Predicting the performance of immobilized enzyme reactors using reversible Michaelis–Menten kinetics

A general mathematical model is developed in the present work for predicting the steady state performance of immobilized enzyme reactor performing reversible Michaelis - Menten kinetics. The model takes into account the effect of external diffusional limitations, the axial dispersion and the equilibrium constant on reactor performance quantified as relative substrate conversion and yield. The performance of reactor is characterized using the dimensionless parameters of Damkohler number, Stanton number, Peclet number, the equilibrium constant and the dimensionless input substrate concentration. The reactor performance is described for the two extreme cases of plug flow reactor (PFR) and continuous stirred tank reactor (CSTR) in addition to the intermediate case of dispersed plug flow reactor (DPFR). The performance of reactor is compared for the two cases of zero order and reversible first order kinetics.     

Effect of initial substrate concentration on the rate of nitrification in a batch experiment

The intrinsic rate of nitrification was observed in a batch reactor by eliminating external and internal diffusional resistances. The former were minimized by means of intense agitation, and the latter by mechanical rupture of the activated sludge flocs using high mixer rotational speeds. The optimum temperature and pH for the intrinsic nitrification rate were found to be 30–35°C and 8.0, respectively. Initial ammonium concentration was found to have a strong effect on the value of the kinetic parameters of the Michaelis–Menten rate expression at low ammonium levels. However, at high initial concentrations both parameters attained a constant maximum value that is independent of the initial substrate level.     

Preparation of an immobilized two-enzyme system, Beta-amylase--pullulanase, to an acrylic copolymer for the conversion of starch to maltose. III. Process kinetic studies on continuous reactors

Kinetic studies on the parameters influencing the potential industrial application of an immobilized two-enzyme system of β-amylase and pullulanase for conversion of starch to a product with high maltose content, have been performed. The apparent Michaelis constant, the apparent product inhibitor constant, and the activation energy have been determined for the immobilized preparation and compared to the values for the corresponding soluble enzyme system. The catalytic activity of the immobilized enzymes was studied in a plug-flow reactor and a continuous feed stirred tank reactor. Mathematical models for these reactors have been formulated and adapted to fit the experimental data. Comparisons of the reactor efficiencies were made and the conditions were found to be such as to favor the plug-flow reactor. Results on operational stability tests at different temperatures and substrate concentrations are given.     

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.     

Ceramic membrane microfilter as an immobilized enzyme reactor.

This study investigated the use of a ceramic microfilter as an immobilized enzyme reactor. In this type of reactor, the substrate solution permeates the ceramic membrane and reacts with an enzyme that has been immobilized within its porous interior. The objective of this study was to examine the effect of permeation rate on the observed kinetic parameters for the immobilized enzyme in order to assess possible mass transfer influences or shear effects. Kinetic parameters were found to be independent of flow rate for immobilized penicillinase and lactate dehydrogenase. Therefore, neither mass transfer nor shear effects were observed for enzymes immobilized within the ceramic membrane. Both the residence time and the conversion in the microfilter reactor could be controlled simply by regulating the transmembrane pressure drop. This study suggests that a ceramic microfilter reactor can be a desirable alternative to a packed bed of porous particles, especially when an immobilized enzyme has high activity and a low Michaelis constant.     

The catalase–hydrogen peroxide system. Kinetics of catalatic action at high substrate concentrations

1. A re-examination of the catalase-hydrogen peroxide reaction at high substrate concentrations, by using the quenched-flow technique, reveals a more complex kinetic behaviour than that previously reported. At constant reaction time the catalatic process obeys Michaelis-Menten kinetics, but the apparent Michaelis constant is markedly time-dependent, whereas the conventional catalase activity is independent of time. 2. The kinetics of the ;time effect' were analysed and it is suggested that the effect derives from the formation of an inactive species (thought to be catalase Compound II). The process shows Michaelis-Menten kinetics, with a Michaelis constant equal to that for the catalatic reaction in the limit of zero reaction time. 3. It has been confirmed that certain buffer components have marked inhibitory effects on the catalatic reaction and that, in unbuffered systems, catalatic activity is substantially independent of pH in the range 4.7-10.5.     

