Evaluation of intrinsic immobilized kinetics in hollow fiber reactor systems.

Immobilized cell and enzyme hollow fiber reactors have been developed for a variety of biochemical and biomedical applications. Reported mathematical models for predicting substrate conversion in these reactors have been limited in accuracy because of the use of free-solution kinetic parameters. This paper describes a method for determining the intrinsic kinetics of enzymes immobilized in hollow fiber reactor systems using a mathematical model for diffusion and reaction in porous media and an optimization procedure to fit intrinsic kinetic parameters to experimental data. Two enzymes, a thermophilic beta-galactosidase that exhibits product inhibition and L-lysine alpha-oxidase, were used in the analysis. The intrinsic kinetic parameters show that immobilization enhanced the activity of the beta-galactosidase while decreasing the activity of L-lysine alpha-oxidase. Both immobilized enzymes had higher Km values than did the soluble enzyme, indicating less affinity for the substrate. These results are used to illustrate the significant improvement in the ability to predict substrate conversion in hollow fiber reactors.     

Continuous coagulation of milk using immobilized enzymes in a fluidized-bed reactor

Milk-clotting enzymes such as pepsin, chymosin, chymotrypsin, and M. miehei proteases were immobilized on porous, alkylamine glass and incorporated into a fluidized-bed continuous coagulation scheme. Only pepsin and calf rennet retained sufficient activity towards skim milk to warrant further studies. Comparison of kinetic data with fixed-bed reactors revealed the overall superior performance of fluidized beds; higher clotting activities were possible while avoiding plugging problems and high pressure drops common to fixed-bed reactors. Film diffusion and catalyst back-mixing appear to be significant factors in the overall kinetics. All enzymes lost activity on exposure to skim milk. The inactivation rates were lower at high substrate pH and insignificantly affected by reactor temperature. Nitrogen and sialic acid accumulation on the porous glass paralleled the loss in activity in the initial stages. Attempts to regenerate the immobilized enzymes were partially successful.     

Immobilized electric eel acetylcholinesterasemii. II. Flow kinetics of acetylcholinesterase chemically attached to nylon tubing.

Acetylcholinesterase has been attached covalently to the inner surface of nylon tubing. An experimental study has been carried out on the flow kinetics; solutions of acetylthiocholine at various concentrations were passed through tubing at various flow rates, and measurements made of the rates of formation of product. The results were analyzed in the light of the theoretical treatment of Kobayashi and Laidler, four different methods of analysis being employed. It is found that at lower substrate concentrations and flow rates the reactions are largely diffusion controlled. The Km(app) values are substantially higher than the Km value for diffusion-free conditions, but approach it as the flow rate is increased, when the diffusion layer becomes less important. The results are entirely consistent with the Kobayaski-Laidler theory, and provide guidelines for the design of open tubular heterogeneous enzyme reactors, both for industrial and analytic purposes.     

Coupled reaction of immobilized aspartate aminotransferase and malate dehydrogenase. A plausible model for the cellular behaviour of these enzymes

To study the effect of facilitated diffusion of the intermediate metabolite, oxaloacetate, on the coupled reaction of aspartate aminotransferase (L-aspartate: 2-oxoglutarate aminotransferase, EC 2.6.1.1) and malate dehydrogenase (L-malate:NAD+ oxidoreductase, EC 1.1.1.37), these enzymes were co-immobilized on the surface of a collagen film. The kinetic properties of the immobilized enzymes were compared with those observed with the enzymes in solution. Since the reactions correspond to the cytosolic enzymes, they have been studied in the direction aspartate aminotransferase toward malate dehydrogenase. Coupled enzymes in solution showed classical behaviour. A lag-time was observed before they reached a steady state and this lag-time was dependent on the kinetic properties of the second enzyme, malate dehydrogenase. The same lag-time was observed when malate dehydrogenase in solution was coupled with aspartate aminotransferase bound to the film. When aspartate aminotransferase in solution was coupled with malate dehydrogenase bound to the collagen film, a very long lag-time was observed. Theoretical considerations showed that in the latter case, the lag-time was dependent on the kinetic properties of the second enzyme and the transport coefficient of the intermediate substrate through the boundary layer near the surface of the film. Then both enzymes were co-immobilized on the collagen film. The coupled activity of aspartate aminotransferase and malate dehydrogenase was compared for films with an activity ratio of 5 and 0.8. In both cases, a highly efficient coupling was observed. In the former case, where malate dehydrogenase was rate-limiting, 81% of this limiting activity was observed. In the latter case, aspartate aminotransferase was rate-limiting and 82% of its rate was obtained for the final product formation. The linear increase of product formation with time corresponded fairly well to the theoretical equations developed in the paper. To interpret these rate equations, one should assume that the intermediate substrate oxaloacetate formed by aspartate aminotransferase was used by malate dehydrogenase in the diffusion layer near the film, before diffusing in the bulk solution.     

