Effectiveness factor, immobilized enzymes

An immobilized enzyme-carrier complex is a special case that can employ the methodology developed for evaluation of a heterogeneous cat ytic system. The enzyme complex also has external diffusional effects, pore diffusional effects, and an effectiveness factor. When carried out in aqueous solutions, heat transfer is usually good, and it is safe to assume that isothermal conditions prevail for an immobihzed enzyme complex. 

Immobilization can give rise to mass transfer limitations that do not occur for freely suspended enzymes in their native state. As a formality, these limitations can be incorporated into an effectiveness factor ... 

Quantitative analytical treatments of the effects of mass transfer and reaction within a porous structure were apparently first carried out by Thiele (20) in the United States, Dam-kohler (21) in Germany, and Zeldovitch (22) in Russia, all working independently and reporting their results between 1937 and 1939. Since these early publications, a number of different research groups have extended and further developed the analysis. Of particular note are the efforts of Wheeler (23-24), Weisz (25-28), Wicke (29-32), and Aris (33-36). In recent years, several individuals have also extended the treatment to include enzymes immobilized in porous media or within permselective membranes. The important consequence of these analyses is the development of a technique that can be used to analyze quantitatively the factors that determine the effectiveness with which the surface area of a porous catalyst is used. For this purpose we define an effectiveness factor rj for a catalyst particle as... 

Considerable progress has been made within the last decade in elucidating the effects of the microenvironment (such as electric charge, dielectric constant and lipophilic or hydrophilic nature) and of external and internal diffusion on the kinetics of immobilized enzymes (7). Taking these factors into consideration, quantitative expressions have been derived for the kinetic behavior of relatively simple enzyme systems. In all of these derivations the immobilized enzymes were treated as simple heterogeneous catalysts. 

In vitro enzymatic polymerizations have the potential for processes that are more regio-selective and stereoselective, proceed under more moderate conditions, and are more benign toward the environment than the traditional chemical processes. However, little of this potential has been realized. A major problem is that the reaction rates are slow compared to non-enzymatic processes. Enzymatic polymerizations are limited to moderate temperatures (often no higher than 50-75°C) because enzymes are denaturated and deactivated at higher temperatures. Also, the effective concentrations of enzymes in many systems are low because the enzymes are not soluble. Research efforts to address these factors include enzyme immobilization to increase enzyme stability and activity, solubilization of enzymes by association with a surfactant or covalent bonding with an appropriate compound, and genetic engineering of enzymes to tailor their catalytic activity to specific applications. 

This study employed conventional diffusion-reaction theory, showing that with diffusion-limited reactions the internal effectiveness factor of a heterogeneous catalyst is inversely related to the Thiele modulus. Using a standard definition of the Thiele modulus [100], the observed reaction rate of an immobilized-enzyme reaction will vary with the square root of the immobilized-enzyme concentration in a diffusion-limited system. In this case, a plot of the reaction rate versus the enzyme loading in the catalyst formulation will be nonlinear. 

How small should the diameter of immobilized enzyme beads be to achieve an effectiveness factor larger than 0.9 under the same reaction conditions as in the case (2) ... 

To measure the extent which the reaction rate is lowered because of resistance to mass transfer, we can define the effectiveness factor of an immobilized enzyme, 17, as... 

After immobilizing this enzyme on the surface of insoluble matrix by physical adsorption, it was found that the Ka% value was increased to 0.08 mol/L whereas the rfl ax value stayed the same as rmax. What is the effectiveness factor of the immobilized enzyme when the substrate concentration is 1 mol/L ... 

An enzyme which hydrolyzes the cellobiose to glucose, /3-glucosidase is immobilized in a sodium alginate gel sphere (2.5 mm in diameter). Assume that the zero-order reaction occurs at every point within the sphere with k0 = 0.0795 mol/sm3, and cellobiose moves through the sphere by molecular diffusion with Ds = 0.6 x 10 5 cm2 /s (cellobiose in gel). Calculate the effectiveness factor of the immobilized enzyme when the cellobiose concentration in bulk solution is 10 mol/m3. 