The kinetic and mass transfer behavior of immobilized invertase on ion-exchange resin beads

Immobilized invertase was prepared by binding native invertase to a polyamine type ion-exchange resin. Kinetic behavior of the immobilized invertase on these small pellets was investigated in a packed-bed reactor. For low flow rates, an effect of interparticle diffusion on the Machaelis constant was observed and a correlation was proposed to evaluate the effect. At high flow rates, Michaelis and inhibition constants were determined and compared with those for native invertase. With large pellets, intraparticle diffusion was found to be important and at high substrate concentrations, the effectiveness factor exceeded unity. Good agreement was found between the theoretical analyses and the experimental data.     

Hydrolysis of particulate tributyrin in a fluidized lipase reactor.

Pancreatic lipase has been immobilized onto stainless steel beads by adsorption followed by crosslinking, and onto polyacrylamide by covalent bonding. The activities of the two types of immobilized enzyme toward the particulate substrate, tributyrin emulsion droplets, were determined experimentally, and rate constants based on Michaelis-Menten kinetics were calculated. The activity of the stainless steel-lipase was determined for various flow conditions and for various support sizes by the use of a differential fluidized bed recycle reactor. The rate constants calculated indicate that the experimental reaction rate is free from mass transfer influences, since the observed Michaelis constant does not vary with the fluidization velocity or with the support particle size. In addition, the Michaelis constant of the stainless steel-lipase was found to be equal to that of the free enzyme, suggesting that adsorption and subsequent crosslinking does not alter the enzyme-substrate affinity. The emulsion substrate mass transfer rates, calculated from the filtration theory, indicate that each substrate particle which contact the immobilized enzyme is hydrolyzed to a significant extent. The experimentally determined kinetic rate constants may be used directly to predict the size of integral fluidized bed reactors.     

Optimum temperature operation mode for glucose isomerase reactor operating at constant glucose conversion

The optimum temperature operation mode required to achieve constant outlet glucose conversion is determined for immobilized glucose isomerase continuous packed bed reactor. The reactor design equation assumes reversible Michaelis-Menten kinetics with both enzyme deactivation and substrate protection. An increasing temperature profiles are determined for different operating periods, residence times and glucose conversions. The temperature increase with time is very small at low degree of glucose conversion and at relatively long residence time. The temperature rise with time increases at high degree of conversion and at relatively short residence time.     

Some characteristics of the kinetics of enzymatic reactions based on the example of catalase]

A method of kinetic analysis for quickly acting enzymes, which are characterized with substrate inhibition, on the catalase model is proposed. Catalase kinetics was shown to be full described, considering changes in the maximal reaction rate and Michaelis constant, by four parameters instead of two usual ones (Vmax, Km equals const.). The method described makes possible to calculate the change the Michaelis constant in time and to estimate real dependencies of the reaction rate on time and on the substrate concentration. Moreover, the enzyme concentration and its inactivation rate at any reaction moment can be calculated under saturation conditions. It is supposed that experimental dependencies of Km on t and of Vmax on t are the results of residual conformation changes accumulated by the enzyme in the reaction process.     

Simulation of glucose isomerase reactor: optimum operating temperature

A design equation for immobilized glucose isomerase (IGI) packed bed reactor is developed assuming enzyme deactivation and substrate protection. The developed equation is used to simulate the performance of the reactor at various temperatures (50–80 °C). Enzyme deactivation is significant at high temperature. Substrate protection showed to have significant effect in reducing enzyme deactivation and increasing the enzyme half-life. Factors affecting the optimum operating temperature are discussed. The optimum operating temperature is greatly influenced by the operating period and to a lesser extent with both initial glucose concentration and glucose conversion.Two modes of reactor operation are tested i.e., constant feed flow rate and constant conversion. Reactor operating at constant conversion is more productive than reactor operating at constant flow rate if the working temperature is higher than the optimum temperature. Although at lower temperatures than the optimum, the two modes of operation give the same result.List of Symbols a residual enzyme activity - E [mg/l] concentration of active enzyme - E _a [kJ/mole] activation energy - E ₀ [mg/l] initial concentration of active enzyme - k [Specific] kinetic parameter - k _d [h^–1] first order thermal deactivation rate constant - k _e equilibrium constant - k _m [mole/l] apparent Michaelis constant - k _p [mole/l] Michaelis constant for product - k _s [mole/l] Michaelis constant for substrate - k ₀ [Specific] pre-exponential factor - Q [1/h] volumetric flow rate - ¯Q [1/h] average volumetric flow rate - R [kJ/mol·k] ideal gas constant - s [mole/l] apparent substrate concentration - s [mole/l] substrate concentration - s _e [mole/l] substrate concentration at equilibrium - s ₀ [mole/l] substrate concentration at reactor inlet - p [mole/l] product concentration - p _e [mole/l] product concentration at equilibrium - P _r [mole fructose/l·h] reactor productivity - T [k] temperature - t [h] time - t _p [h] operating time - V [l] reactor volume - v [mole/l·h] reaction rate - v [mole/l] reaction rate under enzyme deactivation and substrate protection - v _m [mole/l·h] maximum apparent reaction rate - v _p [mole/l·h] maximum reaction rate for product - v _s [mole/l·h] maximum reaction rate for substrate - x substrate fractional conversion - x _e substrate fractional conversion at equilibrium Greek Symbols effectiveness factor - mean effectiveness factor - substrate protection factor - [h] residence time - [h] average residence time - ₀ [h] initial residence time     