Kinetic modeling of a multiple immobilized enzyme system. II. Application of the model

The mathematical model for the reaction sequence catalyzed by immobilized invertase and glucose oxidase discussed in the preceding article has been used successfully to duplicate experimental findings. In addition, it has been used as a tool for the simulation and prediction of effects derived from alterations to system-related and gel-related parameters. The effects of gel diffusivity on the overall conversion of sucrose substrate to reaction products was investigated through use of this model. Changes in the enzyme loading within a gel and the results of varying the ration of invertase activity to glucose activity were also evaluated. Through use of concentrations of the molecular species determined at the collocation points within a gel particle and in the bulk liquid phase, an estimate of the thickness of the diffusion boundary layer around the gel particle was determined which was in close agreement with values obtained from classical mass transfer relationships. For most of this study, the enzymes were coimmobilized within the same polymeric matrix. However, a number of tests were run with the enzymes immobilized individually and placed in separate reactors in a sequential reactor system. The experimental results from these tests were duplicated successfully by means of the model with little modification to the basic computer program. Such an example illustrates the potential flexibility of the model and its overall versatility.     

Reaction rate enhancement by surface diffusion of adsorbates.

Ligands can be captured by a surface target through either direct bulk diffusion or surface diffusion following reversible adsorption to the surface. We have solved a steady state boundary value problem for a perfect sink disk target in the surface, taking into account bulk and surface diffusion coefficients D and Ds and adsorption/desorption kinetic rate constants ka and kd at non-target regions. Solutions have been successfully found by numerical computation. The results show that the rate of capture from the surface depends non-linearly on Ds, D, ka, kd and geometrical dimensions. In particular, we demonstrate that not only is the non-target region equilibrium constant Keq (= ka/kd) important in determining the rate of capture from the surface, but so are the kinetic rate constants ka and kd separately. In all cases, the surface adsorption/diffusion combination enhances the total rate of capture. The results should be useful for predicting reaction rates of biological membrane bound receptor clusters and substrate-immobilized enzymes.     

Mass transport in a microchannel enzyme reactor with a porous wall: Hydrodynamic modeling and applications

A two-dimensional flow model, incorporating mass transport, has been developed to simulate a microchannel enzyme reactor with a porous wall. A two-domain approach based on the finite volume method was implemented. Two parameters are defined to characterize the mass transports in the fluid and porous regions: the porous Damkohler number and the fluid Damkohler number. For reactions close to first-order type (enzyme reactor), the concentration results are found to be well correlated by the use of a reaction–convection distance parameter which incorporates the effects of axial distance, substrate consumption and convection. The reactor efficiency reduces with reaction–convection distance parameter because of reduced reaction (or flux) due to the lower concentration. Increased fluid convection improves the efficiency but it is limited by the diffusion in the fluid region. The correlated results can find applications for the design of enzyme reactors with a porous wall.     

Kinetic properties of enzyme populations in vivo: alkaline phosphatase of the Escherichia coli periplasm.

