Diffusion immobilized enzyme particles

Effects of Diffusion within Immobilized Enzyme Particles... 

Right Profiles of decrease in F(t)/F(0) for intraparticle diffusion-influenced zero-order reaction with spherical immobilized enzyme particles packed in the reactor operated under a constant conversion policy (x = 0.99). Enzyme activity decays as E(t)/E(0) = exp ( kd t). 

Horta A, Alvarez JR, Luque S (2007) Analysis of the transient response of a CSTR containing immobilized enzyme particles. Part II. Minimum existence criterion and determination of substrate efective diffusivity and main reaction rate constant. Biochem Eng J 33 116-125... 

The catalytic behavior of enzymes in immobilized form may dramatically differ from that of soluble homogeneous enzymes. In particular, mass transport effects (the transport of a substrate to the catalyst and diffusion of reaction products away from the catalyst matrix) may result in the reduction of the overall activity. Mass transport effects are usually divided into two categories - external and internal. External effects stem from the fact that substrates must be transported from the bulk solution to the surface of an immobilized enzyme. Internal diffusional limitations occur when a substrate penetrates inside the immobilized enzyme particle, such as porous carriers, polymeric microspheres, membranes, etc. The classical treatment of mass transfer in heterogeneous catalysis has been successfully applied to immobilized enzymes I27l There are several simple experimental criteria or tests that allow one to determine whether a reaction is limited by external diffusion. For example, if a reaction is completely limited by external diffusion, the rate of the process should not depend on pH or enzyme concentration. At the same time the rate of reaction will depend on the stirring in the batch reactor or on the flow rate of a substrate in the column reactor. 

The degradation of heparin by the reactor is a multistep process. Heparin and the heparin-antithrombin complex must first diffuse from the bulk phase to the surface of the immobilized enzyme particle. The two species diffuse into the agarose particles where they encounter immobilized heparinase. The heparin-anti thrombin complex is assumed to be sterically inhibited from binding to immobilized heparinase, and under these conditions only unbound heparin is enzymatically degraded. As unbound heparin is consumed, heparin dissociates from the heparin-antithrombin complex to generate more free heparin. The breakdown of heparin is given by the following chemical reaction ... 

The diffusion coefficient for glucose in the immobilized enzyme particles, D, was estimated to be 6. 10 H (m2/s). A reasonable value if it is compared with the value of 8.8xl0 ll (m /s) obtained by Vellenga ( 5) for a different kind of immobilized glu-coseisomerase. 

At one extreme diffusivity may be so low that chemical reaction takes place only at suface active sites. In that case p is equal to the fraction of active sites on the surface of the catalyst. Such a polymer-supported phase transfer catalyst would have extremely low activity. At the other extreme when diffusion is much faster than chemical reaction p = 1. In that case the observed reaction rate equals the intrinsic reaction rate. Between the extremes a combination of intraparticle diffusion rates and intrinsic rates controls the observed reaction rates as shown in Fig. 2, which profiles the reactant concentration as a function of distance from the center of a spherical catalyst particle located at the right axis, When both diffusion and intrinsic reactivity control overall reaction rates, there is a gradient of reactant concentration from CAS at the surface, to a lower concentration at the center of the particle. The reactant is consumed as it diffuses into the particle. With diffusional limitations the active sites nearest the surface have the highest turnover numbers. The overall process of simultaneous diffusion and chemical reaction in a spherical particle has been described mathematically for the cases of ion exchange catalysis,63 65) and catalysis by enzymes immobilized in gels 66-67). Many experimental parameters influence the balance between intraparticle diffusional and intrinsic reactivity control of reaction rates with polymer-supported phase transfer catalysts, as shown in Fig. 1. 

In the design and operation of various bioreactors, a practical knowledge of physical transfer processes - that is, mass and heat transfer, as described in the relevant previous chapters - are often also required in addition to knowledge of the kinetics of biochemical reactions and of cell kinetics. Some basic concepts on the effects of diffusion inside the particles of catalysts, or of immobilized enzymes or cells, is provided in the following section. 

The immobilization of enzymes may introduce a new problem which is absent in free soluble enzymes. It is the mass-transfer resistance due to the large particle size of immobilized enzyme or due to the inclusion of enzymes in polymeric matrix. If we follow the hypothetical path of a substrate from the liquid to the reaction site in an immobilized enzyme, it can be divided into several steps (Figure 3.2) (1) transfer from the bulk liquid to a relatively unmixed liquid layer surrounding the immobilized enzyme (2) diffusion through the relatively unmixed liquid layer and (3) diffusion from the surface of the particle to the active site of the enzyme in an inert support. Steps... 

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 by copolymerization technique. The diameter of the spherical particle is 2 mm and the number density of the particles in a substrate solution is 10,000/L. Initial concentration of substrate is 0.1 mole/L. A substrate catalyzed by the enzyme can be adequately represented by the first-order reaction with k0 = 0.002 mol/Ls. It has been found that both external and internal mass-transfer resistance are significant for this immobilized enzyme. The mass-transfer coefficient at the stagnant film around the particle is about 0.02 cm/s and the diffusivity of the substrate in the particle is 5 x 10-6 cm2/s. 

