Analysis of the transient response of a CSTR containing immobilized enzyme particles: Part II. Minimum existence criterion and determination of substrate effective diffusivity and main reaction rate constant

A minimum existence criterion in the transient response of the bulk substrate concentration in a CSTR containing immobilized enzyme (IMEs) in porous solid supports has been obtained from simulation results using several kinetic expressions for the main reaction and the enzyme deactivation reaction. A simple method for the determination of the substrate effective diffusivity and the reaction rate constant is also presented, and applied to the decomposition of hydrogen peroxide, that reacts in a CSTR that contains silica–alumina porous catalyst particles, in which horseradish peroxidase enzyme had been previously immobilized.     

A novel method of determination of the internal enzyme distribution within porous solid supports and the deactivation rate constant

This article presents a method for determining the rate constant for deactivation and the internal distribution of immobilized enzyme. This method makes use of the parallel deactivation process in a diffusion-controlled regime, in which the internal activity profile behaves like a penetration front. This front basically traces through the initial active enzymatic profile, and one can determine the internal profile and the rate constant for deactivation from the experimentally observable bulk concentration versus time. This method is applied to the experimental data of the system of hydrogen-peroxide-immobilized catalase on controlled pore glass and Si-Al particles.     

A new method to determine active enzyme distribution, effective diffusivity, rate constant for main reaction and rate constant for deactivation

A new method is presented to determine (1) the rate constant for the main reaction, (2) the rate constant for deactivation, (3) the effective diffusivity, and (4) the active enzyme distribution within a porous solid support by utilizing data of bulk substrate concentration versus time in a continuous stirred basket reactor. The method relies on an assumption of parallel deactivation mechanism with strong pore diffusional resistance with respect to substrate species. The data of hydrogen peroxide-immobilized catalase published in the literature are used to demonstrate the theory. A parameter determination procedure is also presented.     

Deactivation studies of immobilized glucose oxidase

Studies have been performed in a tubular flow reactor to characterize the deactivation of immobilized glucose oxidase. The effects of oxygen concentration in the range of 0.09 to 0.467mM and hydrogen peroxide concentrations in the range of 0.1 to 10mM were studied. A simple mathematical model assuming first-order reaction and deactivation was found to describe the deactivation behavior adequately. The deactivation rate constant was found to increase with increasing levels of feed oxygen. Hydrogen peroxide was found to deactivate the enzyme severely and the deactivation rate constants were higher than those for oxygen deactivation. The influence of external and internal diffusion effects on the deactivation rate constant were examined. Although diffusional restrictions were negligible for oxygen transfer to the pellet, they were significant for transfer of hydrogen peroxide to the bulk stream. Increasing deactivation rates. Severe internal diffusion limitations were observed for the glucose oxidase system. However, for particle sizes in the range of 500 to 2000 μm, no effect on the rate of deactivation of the enzyme was observed.     

Substrate protection of immobilized glucose isomerase

Using commercial immobilized glucose isomerase (SWETASE(R), Nagase Co.), the effect of substrate protection on enzyme deactivation has been studied in a batch manner. The data analysis was carried out based on Briggs-Haldane kinetics in which enzyme deactivation accompanying the protection of substrates was also considered. The protection factor was proposed to elucidate the dependence of the degree of substrate protection. The existence of the protection of glucose isomerase by the substrates has been verified experimentally. Also, the enzyme-substrate complex deactivates with a decay constant which is one-half that of the free enzyme. Theoretical analysis of enzyme deactivation with substrate protection offers an effective understanding which is essential for enzyme replacement and process optimization.     

Analysis of substrate protection of an immobilized glucose isomerase reactor

The effect of substrate protection on enzyme deactivation was studied in a differential bed and a packed bed reactor using a commercial immobilized glucose isomerase (Swetase, Nagase Co.). Experimental data obtained from differential bed reactor were analyzed based on Briggs-Haldane kinetics in which enzyme deactivation accompanying the protection of substrate was considered. The deactivation constant of the enzyme-substrate complex was found to be about half of that of the free enzyme. The mathematical analysis describing the performance of a packed bed reactor under the considerations of the effects of substrate protection, diffusion resistance, and enzyme deactivation was studied. The system equations for the packed bed reactor were solved using an orthogonal collocation method. The presence of substrate protection and the diffusion effect within the enzyme particles resulted in an axial variation of effectiveness factor, eta(D), along the length of the packed bed. The axial distribution profile of eta(D) was found to be dependent on the operation temperature, Based on the effect of substrate protection, a better substrate feed policy could be theoretically found for promoting productivity in long-term operation. (c) 1993 John Wiley & Sons, Inc.     