Studies were conducted to determine the role that diffusion may play in the in vivo kinetics of the Escherichia coli periplasmic enzyme, alkaline phosphatase (AP, encoded by the gene pho A). Passive diffusion of solutes, from solution into the periplasm, is thought to occur mainly through porins in the outer membrane. The outer membrane therefore serves as a diffusion barrier separating a population of periplasmic enzymes from bulk substrate. E. coli strains containing a plasmid with the pho A gene linked to the lac promoter were used in this study in order to vary the amount of enzyme per cell. Alkaline phosphatase assays were conducted with intact cells, and the substrate concentration at half-maximum velocity (normally the Km for the enzyme) was determined as a function of enzyme concentration per cell. The results showed that diffusion of substrate to the enzyme caused as much as a 1000-fold change in this parameter, compared to that of purified enzyme. This suggested that diffusion was the rate-limiting step of the enzymatic reaction in these cells. In agreement with this type of reaction, Eadie-Hofstee and Lineweaver-Burk plots were not linear. At their extremes, these plots represented two types of kinetics. At high substrate concentration, equilibrium of substrate between bulk solution and the periplasm was achieved, and the kinetic properties conformed to Michaelis-Menten. At low substrate concentrations, there were a large number of free (unbound) enzymes, and each substrate molecule that entered the periplasm, through the diffusion barrier, resulted in product formation.(ABSTRACT TRUNCATED AT 250 WORDS)     

Depolymerization of starch and pectin using superporous matrix supported enzymes

Immobilized enzyme catalyzed biotransformations involving macromolecular substrates and/or products are greatly retarded due to slow diffusion of large substrate molecules in and out of the typical enzyme supports. Slow diffusion of macromolecules into the matrix pores can be speeded up by use of macroporous supports as enzyme carriers. Depolymerization reactions of polysaccharides like starch, pectin, and dextran to their respective low molecular weight products are some of the reactions that can benefit from use of such superporous matrices. In the present work, an indigenously prepared rigid cross-linked cellulose matrix (called CELBEADS) has been used as support for immobilizing alpha amylase (1,4-alpha-D-glucan glucanohydrolase, EC 3.2.1.1.) and pectinase (endo-PG: poly(1,4-alpha-galactouronide) glycanohydrolase, EC 3.2.1.15). The immobilized enzymes were used for starch and pectin hydrolysis respectively, in batch, packed bed and expanded bed modes. The macroporosity of CELBEADS was found to permit through-flow and easy diffusion of substrates pectin and starch to enzyme sites in the porous supports and gave reaction rates comparable to the rates obtained using soluble enzymes.     

Probing of the substrate binding domain of lactose permease by a proton pulse

The lactose permease of Escherichia coli coupled proton transfer across the bacterial inner membrane with the uptake of beta-galactosides. In the present study we have used the cysteine-less C148 mutant that was selectively labeled by fluorescein maleimide on the C148 residue, which is an active component of the substrate transporting cavity. Measurements of the protonation dynamics of the bound pH indicator in the time resolved domain allowed us to probe the binding site by a free diffusing proton. The measured signal was reconstructed by numeric integration of differential rate equations that comply with the detailed balance principle and account for all proton transfer reactions taking place in the reaction mixture. This analysis yields the rate constants and pK values of all residues participating in the fast proton transfer reaction between the bulk and the protein's surface, revealing the exposed residues that react with free protons in a diffusion controlled reaction and how they transfer protons among themselves. The magnitudes of these rate constants were finally evaluated by comparison with the rate predicted by the Debye-Smoluchowski equation. The analysis of the kinetic and pK values indicated that the protein-fluorescein adduct assumes two conformation states. One is dominant above pH 7.4, while the other exists only below 7.1. In the high pH range, the enzyme assumes a constrained configuration and the rate constant of the reaction of a free diffusing proton with the bound dye is 10 times slower than a diffusion controlled reaction. In this state, the carboxylate moiety of residue E126 is in close proximity to the dye and exchanges a proton with it at a very fast rate. Below pH 7.1, the substrate binding domain is in a relaxed configuration and freely accessed by bulk protons, and the rate of proton exchange between the dye and E126 is 100,000 times slower. The relevance of these observations to the catalytic cycle is discussed.     