Internal diffusional limitations are possible any time that a porous immobilized enzymatic preparation is used. Bernard et al. (1992) studied internal diffusional limitations in the esterification of myristic acid with ethanol, catalyzed by immobilized lipase from Mucor miehei (Lipozyme). No internal mass diffusion would exist if there was no change in the initial velocity of the reaction while the enzyme particle size was changed. Bernard found this was not the case, however, and the initial velocity decreased with increasing particle size. This corresponds to an efficiency of reaction decrease from 0.6 to 0.36 for a particle size increase from 180 pm to 480 pm. Using the Thiele modulus, they also determined that for a reaction efficiency of 90% a particle size of 30 pm would be necessary. While Bernard et al. found that their system was limited by internal diffusion, Steytler et al. (1991) found that when they investigated the effect of different sizes of glass bead, 1 mm and 3 mm, no change in reaction rate was observed. 

The specific activity of an enzyme almost always decreases on immobilization. The active sites are less accessible to substrate, and the diffusion of substrates and products across the stagnant layer of solution at the particle surface, and within polymer networks, lowers apparent values of Vmax and raises apparent Km values. The activity of an immobilized enzyme should be expressed as specific activity... 

As noted earlier in this chapter, the apparent Km values of immobilized enzymes vary with the thickness of the diffusion layer surrounding the particles. In packed-bed enzyme reactors, the thickness of this layer varies with the mobile phase flow rate. Faster flow rates produce smaller diffusion layers and therefore K m values that more closely approximate the true Km of the enzyme. This effect has also been observed with the ficin-CM-cellulose reactor, and plots of K m against flow rate Q obtained at different mobile phase flow rates are shown in Figure 4.14. 

When the mass of carrier material is large relative to that of the enzyme, the physical and chemical properties of the carrier (Table 6-5) will, in large part, determine properties of the resultant immobilized enzyme. Often, the carrier will impart mechanical strength to the enzyme, allowing repetitive recovery by simple filtration of the solid particles and reuse of the enzyme. The degree of porosity and pore volume will determine the resistance to diffusion and molecular size selectivity of the biocatalyst. When used in non-aqueous media, dispersion of the enzyme over a large surface area can greatly increase its activity. Table 6-3 summarizes many of the key properties and considerations for enzyme carrier materials. 

The heparin degradation rate at any radial position inside the catalyst particle is proportional to the bound heparinase concentration at that position. If the immobilized enzyme concentration is not uniform, the conventional analysis of simultaneous diffusion and reaction within a porous catalytic particle must be modified. The reaction rate within the catalyst particle will have an explicit radial dependence introduced via the enzyme concentration, as well as a dependence on the substrate concentration. 

In some biochemical systems the limiting mass transfer step shifts from a gas-liquid or solid-liquid interface (as discussed earlier) to the interior of solid particles. The most important cases are solid substrates and cell aggregates (such as microbial floes, cellular tissues, etc.) and immobilized enzymes (gel-entrapped or supported in solid matrices). In the former, diffusion of oxygen (or other nutrients) through the particle limits metabolic rates, while in the latter, substrate reactant or product diffusion into or out of the enzyme carrier often limits the overall global bioreaction rates. 

To improve an analytical immobilized enzyme packed reactor one of the most advantageous approaches is optimization of the support size. A decrease in carrier diameter would result in three advantages decreased dispersion, a decrease in internal diffusion with an increase in efficiency, and an increased surface area to volume ratio which would result in increased external mass transfer rates. To date, the smallest particles commonly used in analytical applications are 400 mesh (37 /im I.D.) The smaller particles may require a large driving force with increased cost and mechanical complexity. The pressure drop and column dimensions are related so that the final system parameters will be determined by the specific application requirements. 

Consider the situation of catalytic particles dispersed in a reasonably thin polymeric film, where the substrate/product reaction occurs via Michaelis-Menten kinetics. This problem is directly relevant to the associated problems of immobilized enzyme catalysis and diffusion/chemical reaction processes in chemical engineering. Aspects of the theory presented in here have recently been described by Albery and coworkers for enzyme electrodes. 

To increase the amount of immobilized enzyme per unit weight of the support, immobilization is carried out in porous supports with large internal surface areas. However, the substrate has to diffuse through the internal pores of the particle in order to reach the active site. This results in additional diffusion resistance. The substrate concentration profile in this case is shown in Figure 4.4. Internal diffusion resistance depends on particle size and shape, external substrate concentration, and effective diffusion within the particle, D. The latter depends on the molecular diffusion of the substrate in the support matrix, and on the porousness (ep and tortuosity (t) of the pores in the particle (Park et al., 2006 Young and Al-Duri, 1996). The effective diffusion can be determined from different mathematical expressions as shown in (Equations 4.50 to 4.52) (Pilkington et al, 1998) ... 

Generally, internal diffusion restrictions can be minimized and r approaches unity as cp decreases, or the substrate concentration increases. Therefore, for better utilization of the enzyme catalytic potential, the reactor should operate at a lower cp value, which can be manipulated by varying the particle size and the amount of immobilized enzyme per unit mass of the support, as shown in Figure 4.5. 

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