An annular bound-enzyme reactor

A column reactor with an annular cross section was formed by rolling up DEAE cellulose paper and a screening spacer. Glucoamylase was attached by ion adsorption. For the spacer used, pressure drop was very low, suggesting that this form may be useful with feed streams that are not completely particle-free. Tests of this reactor at the high substrate concentrations characteristic of commercial reactors showed very little diffusional resistance, exhibiting zero-order behavior over most of the concentration range. At low concentrations, the reactor had an apparent “half-order” behavior caused by diffusional limitation in the paper. In this range, flow rate influenced the reaction rate, showing that mass transfer in the main stream also is a contributing factor in this range. Because of the high concentrations and the low Michaelis constant (0.0011 M) the reactor does not show first-order behavior, even at very high conversions. The design of a plant-scale reactor was formulated from these data. The increase in the quantity of enzyme necessary to compensate for the effects of diffusion was only a few percent. Two reactors were formed with sheets nonporous to the enzyme, binding the enzyme with cyanogen bromide after forming the reactor. The amount of enzyme bound was about one monolayer, and there appeared to be no diffusional limitations, even at low substrate concentrations.     

Three-dimensional numerical approach to investigate the substrate transport and conversion in an immobilized enzyme reactor

This numerical study evaluates the momentum and mass transfer in an immobilized enzyme reactor. The simulation is based on the solution of the three-dimensional Navier-Stokes equation and a scalar transport equation with a sink term for the transport and the conversion of substrate to product. The reactor consists of a container filled with 20 spherical enzyme carriers. Each of these carriers is covered with an active enzyme layer where the conversion takes place. To account for the biochemical activity, the sink term in the scalar transport equation is represented by a standard Michaelis-Menten approach. The simulation gives detailed information of the local substrate and product concentrations with respect to external and internal transport limitations. A major focus is set on the influence of the substrate transport velocity on the catalytic process. For reactor performance analysis the overall and the local transport processes are described by a complete set of dimensionless variables. The interaction between substrate concentration, velocity, and efficiency of the process can be studied with the help of these variables. The effect of different substrate inflow concentrations on the process can be seen in relation to velocity variations. The flow field characterization of the system makes it possible to understand fluid mechanical properties and its importance to transport processes. The distribution of fluid motion through the void volume has different properties in different parts of the reactor. This phenomenon has strong effects on the arrangement of significantly different mass transport areas as well as on process effectiveness. With the given data it is also possible to detect zones of high, low, and latent enzymatic activity and to determine whether the conversion is limited due to mass transfer or reaction resistances.     

