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.     

Whole-cell hollow-fiber reactor: Effectiveness factors

Analytical expressions, which allow the generation of effectiveness factor graphs for a reactor system employing immobilized whole cells a biocatalyst, are presented. In particular hollow-fiber devices (such as dialysis or ultrafiltration units) are considered. Such devices are analogs to a shell-and-tube heat exchanger. Whole cells are entrapped on the shell side: a nutrient solution is circulated through the tubes, substrate diffuses from the tube side, across the fiber, and into the cell mass on the shell side, where it irreversibly reacts to form product. The product back-diffuses into the circulating nutrient solution. The overall substrate mass-transfer process is hypothesized to be either diffusion limited in the hollow-fiber tube wall and/or the shell-side cell suspension and/or reaction limited at the enzyme sites within the whole cells. The first- and zero-order limits of the Michaelis-Menten rate law are used in generating effectiveness factor expressions. The effectiveness factor is a function of reaction order, Thiele modulus, diffusion coefficient ratio (defined as the effective substrate diffusivity in the hollow-fiber membrane wall divided by the effective substrate diffusivity in the cell suspension), partition coefficient, volume of the cell suspension, and hollow-fiber width. Equations for the effectiveness factor are also detailed when the hollow-fiber mass-transfer resistance is far greater than the cell suspension mass-transfer resistance. An effectiveness factor chart is presented specifically for the commercially available C-DAK 4 dialyzer (Cordis Dow Co., Miami, Florida). In general terms the effectiveness factor expressions are applicable for characterizing diffusion and reaction within a catalytically active cylindrical annulus, Whose inner surface offers a diffusional resistance and whose outer surface is impermeable to reactants. Some generalization of the Thiele modulus is undertaken which serves to draw the asymptotes on the effectiveness factor charts together. Comment is made on the variation of the slope of the effectiveness factor graph and its relation to the change in the observed reaction activation energy. Possible application of the model to the catalytic tube wall reactor is discussed.     

Lipase kinetics: hydrolysis of triacetin by lipase from Candida cylindracea in a hollow-fiber membrane reactor

The aptitude of a hollow-fiber membrane reactor to determine lipase kinetics was investigated using the hydrolysis of triacetin catalyzed by lipase from Canadida cylindracea as a model system. The binding of the lipase to the membrane appears not to be very specific (surface adsorption), and probably its conformation is hardly altered by immobilization, resulting in an activity comparable to that of the enzyme in its native form. The reaction kinetics defined on the membrane surface area were found to obey Michaelis-Menten kinetics. The specific activity of the lipase in the membrane reactor was found to be significantly higher than in an emulsion reactor. The activity and stability of the enzyme immobilized on a hydrophilic membrane surface seem not to be influenced significantly by the choice of the membrane material. The hollow-fiber membrane reactor is a suitable tool to assess lipase kinetics in a fast and convenient way.     

Mass-transfer limitations for immobilized enzyme-catalyzed kinetic resolution of racemate in a fixed-bed reactor

A mathematical model has been developed for immobilized enzyme-catalyzed kinetic resolution of racemate in a fixed-bed reactor in which the enzyme-catalyzed reaction (the irreversible uni-uni competitive Michaelis-Menten kinetics is chosen as an example) was coupled with intraparticle diffusion, external mass transfer, and axial dispersion. The effects of mass-transfer limitations, competitive inhibition of substrates, deactivation on the enzyme effective enantioselectivity, and the optical purity and yield of the desired product are examined quantitatively over a wide range of parameters using the orthogonal collocation method. For a first-order reaction, an analytical solution is derived from the mathematical model for slab-, cylindrical-, and spherical-enzyme supports. Based on the analytical solution for the steady-state resolution process, a new concise formulation is presented to predict quantitatively the mass-transfer limitations on enzyme effective enantioselectivity and optical purity and yield of the desired product for a continuous steady-state kinetic resolution process in a fixed-bed reactor.     

Enzymes are open systems

The exchange of mass, energy, and information with the environment typical of open systems can also be found in enzymes. An enzyme is able to receive information on substrate concentration in an arbitrary concentration range. This actually follows from the elementary solution of Michaelis-Menten kinetics. The Michaelis constant can be seen as a relation between the decreasing parameter of a zero-order reaction and the increasing parameter of a first-order reaction over a certain time interval. This excludes the state of zero-order kinetics and consequently the state of zero content of concentration information.     