Polymeric collagen fibrils. An example of substrate-mediated steric obstruction of enzymic digestion.

Polymeric collagen fibrils have been reacted with fluorescein and rhodamine isothiocyanates to produce fluorescent dye-labelled fibrils, containing seven dye substituents per molecule of tropocollagen within the polymeric collagen fibrils. Two dye-labelled peptides per molecule of tropocollagen were solubilised by trypsin (EC 3.4.21.4) from the telopeptide regions and four dye-labelled peptides were located in the helical regions solubilised by bacterial collagenase (EC 3.4.24.3). The solubilisation of dye-labelled peptides from these insoluble substrates were employed to measure the kinetics of trypsin and collagenase digestion of the telopeptide and helical regions, respectively, of the insoluble polymeric collagen fibrils. These studies demonstrated an apparent excess of enzyme for the readily available substrate under conditions when it was known that a vast excess of substrate existed in the reaction mixture calculated in terms of a molecular ratio. A point of equivalence was established for both trypsin and bacterial collagenase, approximately one enzyme molecule per 870 substrate molecules. On either side of this point the quantity of products formed was controlled by either the enzyme concentration or the substrate concentration. The results can be explained in terms of the inaccessibility of tropocollagen molecules within the molecular architecture of the polymeric collagen fibrils. The external layer of tropocollagen molecules obstruct collagenolytic enzymes penetrating to, and forming enzyme-substrate complexes with, the bulk of the substrate within the interior of the fibrils.     

Substrate channeling of oxalacetate in solid-state complexes of malate dehydrogenase and citrate synthase

Current evidence suggests that mitochondrial matrix enzymes exist in solid-state, multienzyme complexes in vivo. Addition of polyethylene glycol to a solution containing malate dehydrogenase and citrate synthase generates such a solid-state, enzyme complex in vitro at enzyme concentrations permitting kinetic measurements. Suspensions of the isolated, solid-state, hetero-complex of these enzymes were used to study the coupled reactions of citrate synthesis from malate, NAD, and CoASAc. The particles appear to be about 1 microgram in diameter. Considering the ratio of enzyme to oxalacetate molecules in or at the surface of the solid-state particles, one would expect oxalacetate to be converted to citrate within a few molecular distances of the site of oxalacetate generation. This model of "substrate channeling" (or alternatively a direct transfer of oxalacetate between enzymes) is supported by experiments with excess aspartate aminotransferase and glutamate added to the solution phase to give a reaction competing with the synthase for bulk phase oxalacetate. Quantities of aminotransferase that reduce the citrate reaction rate with soluble dehydrogenase and synthase by 90% do not significantly affect rates with comparable amounts of the dehydrogenase-synthase complex. We suggest that similar substrate channeling can occur in vivo and discuss the possible advantages provided thereby.     

Operational effectiveness factors of immobilized enzyme systems

The steady-state and operational effectiveness factors for hydrolytic enzymes immobilized in spherical gel particles have been calculated by the collocation method for a wide range of microenvironmental conditions (given by the Thiele modulus) and macroenvironmental conditions (given by the Sherwood number and the relative substrate content). The operational effectiveness factor is a measure of the ratio of the times required to convert a defined amount of substrate with the same amount of free and immobilized enzyme, respectively. Calculations were made for reactors where the diffusion layers of the different enzyme-containing gel particles do not overlap. The theoretical values were compared with experimental values for stirred reactors with chymotrypsin and trypsin immobilized in spherical particles (Sepharose and Sephadex). Low molecular weight substrates were used. The theoretical and experimental values were found to agree within the experimental error. This demonstrates the predictive capacity of the collocation method in estimating steady-state and operational effectiveness factors for enzyme reactors. The microenvironment and macroenvironment were both found to influence the effectiveness over a wide range of substrate concentrations. However, the macroenvironmental influence is negligible when the Sherwood number of the reactor is larger than ～50. Then, the diffusion layer thickness is small compared with the dimensions of the enzyme-containing particles. The effectiveness factors calculated here can also be used to predict the performance of continuous stirred tank and plug-flow reactors.     

