Michaelis-Menten immobilized enzymes

The initial condition for [SE] assumes that the enzyme was charged to the reactor in pristine condition. It makes no difference whether the enzyme is free or immobilized provided the reaction follows Michaelis-Menten kinetics. 

These problems were overcome by immobilizing the enzyme. Since the usual methods for immobilization of laccase did not work, we adopted a new method, details of which will be described elsewhere (29). Reasonable measurements were possible with this technique. Typical patterns of laccase activity could be monitored via the changes of absorbance of 2,6 DMP and syringaldazine. When the reaction took place in organic solvents, the absorption spectra of the products were similar to those obtained for the same reaction in buffer. Furthermore, the catalytic action of the T. versicolor laccase followed Michaelis-Menten-kinetics in most of the organic solvents which were tested (see Table II for specific examples). 

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) ... 

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. 

An enzyme is immobilized on solid surface. Assume that the external mass-transfer resistance for substrate is not negligible and that the Michaelis-Menten equation describes the intrinsic kinetics of enzyme reaction. 

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. 

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 ... 

Unfortunately, most enzymes do not obey simple Michaelis-Menten kinetics. Substrate and product inhibition, presence of more than one substrate and product, or coupled enzyme reactions in multi-enzyme systems require much more complicated rate equations. Gaseous or solid substrates or enzymes bound in immobilized cells need additional transport barriers to be taken into consideration. Instead of porous spherical particles, other geometries of catalyst particles can be apphed in stirred tanks, plug-flow reactors and others which need some modified treatment of diffusional restrictions and reaction technology. 

When an enzyme is immobilized on a smface, there may be a mass transfer resistance that limits the concetration of the reacting species on the surface. The following problem (from Shuler, 1988) finds the concentration of substrate on the surface when there is a reaction accompanied by mass transfer resistance. The Michaelis-Menten reaction on a surface is governed by... 

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). 

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