Enzymatic breakdown of threonine by threonine aldolase

1. The enzyme which splits threonine to acetaldehyde and glycine has been partially purified from rat liver (five- to sixfold purification) and the name threonine aldolase proposed for it. 2. The general properties of threonine aldolase have been studied. The enzyme is unstable to a pH below 5. The pH optimum of the enzyme reaction is at 7.5-7.7. The initial rate of production of acetaldehyde is proportional to the enzyme concentration, and when the enzyme concentration is constant, the production of acetaldehyde is proportional to the time, provided that the substrate is in excess. The enzyme is inhibited by the carbonyl group reagent, hydroxylamine. Attempts to demonstrate that pyridoxal phosphate is a cofactor were unsuccessful. 3. The enzyme splits only L-allothreonine and L-threonine and is inactive against the D-forms of these amino acids. 4. The enzyme reaction on DL-allothreonine follows first order kinetics. From the first order velocity constants and the initial rates of the rates of the reaction at various substrate concentrations the Michaelis constant, Ks, for this substrate has been evaluated. Michaelis constants have also been determined for threonine. 5. The optimum temperature for the enzymatic breakdown of DL-allothreonine at pH 7.65 was found to be 50 degrees C. in phosphate buffer and 48 degrees C. in tris-maleate buffer. The rate of thermal inactivation of the enzyme threonine aldolase obeys a first order reaction. The heat of thermal inactivation was calculated by the aid of the van't Hoff-Arrhenius equation to be 43,000 cal. per mole for the temperature range 41.2-46.6 degrees C. 6. Equivalent amounts of acetaldehyde and glycine were formed from DL-allothreonine and the enzymatic breakdown of DL-allothreonine was found to be irreversible.     

Backmixing and mass transfer in the design of immobilized-enzyme reactors

The effects of dispersion and mass transfer resistance on the degree of conversion in an immobilized-enzyme reactor have been considered theoretically. It is assumed that the immobilized enzymes obey a Michaelis–Menten relationship and backmixing can be characterized by a dispersion model. For two extreme cases (perfect mixing and piston flow), approximate equations are obtained, which can be readily used to evaluate the effect of mass transfer on degree of conversion. Numerical solutions are obtained for other intermediate cases. Design charts are given which set practical limits of enzyme reactor design.     

Activation of 17beta-hydroxysteroid dehydrogenase from human red blood cells

Experiments designed to elucidate the nature of 17β-hydroxysteroid dehydrogenase from human red blood cells have shown that NADP⁺ activates and protects the enzyme, while also serving as substrate for the reaction. Enzyme activity was measured by the conversion of 17β-estradiol to estrone and by the production of NADPH with 17β-estradiol-3-sulfate as substrate. It appears that the reaction sequence is first, binding with NADP⁺ and second, binding with the steroid. The binding with NADP⁺ is essentially irreversible: the activated enzyme is completely protected against loss of activity by dilution. On dilution of the unactivated enzyme, much of the activity is lost. The bireactant rate equation of the sequential type has been restated for the case of activation by one of the reactants. Since it has been found that activation of enzyme is linear with NADP⁺ concentration, it follows that the Michaelis constant for the steroid substrate is independent of the concentration of NADP⁺ activating the enzyme. This is substantiated by the determination of the Michaelis constant for 17β-estradiol-3-sulfate from data on double-reciprocal plots of activated and unactivated enzyme with limiting amounts of steroid. The activating effect increases linearly up to a concentration of 1.2 × 10^?5m of NADP⁺ and then levels off. The activation is highly specific for NADP⁺; neither NAD⁺, ATP, NADPH, nicotinic acid, ncr nicotinamide prevent the loss of activity after storing the enzyme for 1 hr at 37 °C. The steroid substrate appears to interfere with the activation of NADP⁺.     

Evaluation of half-life of immobilized enzyme during continuous reaction in bioreactors: A theoretical study

A theoretical study has been carried out on the evaluation of the apparent half-life of immobilized enzyme activity during continuous reaction both in a plug-flow reactor (PFR) and in a continuous-flow stirred-tank reactor (CSTR). Two apparent half-lives have been defined: the elapsed time at which the feedrate becomes half of the initial one when the feedrate of the substrate solution is lowered to keep the conversion fixed (constant-conversion policy), and the elapsed time at which the conversion becomes half of the initial one when the feedrate (or space velocity) is kept constant (constant-feedrate policy or constant-space-velocity policy). Under no intraparticle diffusional limitation, the constant-conversion policy of operation in the PFR and CSTR gives the same half-life as that of the enzyme inactivation regardless of the formula of the reaction rate, and the constant-feedrate policy of operation in the PFR and CSTR offers the same half-life as that of the enzyme inactivation only when the reaction is zero-order. Under intra-particle diffusional limitation, apparent half-lives are always greater than that of enzyme denaturation, depending on many factors such as order of reaction, feeding policy (constant-conversion and constant-feedrate policies), initial conversion, and bioreactor configuration. It is suggested to perform the continuous operation with changing feedrate to keep the conversion (or outlet substrate concentration) fixed under the domain of zero-order kinetics so as to obtain an apparent half-life as close to the real one in industrial operation.     