Tubular bioreactor models that include Onsager-Curie scalar cross-phenomena to describe stress-dependent rates of cell proliferation

The theory of heterogeneous catalysis in chemical reactors is employed to simulate laminar flow through tubes at large mass transfer Peclet numbers in which anchorage-dependent cells (i) adhere to a protein coating on the inner surface at r = R_wall, (ii) receive nutrients and oxygen from an aqueous medium via transverse diffusion toward the active wall, and (iii) proliferate in the presence of viscous shear at the cell/aqueous-medium interface. This process is modeled as convective diffusion in cylindrical coordinates with chemical reaction at the boundary, where chemical reaction describes the rate of nutrient consumption. The formalism of irreversible thermodynamics is employed to describe an unusual coupling between viscous shear, or velocity gradients at the cell/aqueous-medium interface, and rates of nutrient consumption. Linear transport laws in chemically reactive systems that obey Curie's theorem predict the existence of cross-phenomena between fluxes (i.e., scalar reaction rates) and driving forces (i.e., 2nd-rank velocity gradient tensor) whose tensorial ranks differ by an even integer—in this case, two. This methodology for stress-dependent chemical reactions yields an additional zeroth-order contribution, via the magnitude of the velocity gradient tensor, to heterogeneous kinetic rate expressions because nutrient consumption and cell proliferation are stress-sensitive. Computer simulations of nutrient consumption suggest that bioreactor designs should consider stress-sensitive reactions when the shear-rate-based Damköhler number (i.e., defined for the first time in this study as the stress-dependent zeroth-order rate of nutrient consumption relative to the rate of nutrient diffusion toward active cells adhered to the tube wall) is greater than 10–20% of the stress-free Damköhler number. Models of bioreactor performance are presented for simple 1st-order, simple 2nd-order, and complex chemical kinetic rate expressions, where the latter considers adsorption/desorption equilibria via the Fowler–Guggenheim modification of the Langmuir isotherm for cell–protein docking on active sites, accompanied by cell–cell attraction. Stress sensitivity is magnified in physically realistic cell-based tubular bioreactors with complex stress-free kinetic rate expressions relative to simulations with simple 1st- and 2nd-order kinetics.     

Immobilized enzymes: Electrokinetic effects on reaction rates under external diffusion

The rates of reactions catalyzed by enzymes immobilized on a nonporous solid surface have been computed employing a Nernst film model. The Nernst-Planck equations for the transport of the charged substrate and product species in the film and the Poisson equation for the distribution of electrical potential are solved numerically with the appropriate boundary conditions. The electrical charge at the surface is assumed to arise from the dissociation equilibria of the acidic and basic surface groups of the enzyme. The pH at the surface affects both the surface charge as well as the intrinsic kinetics of the enzyme-catalyzed reaction. Factors which determine the pH at the surface include the pH in the bulk solution and the release of H(+) ions in the enzyme-catalyzed reaction. The latter causes a lowering of pH at the surface, causing the reaction rate to differ from that computed assuming an equilibrium distribution of electrical potential. Another kind of nonequilibrium contribution is caused by unequal charges or diffusivities of the substrate and products, which results in a diffusion potential being set up. Two moduli are introduced to evaluate the significance of the reaction-generated lowering of pH and the diffusion potential effect. The effect of changing various parameters, e.g., reaction rate constant, substrate concentration, enzyme concentration, pH, etc., on the overall reaction rate are studied.     

Analysis and Modeling of Lithium Flows in Porous Materials

One of the primary conditions necessary for the success of magnetic fusion reactors is the ability to mitigate damage to the first wall during ELMs and plasma disruptions. A potential solution involves the use of flowing liquid metals such as lithium as a first wall, but ensuring its stability under the extreme environments in the reactor would be imperative. The conditions leading to instabilities on the free surface of flowing liquid lithium (LL) layers on a substrate and in a porous material are investigated using both analytical methods and computational modeling, with consideration for the effects of LL velocity, LL layer thickness, substrate porosity, LL permeability, and hydrogen (H) plasma velocity. Linear stability analysis is used to predict the critical velocity and wavelength-dependence of wave growth, as well as the onset of instability. The modeling of LL flows is performed on a flat substrate and in a porous material for various LL thicknesses, LL and H plasma velocities to analyze the conditions leading to droplet formation and ejection.     