The effect of porosity on the catalytic performance of constant-mass, spherical beads containing immobilized enzyme

The mass balances to a spherical bead with increasing porosity, ? (obtained by plain expansion of an otherwise compact bead), containing an immobilized enzyme and surrounded by a stagnant film are developed in dimensionless form for the case of Michaelis-Menten kinetics by considering three alternative situations in terms of pore structure (either setting the pore number, the pore radius or the pore length as a constant). The pore pattern of the porous bead does not play a major role in the variation of the lowest concentration of substrate ever reached in the bulk of the bead, which increases as ? increases and eventually levels off when ? approaches unity. The ratio between the rate of reaction brought about by the immobilized enzyme within the porous bead and that obtained for a compact bead is greater when ? is higher, and a vertical asymptote is apparently reached when the porosity approaches unity, a trend that is similarly observed for all pore patterns considered.     

Operational stability of immobilized d-glucose isomerase in a continuous feed stirred tank reactor

d-Glucose isomerization has been studied using immobilized cells of Streptomyces phaeochromogenes in a continuous feed stirred tank reactor (CSTR) where the external film diffusion resistance was negligible. Experiments conducted with various sizes of enzyme particles indicated that a strong internal diffusion resistance improved the apparent stability of these particles. The performance equations of the CSTR were constructed by associating the material balances for the inside porous support matrix with the bulk liquid phase, and enzyme deactivation was also taken into consideration. An iterative method together with the orthogonal collocation method is proposed for the evaluation of effectiveness factor and the substrate concentration profile within the enzyme particles. The numerical results offer an alternative analytical proof for the observation that under strong internal diffusion control the apparent operational stability of immobilized enzyme is improved.     

On the mechanism of immobilized glucose oxidase deactivation by hydrogen peroxide

The result of experiments in a fixed-bed reactor containing glucose oxidase immobilized on a nonporous support and conducted in the absence of diffusional limitations are reported. Kinetic parameters were established by separate batch experiments. The key observation was that, in every case, poisoning by product hydrogen peroxide resulted in a minimum in enzyme activity in the interior of the bed, well away from the ends. The deactivation data were interpreted by fitting the rate constant for poisoning, the only free parameter, to a previously reported theory. The theory postulates several deactivation mechanisms each of which leads to self-consistent kinetics, but the only mechanism which fitted the data assumes that peroxide attack the enzyme when it is the from complexed with glucose. Theory and experiment agreed to within the accuracy (+/- 2%) of the activity measurements.     

Prediction of continuous reactors performance based on batch reactor deactivation kinetics data of immobilized lipase

Experiments on deactivation kinetics of immobilized lipase enzyme fromCandida cylindracea were performed in stirred batch reactor using rice bran oil as the substrate and temperature as the deactivation parameter. The data were fitted in first order deactivation model. The effect of temperature on deactivation rate was represented by Arrhenius equation. Theoretical equations were developed based on pseudo-steady state approximation and Michaelis-Menten rate expression to predict the time course of conversion due to enzyme deactivation and apparent half-life of the immobilized enzyme activity in PFR and CSTR under constant feed rate policy for no diffusion limitation and diffusion limitation of first order. Stability of enzyme in these continuous reactors was predicted and factors affecting the stability were analyzed.     

Catalytic properties of the immobilized Aspergillus tamarii xylanase

Xylanase from Aspergillus tamarii was covalently immobilized on Duolite A147 pretreated with the bifunctional agent glutaraldehyde. The bound enzyme retained 54.2% of the original specific activity exhibited by the free enzyme (120 U/mg protein). Compared to the free enzyme, the immobilized enzyme exhibited lower optimum pH, higher optimum reaction temperature, lower energy of activation, higher K_m (Michaelis constant), lower V_max (maximal reaction rate). The half-life for the free enzyme was 186.0, 93.0, and 50.0 min for 40, 50, and 60°C, respectively, whereas the immobilized form at the same temperatures had half-life of 320, 136, and 65 min. The deactivation rate constant at 60°C for the immobilized enzyme is about 6.0 × 10⁻³, which is lower than that of the free enzyme (7.77 × 10⁻³ min). The energy of thermal deactivation was 15.22 and 20.72 kcal/mol, respectively for the free and immobilized enzyme, confirming stabilization by immobilization. An external mass transfer resistance was identified with the immobilization carrier (Duolite A147). The effect of some metal ions on the activity of the free and immobilized xylanase has been investigated. The immobilized enzyme retained about 73.0% of the initial catalytic activity even after being used 8 cycles.     