Kinetics, mechanism, and time course analysis of lipase-catalyzed hydrolysis of high concentration olive oil in AOT-isooctane reversed micelles

Candida rugosa lipase has been used to investigate the hydrolysis of high concentration olive oil in the AOT-isooctane reversed micellar system at W(o) = 10, pH 7.1, and 37 degrees C. Results from this work show the hydrolytic reaction obeys Michaelis-Menten kinetics up to the initial substrate concentration of 1.37M, with turnover number k(cat) and Michaelis constant K(M) of 67.1 mumol/min mg enzyme and 0.717M, respectively. A competitive inhibition by the main product, oleic acid, has been found with a dissociation constant K(I) for the complex EP* of 0.089M. The rate equation was further analyzed in the time course reaction and was found in agreement with the experimental results for lower substrate concentrations, up to 0.341M. Large deviation occurred at high substrate concentrations, which may be due to the effects of large consumption of water on kinetics, on the formation of glycerol, and on the deactivation of lipase in the hydrolysis reaction as well.     

The kinetics of penicillin-V deacylation on an immobilized enzyme

An immobilized Penicillin-V-acylase (commercial name, Novozym 217) with high specificity for the phenoxyacetyl-(V)- side chain was investigated in a recycle reactor and in a batch reactor to find the enzymatic reaction rate as a function of conversion, x, substrate concentration, c(A) (0) and pH. The reaction rate depends strongly on pH, and both products, phenoxy-acetic acid and 6-APA, inhibit the reaction. Nonspecific side reactions amount to only a few per cent when c(A) (0) <150mM and pH& gt; 6.5. The effectiveness factor for commercial-size particles is found to be about 0.65, and a value of 1.3mM is obtained for the equilibrium constant, K(eq), of the deacylation reaction. A kinetic model for the deacylation process which includes the effect of pH and of the reverse (acylation) reaction is proposed. Rate data for particles of different size are fitted to the nonlinear model. Five kinetic parameters and an effective diffusivity for the immobilized enzyme particles are determined.     

Acid-base chemistry of the reaction of aromatic L-amino acid decarboxylase and dopa analyzed by transient and steady-state kinetics: preferential binding of the substrate with its amino group unprotonated

Transient and steady-state kinetic analysis of the reaction of aromatic L-amino acid decarboxylase (AADC), a pyridoxal 5'-phosphate- (PLP-) dependent enzyme, with its substrate dopa was carried out at various pH. The association of AADC and dopa to form the Michaelis complex and the subsequent transaldimination reaction to form the dopa-PLP Schiff base (external aldimine) were followed with a stopped-flow spectrophotometer. Combined with the steady-state k(cat) value, we could present a minimum mechanism for the reaction of AADC and dopa. In the mechanism, the association of the aldimine-protonated form of the enzyme (EH(+)) and the alpha-amino-group-unprotonated form of the substrate (S) is the main route leading to the Michaelis complex. In addition, the association of EH(+) and the alpha-amino-group-protonated form of the substrate (SH(+)) to form a Michaelis complex EH(+).SH(+) was also found as a minor route. The pK(a) of the alpha-amino group of dopa was expected to be decreased in the Michaelis complex, promoting the conversion of EH(+).SH(+) to EH(+).S, the species that directly undergoes transaldimination to form the external aldimine complex. The association of EH(+) and S had been identified as a minor route for the reaction of aspartate and aspartate aminotransferase (AspAT), which has an unusually low pK(a) value of the aldimine and can use the aldimine-unprotonated form (E) of the enzyme for adsorbing the prevalent species SH(+) [Hayashi and Kagamiyama (1997) Biochemistry 36, 13558-13569]. The present study implies that, in most PLP enzymes that have a high pK(a) value of the aldimine like AADC, S preferentially binds to the enzyme (EH(+)). The minor route of EH(+) + SH(+) in AADC may be related to the flexibility of the protein in the Michaelis complex, and a simulation analysis showed that the presence of this route decreases the k(cat) value while increasing the k(cat)/K(m) value. It also suggested that AADC has evolved to suppress the minor route to the extent necessary to obtain the maximal k(cat) value at neutral pH.