Kinetics of the immobilization of trypsin on activated silichrome

Trypsin is studied for kinetics of its immobilization on the surface of a porous spheric inorganic carrier with the grafted aldehyde groups in the surface layer. This process is found to be controlled by the enzyme diffusion. It is shown possible to use a body of mathematics known for kinetics of physical adsorption on the porous adsorbents to describe kinetics of protein chemosorption on the analogous carriers. A simple method is suggested for plotting a kinetic curve of the enzyme immobilization on the matrix with any sizes of particles from the experimentally obtained kinetic curve of its binding on the carrier with a definite diameter of particles.     

Perturbations in the sof the double layer at an enzymic surface

The surfaces of cells are both charged and enzymically active; furthermore, mass transfer across the surface is occurring constantly. These dynamic processes are capable of perturbing the equilibrium double layer that would be present in the absence of mass transfer and reactions. This paper investigates the influence of enzymic surface reactions on the structure of the diffuse double layer, and conversely the influence of potential on concentration profiles and reaction rates. It is shown that (1) mobility differences in substrate and product can lead to more or less extended double layers and to extrema in the potential profile depending on kinetic factors such as reaction rate and ion mobility of substrate and product and (2) surface reactions can act as a surface concentration switch or amplifier wherein comparatively small variations in bulk concentration produce large variations in surface concentration. Deviations from equilibrium potentials are described by a dimensionless parameter involving reaction rate, ionic strength and the substrate-product mobility difference. Deviations from equilibrium concentrations are described by two electrostatic reaction-diffusion moduli. One of these expresses the effect of differing ion mobilities between substrate and product. Depending on the sign of this parameter, the surface substrate concentration may be either displaced above or below the case (usually hypothetical) of equal ion mobilities. The physiological significance of a reaction or mass flow perturbed surface potential is discussed.     

三乙醇胺基强碱性聚苯乙烯树脂共价固定胰酶的研究

用多孔强碱型三乙醇胺基聚苯乙烯阴离子交换树脂做为载体,用CNBr与载体上的多羟基作用共价偶联了胰酶。红外光谱表明:其共价偶联反应机理与用CNBr活化多糖类载体并接酶的机理相类似。最适偶联条件研究表明:CNBr用量增多,酶蛋白载量增加。但比活下降。偶联pH为10时,固定化酶有适宜的载量和较高的比活。由于胰酶水解蛋白反应释放出H~+质子,这些质子在载体内积累,使微环境内H~+质子浓度增加,进而使得固定化胰酶的pH—活性曲线在pH9～11范围内未出现下降。在变温和60℃恒温下对固定化酶的热稳定性测试表明:固相酶的热稳定性比天然酶的热稳定性有所提高。     

Utilization of newly developed immobilized enzyme reactors for preparation and study of immunoglobulin G fragments

The newly developed immobilized enzyme reactors (IMERs) with proteolytic enzymes chymotrypsin, trypsin or papain were used for specific fragmentation of high molecular-mass and heterogeneous glycoproteins immunoglobulin G (IgG) and crystallizable fragment of IgG (Fc). The efficiency of splitting or digestion were controlled by RP-HPLC. The specificity of digestion by trypsin reactor was controlled by MS. IMERs (trypsin immobilized on magnetic microparticles focused in a channel of magnetically active microfluidic device) was used for digestion of the whole IgG molecule. The sufficient conditions for IgG digestion in microfluidic device (flow rate, ratio S:E, pH, temperature) were optimized. It was confirmed that the combination of IMERs with microfluidic device enables efficient digestion of highly heterogeneous glycoproteins such as IgG in extremely short time and minimal reaction volume.