Modeling and simulation of a pressure-swing reactor for the conversion of poorly soluble substrate by immobilized enzyme: the case of d-hydantoinase reaction

An immobilized enzyme reactor system for converting poorly soluble substrate is proposed. In this stirred batch reactor, the solid substrate and immobilized enzyme suspensions are separated by a microporous filter. The advantage of separating the solid substrate from immobilized enzyme is that the fouling and breakage of the immobilized enzyme usually encountered in the stirred tank reactor can be prevented. Pressure swing can be applied to enhance the mass transfer between the two compartments. The hydrolytic reaction converting the poorly soluble substrate p-hydroxyphenylhydantoin (pHPH) into soluble N-carbamoyl-p-d-hydroxyphenylglycine (CpHPG) by immobilized d-hydantoinase is carried out in this reactor. The performance of this pressure-swing reactor is studied by simulation using a simple kinetic model. The pressure-swing operation increases the overall production rate significantly. The pressure swing also makes the reactor perform better for converting the solid substrate at higher concentration.     

Effect of immobilized enzyme deactivation in fixed- and fluid-bed reactors

A two-parameter theoretical model is developed to evaluate the effect of immobilized enzyme deactivation on substrate conversion in fixed- and fluid-bed reactors under diffusion-free conditions. The method describes a simple reaction in which three different immobilized enzyme deactivation forms are considered, and an expression is developed to evaluate the effect of immobilized enzyme deactivation on yield in a consecutive reaction. Comparison of reactor performances for the two reactor types reduces to a comparison of the appropriate dimensionless parameters. The practical implications of the development are illustrated through an example.     

A model of enzyme adsorption and hydrolysis of microcrystalline cellulose with slow deactivation of the adsorbed enzyme

Reduction in the activity and the concentration of the adsorbed enzyme are noted in the experimental data. Two alternative mechanisms, inactivation of the adsorbed enzyme and mass transfer of the enzyme from the bulk solution to the solution within the cellulose fibril where the cellulase is assumed to be inactive, are used to represent the decline in activity. The decline in concentration of the adsorbed enzyme is represented by a modest product inhibition and, more importantly, the assumption that the concentration of the adsorption sites is proportional to the square of the remaining substrate concentration. Measurements of both adsorbed enzyme and product concentration over time are used in determining parameter values. The model is applied to a series of experiments having a 10-fold range of substrate concentration and to an experiment in which the product is removed continuously. For both deactivation mechanisms, a very good representation of product concentration (standard deviation 3.6%) is obtained over the full period (168 h) of hydrolysis; the representation of adsorbed enzyme is, however, less accurate (standard deviation 6.7-6.8%).     

General theory of determining intraparticle active immobilized enzyme distribution and rate parameters

A general theory is presented in this article for determining the intrinsic rate constants for the main reaction and deactivation reaction, the effective diffusivity of the substrate, and the active enzyme distribution within porous solid supports from deactivation study of a continuous stirred-basket reactor (CSBR). For the parallel deactivation five reaction kinetics are considered: (a) Michaelis-Menten, (b) substrate inhibition, (c) product inhibition (competitive), (d) product inhibition (anticompetitive), and (e) zero-order kinetics. The experimental results of the system of hydrogen-peroxide-immobilized catalase on controlled-pore glass particles are analyzed to demonstrate the application of the theory developed for parallel deactivation of active immobilized enzyme (IME). For series deactivation only first-order kinetics is treated, and a numerical procedure is proposed to deter mine the rate parameters and the internal active enzyme distribution. The experimental data of the system of glucose-immobilized glucose oxidase on silica-alumina and controlled-pore glass particles are used to verify the theory.     

