will be analyzed under enzyme inactivation and external diffusional restrictions (EDR). Eq. 5.31 can be rewritten as ... 

Fig. 4.6 Schematic representation of external (EDR) and internal (IDR) diffusional restrictions...

Combined Effect of External and Internal Diffusional Restrictions... 

Ishikawa H, Tanaka T, Kuro K et al. (1987) Evaluation of tme kinetic parameters for reversible immobihzed enzyme reactions. Biotechnol Bioeng 29 924-933 Jeison D, Ruiz G, Acevedo F et al. (2003) Simulation of the effect of intrinsic reaction kinetics and particle size on the behavior of immobihzed enzymes under internal diffusional restrictions and steady state operation. Proc Biochem 39(3) 393-399 Katchalski-Katzir E, Kraemer DM (2000) Eupergit C, a carrier for immobDization of enzymes of industrial potential. J Mol Catal B Enzym 10 157-176 Kheirolomoom A, Khorasheh F, Fazehnia H (2002) Influence of external mass transfer limitation on apparent kinetic parameters of peniciUin G acylase immobihzed on nonporous ultrafine silica particles. J Biosci Bioeng 93 125-129... 

Mass transfer limitations can be relevant in heterogeneous biocatalysis. If the enzyme is immobilized in the surface or inside a solid matrix, external (EDR) or internal (IDR) diffusional restrictions may be significant and have to be considered for proper bioreactor design. As shown in Fig. 3.1, this effect can be conveniently incorporated into the model that describes enzyme reactor operation in terms of the effectiveness factor, defined as the ratio between the effective (or observed) and inherent (in the absence of diffusional restrictions) reaction rates. Expressions for the effectiveness factor (rj), in the case of EDR, and the global effectiveness factor (t ) for different particle geometries, in the case of IDR, were developed in sections 4.4.1 and 4.4.2 (see Eqs. 4.39-4.42,4.53,4.54,4.71 and 4.72). Such functions can be generically written as ... 

---