Section B. Reaction analysis: Glucose syrup (S) (40% w/w) reacts with immobilized sweetzyme® to fructose. Glucoseisomerization is a reversible reaction given by equation (1) and has been shown to follow reversible modified Michaelis-Menten kinetics. The reaction is limited to equilibrium and takes place in a continuous fixed-bed reactor in which the enzyme is immobilized. The reactor model should be developed, evaluated and used as a tool to study the more efficient operation of a typical GI reactor facility. The development of the multi-scale reactor model is illustrated by a modelling framework developed by Heitzig (2011). The facility with multi-scale reactors (Figure 2) requires a model that describes reaction kinetics, decay of enzyme activity and internal diffusion as a function of temperature. The framework consists of five phases (Heitzig, 2011): Phase I: Modelling/System Information Objective, Phase II: Model Design, Phase III: Model Identification/Discrimination, Phase IV: Model Evaluation/Validation, and Phase V: Application. Phase II: Model construction: In order to achieve the objectives, models for reaction kinetics, fixed bed reactor, diffusion in the reaction pellet and decay of enzyme activity must be developed and combined in a multi-scale reactor model. Consider a first-order reaction that occurs on the pore walls of an equimolar backscatter catalyst. Suppose that isothermal conditions are maintained and that a catalyst with simple slab geometry is used (Fig. 9.1).

If the y-coordinate is aligned from the center line to the surface, estimate the efficiency factor. The amount of carbon monoxide absorbed into the pulmonary circulation depends on the diffusion properties of the alveolar capillary membrane, not the amount of pulmonary capillary blood flow. Absorption of carbon monoxide should be limited by diffusion. The amount of nitrous oxide absorbed in the pulmonary capillaries depends entirely on pulmonary blood flow, not on the diffusion properties of the alveolar capillary membrane. Therefore, nitrous oxide transfer is described as limited to infusion. Figure 9.2 shows the concentration profile for different values of φ the Thiele modulus defined by Lkv/De. This solution shows that diffusion resistance causes a concentration profile in the pellet when the reagent cannot diffuse out of mass fast enough. If the resistance is low due to a large value of De, the concentration profile becomes flat, while it behaves the opposite for a high resistance to diffusion.

In practice, however, the possible negative influence of diffusion resistance on reaction rate is strongly compensated by the sharp increase in pore surface. Figure 9.3 is a diagram of equation (a) showing that if 0 φ →, then 1 η →, which means that there is no significant resistance to diffusion. If the resistance to diffusion increases, we have φ → ∞ and therefore η → 0. These can occur at low diffusivity, at a large granule size L, or at a very fast reaction rate, or all three factors. This regimen, in which diffusion greatly affects the reaction rate, is called strong pore resistance. For a first-order reaction, a general criterion of kinetically perfect enzymes has a specificity constant, kcat/Km, of the order of 108 to 109 M−1 s−1. The rate of reaction catalyzed by the enzyme is limited by diffusion, so the enzyme “processes” the substrate long before it hits another molecule. [1] However, in various disease states, the balance of alveolar and blood partial pressure of oxygen with respect to capillary transit time of red blood cells may be delayed, which also leads to restriction of diffusion. Limitation refers to the process that limits the absorption of gases into the blood: apparent activity is defined as the ratio of the efficiency factors of the poisoned and non-toxic catalyst under conditions of pore diffusion restrictions. Islands are particularly sensitive to oxygen supply restrictions because they have a relatively high rate of oxygen consumption (Dionne et al., 1993). In the normal physiological state, they are highly vascularized and are supplied with arterial PO2 blood.

In vitro culture under normoxic environmental conditions, the islets develop a necrotic nucleus that increases in size with increasing island size, as would be expected from the diffusion and consumption of oxygen on the island (Dionne et al., 1993). Central necrosis of the encapsulated islet occurs after islet microcapsule transplantation, resulting in a reduction in graft volume when only a small portion (∼10%) of the capsules is fibrotically invaded (De Vos et al., 1999). The fact that the necrotic tissue is located in the center and not on the periphery of the island suggests that it is likely a restriction of nutrient or oxygen supply that causes necrosis, rather than a mechanism of the immune system. Hypoxia causes necrosis of encapsulated islets in culture, upregulating iNOS (inducible nitric oxide synthase), indicating that the islets produce NO, which can self-harm, and upregulate MCP-1 (monocytic chemoattractant protein 1), which can attract macrophages and thus also induce islet damage after implantation (De Groot et al., 2003). The results of all these studies suggest that oxygen transport restrictions exist in transplanted islet microcapsules and may have serious effects on the survival of the island. From now on, the net diffusion of O2 can no longer occur unless blood flow increases to bring in more oxygen-hungry blood. Before entering into diffusion, perfusion and their limitations, remember that gas exchange through the alveolo capillary membrane occurs according to Fick`s law. But the speed and efficiency of gas transfer also depends on whether blood flows through the pulmonary capillaries – or infusion. And the speed of blood flow (or perfusion rate) is important – it determines when blood is available in the capillary for diffusion.

Under normal, dormant circumstances, a red blood cell spends about 0.75 seconds in a pulmonary capillary. Nanomagnetite particles (MNS) were used as a carrier for enzyme immobilization. In addition to the larger surface area due to the nanoscale size used, immobilization on magnetite materials allows easy enzymatic recovery of the medium under the magnetic force due to the magnetic reaction of the carrier material. This eliminates the need for expensive liquid chromatography systems, centrifuges or filters. However, the efficient loading of enzymes on nanomagnetite particles (MNS) requires surface functionalization by polymerization or sol-gel confinement, which reduces the magnetic response of NSM particles (Lee et al., 2009). To avoid this limitation, Huang et al. (2003) immobilized lipase by covalence to NSM particles. However, covalent binding leads to structural changes that can significantly reduce the activity of the enzyme. Therefore, it has been proposed to coordinate NMS particles with a low molecular weight ligand to overcome the above problem, as binding in this case would occur by physical adsorption rather than covalent bonding (Lee et al., 2009). At the same time, particle size does not increase, as when NSM particles are wrapped in polymers (Ma et al., 2003).

In addition, the ligand acts as a spacer between NSM and the immobilized enzyme to prevent direct contact of lipase with the surface of the magnetis, which can hinder the flexible enzyme structure. Immobilized lipase on NSM particles showed higher specific activity and thermal stability than free lipase, and immobilized lipase activity remained almost constant for five applications and recoveries (Bastida et al., 1998). The stable reuse as well as the convenience of magnetic separation recovery ensure that a surface-modified NSM particle is a good carrier material for lipase immobilization. The law states that the net diffusion rate – V of a certain gas through the alveolar capillary membrane is proportional to the pressure gradient through the wall; It is the difference between the partial pressure of the gas in the air sacs or PA and the partial pressure of the gas in the blood or Pa, and also proportional to the surface of the wall or A, but inversely proportional to the wall thickness – T. And it is always the diffusion constant – D, which varies from one gas to another. V=(PA-Pa)ADT Diffusion-limited gas exchange therefore means that a gas such as oxygen or carbon dioxide can diffuse through the alveolo capillary membrane as long as the partial pressure gradient is maintained. Unlike carbon monoxide, inspired nitrous oxide (N2O) does not combine with hemoglobin. On the contrary, it remains dissolved in plasma, which leads to an increase in the partial pressure of nitrous oxide in the pulmonary capillary and a drop in the pressure gradient to zero.