Optimal temperature policy for immobilized enzyme packed bed reactor performing reversible Michaelis-Menten kinetics using the disjoint policy.

The optimal temperature policy that maximizes the time-averaged productivity of a continuous immobilized enzyme packed bed reactor is determined. This optimization study takes into consideration the enzyme thermal deactivation with substrate protection during the reactor operation. The general case of reversible Michaelis-Menten kinetics under constant reactor feed flow rate is assumed. The corresponding nonlinear optimization problem is solved using the calculus of variations by applying the disjoint policy. This policy reduces the optimization problem into a differential-algebraic system, DAE. This DAE system defines completely the optimal temperature-time profiles. These profiles depend on the kinetic parameters, feed substrate concentration, operating period, and the residence time and are characterized by increasing form with time. Also, general analytical expressions for the slopes of the temperature and residual enzyme activity profiles are derived. An efficient solution algorithm is developed to solve the DAE system, which results into a one-dimensional optimization problem with simple bounds on the initial feed temperature. The enzymatic isomerization of glucose into fructose is selected as a case study. The computed productivities are very close to that obtained by numerical nonlinear optimization with simpler problem to solve. Moreover, the computed conversion profiles are almost constant over 90% of the operating periods, thus producing a homogeneous product.     

Catalytic properties of the immobilized Aspergillus tamarii xylanase

Xylanase from Aspergillus tamarii was covalently immobilized on Duolite A147 pretreated with the bifunctional agent glutaraldehyde. The bound enzyme retained 54.2% of the original specific activity exhibited by the free enzyme (120 U/mg protein). Compared to the free enzyme, the immobilized enzyme exhibited lower optimum pH, higher optimum reaction temperature, lower energy of activation, higher K_m (Michaelis constant), lower V_max (maximal reaction rate). The half-life for the free enzyme was 186.0, 93.0, and 50.0 min for 40, 50, and 60°C, respectively, whereas the immobilized form at the same temperatures had half-life of 320, 136, and 65 min. The deactivation rate constant at 60°C for the immobilized enzyme is about 6.0 × 10⁻³, which is lower than that of the free enzyme (7.77 × 10⁻³ min). The energy of thermal deactivation was 15.22 and 20.72 kcal/mol, respectively for the free and immobilized enzyme, confirming stabilization by immobilization. An external mass transfer resistance was identified with the immobilization carrier (Duolite A147). The effect of some metal ions on the activity of the free and immobilized xylanase has been investigated. The immobilized enzyme retained about 73.0% of the initial catalytic activity even after being used 8 cycles.     

Effect of pH on the production of lipolyzed butter oil by a calf pregastric esterase immobilized in a hollow-fiber reactor: I. uniresponse kinetics

A calf pregastric esterase immobilized in a hollow-fiber reactor was employed to hydrolyze milkfat, thereby producing a lipolyzed butteroil. The reaction kinetics can be modeled by a two-parameter model of the general Michaelis-Menten form based on a ping-pong bi-bi mechanism; the rate of enzyme deactivation can be modeled as a first-order reaction. The initial concentration of accessible glyceride bonds, [G](O), was estimated by complete saponification of the substrate butteroil as 2400 mM. An extra sum of squares test indicated that not only the parameters of the kinetic generalized Michaelis-Menten model, but also the deactivation-rate constant varied significantly with pH. The optimum pH, for lypolysis is near 6.0 at a temperature of 40 degrees C because at this pH the rate of deactivation of the esterase is minimized.     

Nonisothermal immobilized enzyme reaction in a packed-bed reactor

Summary This work investigates the reaction behavior of immobilized enzymes in a packed-bed reactor. The effect of heat generation due to exothermic enzyme reaction is considered. Conservations of substrate and energy constitute two coupled nonlinear partial differential equations which are simultaneously solved by a numerical method. It is found that substrate conversion is generally increased at higher temperature. However, the extent of temperature heavily depends on the magnitude of the dimensionless Michaelis constant which is defined as the ratio of Michaelis constant to inlet substrate concentration. At low dimensionless Michaelis constant, substrate conversion is considerably affected by temperature, but at high dimensionless Michaelis constant, the temperature effect is negligibly small. It is also found that maximum bulk temperature of reaction mixtures occurs around a dimensionless reactor length of 1.3 for the case with high substrate conversion.