Figure 5.11 Influence of radius on the effectiveness factor of a spherical porous immobilized enzyme particle (enzyme contents [mg cm-3] are listed besides curves) (specific activity 100 IU, Defr= 4 x 10"8 m2 s" [S)/KM = 10) (Regan, 1974).

Kinetics of Immobilized Enzymes. Another major factor in the performance of immobilized enzymes is the effect of the matrix on mass transport of substrates and products. Hindered access to the active site of an immobilized enzyme can affect the kinetic parameters in several ways. The effective concentration of substrates and products is also affected by the chemistry of the matrix especially with regard to the respective partition coefficients between the bulk solution and the matrix. In order to understand the effects of immobilization upon the rate of an enzyme-catalyzed reaction one must first consider the relationship between the velocity of an enzyme-catalyzed reaction and the... 

In many cases the influence of particle mass transfer on the reaction rate can be neglected (value of Thiele modulus approaches zero or the enzyme is immobilized exclusively on the particle surface). Then, value of the effectiveness factor is unity and the solution of Eqs. (1) - (3) is substantially simpler. 

There are two basic procedures for enzyme immobilization by adsorption. Both share the same first steps preparation of the immobilization matrices (discussed above) and the aqueous enzyme solution. Typically, the aqueous solution is fairly concentrated in enzyme (approximately 5 to 40 mg/ml) and buffered (approximately 10 mM) to the optimal pH value of the enzyme. In addition, necessary co-factors, such as NAD(P)+ or NAD(P)H, should be included. Also, the presence of albumin or high-molecular-weight PEG at concentrations of 2 mg per g of matrix have been shown effective in protecting enzymes during the water removal stage of immobi-lization. °° Furthermore, the presence of sorbitol can increase activity and reduce side reactions, such as hydrolysis. -It is recommended that the aqueous solutions be centrifuged prior to use to remove any nonsolubilized matter. 

If the internal mass transfer resistance is negligible, what is the concentration of the substrate at the surface of the particle What is the effectiveness factor for this immobilized enzyme ... 

This definition recognizes that immobilization (e.g., at cellular membranes) is the native state for some enzymes. Although interesting mathematics are possible, effectiveness factors are measured experimentally, as was the case for the solid-catalyzed gas phase reactions discussed in Chapter 10. Effectiveness factors greater than 1 are possible. 

Since (ds dr)T l depends only on the Thiele modulus and saturation parameter, the catalyst effectiveness factor for immobilized enzyme catalysis also depends only on these two parameters. 

In the general case of immobilized enzymes not only the internal diffusion addressed above, but also diffusion through the film should be taken into account. Similarly to heterogeneous catalysis the catalyst effectiveness factor for slab geometry and low substrate concentrations (first order kinetics) is decribed by eq. (9.173) in a somewhat different form... 

Figure 9.16. Effectiveness factor for immobilized enzyme catalysts with Michaelis-Menten kinetics (J. E. Bailey, D.F. Ollis, Biochemical engineering fundamentals, McGraw-Hill, 1986).

Enzymes are an attractive tool in asymmetric catalysis and efficiently complement traditional chemical methods [32,33]. The use of biocatalysts makes it possible to carry out chemical transformations without the need for laborious protection and deprotection steps [34]. Immobilized enzymes are preferred over free enzymes in solution, due to the possibility of repeated use, higher resistance to denaturing effects, and easy separation. The use of a structured support material could be an interesting alternative for conventional particulate enzyme carriers. When optimizing the use of immobilized enzymes, the immobilization method chosen is a very important factor to consider [35]. In this study, a reaction in an organic medium is considered most enzymes do not readily dissolve in organic media, and the enzyme will not detach from the support. This makes physical adsorption a very suitable technique to prepare a biocatalyst for use in an organic medium... 

Intraparticle diffusion can have a significant effect on the kinetic behavior of enzymes immobilized on solid carriers or entrapped in gels. In their basic analysis of this problem. Moo-Young and Kobayashi (1972) derived a general modulus and effectiveness factor. The results also predicted possible multiple steady-states as well as unstable situations for certain systems. While these results are very interesting it should be remembered that they are primarily mathematical and await extensive experimental support data. 

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