Michaelis immobilized enzyme

Apparent reaction rates with immobilized enzyme particles also decrease due to the mass transfer resistance of reactants (substrates). The Thiele modulus of spherical particles of radius R for the Michaelis-Menten type reactions is given as... 

Consider an idealized simple case of a Michaelis-Menten type bioreaction taking place in a vertical cylindrical packed-bed bioreactor containing immobilized enzyme particles. The effects of mass transfer within and outside the enzyme particles are assumed to be negligible. The reaction rate per dilfcrential packed height (m) and per unit horizontal cross-sectional area of the bed (m ) is given as (cf. Equation 3.28) ... 

The membrane containing the immobilized enzyme is handled by partitioning it into a specified number of volume elements so that Equations 20.23 and 20.24 are valid in this model. While the concentration of each species may vary from element to element, the steady-state assumption (d[ES]/dt = 0) may be invoked independently for each volume element. This results in the definition of the Michaelis-Menton constant, KM ... 

During the enzymatic reaction of an immobilized enzyme, the rate of substrate transfer is equal to that of substrate consumption. Therefore, if the enzyme reaction can be described by the Michaelis-Menten equation,... 

When the rate of diffusion is very slow relative to the rate of reaction, all substrate will be consumed in the thin layer near the exterior surface of the spherical particle. Derive the equation for the effectiveness of an immobilized enzyme for this diffusion limited case by employing the same assumptions as for the distributed model. The rate of substrate consumption can be expressed by the Michaelis-Menten equation. 

Mass transfer can alter the observed kinetic parameter of enzyme reactions. Hints of this are provided by non-linear Lineweaver-Burk plots (or other linearization methods), non-linear Arrhenius plots, or differing Ku values for native and immobilized enzymes. Different expressions have been developed for the description of apparent Michaelis constants under the influence of external mass transfer limitations by Homby (1968) [Eq. (5.69)], Kobayashi (1971), [Eq. (5.70)], and Schuler (1972) [Eq. (5.71)]. 

Enzyme immobilization has been reported to improve the thermal stability of enzymes (1,2) and may also affect binding of substrates and inhibitors to the enzyme, thereby affecting the Michaelis constant and enzyme inhibition. Several previous studies have considered the advantages of immobilized enzymes with soluble substrates, and a few studies have also investigated the properties of immobilized enzymes with insoluble substrates. The main objective of the present work was to establish the effect of immobilization on the thermal stability of these enzymes, so that they may be used at elevated temperatures without significant activity loss. The immobilization conditions were varied, and their effect on the performance of the immobilized enzymes was analyzed with reference to their physiochemical and structural properties. 

Another enzyme that was studied extensively in microreactors to determine kinetic parameters is the model enzyme alkaline phosphatase. Many reports have appeared that differ mainly on the types of enzyme immobilization, such as on glass [413], PDMS [393], beads [414] and in hydrogels [415]. Kerby et al. [414], for example, evaluated the difference between mass-transfer effects and reduced effidendes of the immobilized enzyme in a packed bead glass microreactor. In the absence of mass-transfer resistance, the Michaelis-Menten kinetic parameters were shown to be flow-independent and could be appropriately predicted using low substrate conversion data. 

Acetylcholineesterase, urease, glucose oxidase and butyryl chloinesterase. Immobilized enzyme on to the sensor chip by corsslinking with glutaraldehyde and BSA. Conductivity changes, produced by the enzyme-catalyzed hydrolysis of ACh were measured for the analysis. Detection limits for ACh was 0.07 mM with corresponding sensitivity of 5.6 0.2 pS/mM. The device could be also used for apparent Michaelis constant determination. [85]... 

The characteristics of immobilized enzymes are likely to be somewhat different than those of the original enzyme. The pH optimum can be shifted this depends on the surface charge of the carrier (Figure 10-24). Another property that can be changed is the Michaelis constant, Km. This value can become either larger or smaller. Immobilizing may result in increased thermal stability (Figure 10-25), but in some cases the thermal stability is actually decreased. 

The Michaelis-Menten equation and other similar nonhnear expressions characterize immobilized enzyme kinetics. Therefore, for a spherical porous carrier particle with enzyme molecules immobilized on its external as well as internal surfaces, material balance of the substrate will result in the following ... 

The increase in apparent Km values observed following the immobilization of enzymes is also readily explained by considering local effects at the carrier surface. Recalling the Michaelis-Menten equation (v = Vmax[S]/ m+ [S] ), and its derivation (Chapter 2), we know that for soluble enzymes, Km is independent of enzyme concentration and is a constant under a given set of conditions. Immobilized enzymes suspended in an aqueous medium have an unstirred solvent layer surrounding them, called the Nernst or diffusion layer. Substrates and products must diffuse across this layer, and, as a result, a concentration gradient is established for both substrates and products, as shown in Figure 4.7. 

An equation equivalent to the Michaelis-Menten equation has been derived for immobilized enzymes in packed-bed reactor systems, and is given in Eq. 4.24 ... 

Immobilization of the enzyme may also have direct effects on its catalytic ability in that conformational changes may lead to partial inactivation which affects the Michaelis-Menten parameters. Allosteric enzymes may, moreover, loose their ability to undergo allosteric activation. Steric restrictions may also be responsible for lower activities of immobilized enzymes by preventing or hindering the access of the substrate or effectors. On the other hand the stability or activity of enzymes on a solid phase is often better than in the fluid phase, probably due to the local high concentration of enzyme. Certain solid phases may, however, directly inactivate the enzyme, such as polystyrene for horseradish POase (Berkowitz and Webert, 1981). 

As far as Michaelis-Menten enzymes are concerned, i vs diagrams have been produced109 for various immobilized enzyme configurations. They can, therefore, be used provided that the geometry of the segregated regions is defined and that external resistances are taken into account. 

The kinetic investigations so far carried out on immobilized enzymes have indeed provided evidence for various degrees of diffusion control. Enzymes that obey the Michaelis-Menten equation (equation (10.25)) when they are in free solution generally obey it to a good approximation when they are immobilized, but the Michaelis constant is usually significantly different. The rate equation for the immobilized system is... 

In section 9.5.3 the arbitrary kinetics for the slab geometry was considered. In this section we will use Michaelis-Menten kinetics for describing immobilized enzymes and spherical particles following the nomenclature and approaches frequently encounted in the literature on bioreaction engineering for instance in the treatment provided by J.E. Bailey and D.F.011is presented here with the details of the derivation. 

We are presuming that the intrinsic reaction kinetics of the immobilized enzyme catalyzed reaction is of the Michaelis-Menten type, therefore eq. (9.231) takes the 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).

For immobilized enzymes when only external mass transfer is essential, eq. (9.269) should be modified to account for the Michaelis-Menten kinetics... 

Fig. 4.13 Global effectiveness factor (mean integral value) of a membrane immobilized enzyme with Michaelis-Menten kinetics as a function of bulk substrate concentration and Thiele modulus...

Figure 20.2 Effectiveness factor vs. the observable modulus (f> for immobilized enzyme catalysts with Michaelis-Menten intrinsic kinetics (/ = [i4]j,/AfM) (Bailey and Ollis, 1986)...

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