Determination of effective diffusion coefficient of substrate in gel particles with immobilized biocatalyst

A method of determining of the effective diffusion coefficient of substrate in a particle, where the diffusion and consumption of substrate by biocatalytic reaction are present simultaneously, was designed and experimentally verified. The method is based on measuring the overall rate of heterogeneous biocatalytic reaction in particles of varying diameter. The effective diffusion coefficient, D_e, was determined by fitting the measured reaction rates with the solution of the reaction-diffusion equation. The method is tailored for cases where the enzyme reaction is governed by the Michaelis-Menten kinetics. The value of K_m required for the solution of the mathematical model was adopted from the measurement of the kinetics of free cells, whereas the rate parameter, k₂, was optimized together with D_e. As an experimental model, the sucrose hydrolysis catalyzed by Ca-alginate-entrapped yeast cells was examined. The particle diameter varied in the range of 1.2–3.9 mm and the initial reaction rates were measured in a batch-stirred reactor at a sucrose concentration of 100 m . The D_e of sucrose at 30°C was found to be 2.9 · 10⁻¹⁰ m²s⁻¹.     

External and internal diffusion in heterogeneous enzymes systems

The intrusion of diffusion in heterogeneous enzyme reactions, which follow. Michaelis-Menten kinetics, is quantitatively characterized by dimensionless parameters that are independent of the substrate concentration. The effects of these parameters on the overall rate of reaction is illustrated on plots commonly employed in enzyme kinetics. The departure from Michaelis-Menten kinetics due to diffusion limitations can be best assessed by using Hofstee plots which are also suitable to distinguish between internal and external transport effects. A graphical method is described for the evaluation of the reaction rate as a function of the surface concentration of the substrate from measured data.     

Estimation of intrinsic kinetic constants for pore diffusion-limited immobilized enzyme reactions

A simple method is presented that establishes intrinsic rate parameters when slow pore diffusion of substrate limits immobilized enzyme reactions that obey Michaelis-Menten kinetics. The Aris-Bischoff modulus is employed. Data at high substrate concentrations, where the enzyme would be saturated in the absence of diffusion limitation, and at low substrate concentrations, where effectiveness factors are inversely proportional to reaction modulus, are used to determine maximum rate and Michaelis constant, respectively. Because Michaelis-Menten and Langmuir-Hinshelwood kinetics are formally identical, this method may be used to estimate intrinsic rate parameters of many heterogeneous catalysts. The technique is demonstrated using experimental data from the hydrolysis of maize dextrin with diffusion-limited immobilized glucoamylase. This system yields a Michaelis constant of 0.14%, compared to 0.11% for soluble glucoamylase and 0.24% for immobilized glucoamylase free of diffusional effects.     

Theory of the kinetics of reactions catalyzed by enzymes attached to membranes

A theoretical treatment has been worked out for the kinetics of solid-supported enzyme systems, with diffusive and electrostatic effects taken into account. A utilization factor, defined as the ratio of the actual reaction rate to the rate of substrate consumption in the outer solution, is defined, and equations to evaluate the utilization factor are given for five kinetic conditions: (a) Michaelis-Menten behavior, (b) substrate inhibition, (c) product inhibition (competitive), (d) product inhibition (noncompetitive), and (e) product inhibition (anticompetitive). When the solid-supported enzymes obey a Michaelis-Menten relationship, an equation for the apparent Michaelis constant is given and a criterion for insignificant diffusion effects is shown. A substrate-inhibited enzyme reaction may display multiple steady-state behavior, and a criterion for uniqueness is presented. In the case of product-inhibited enzyme reactions, the utilization factor is always less than that which corresponds to a Michaelis-Menten relationship. Equations to evaluate the apparent Michaelis and inhibition constants are given.     

Performance of a β-d-galactosidase hollow fibre reactor

β-d-Galactosidase was immobilized in a hollow fibre ultrafiltration module. The hydrolysis of 2-nitrophenyl β-d-galactopyranoside (ONPG) was significantly affected by enzyme loading, flow rate and substrate concentration. Pretreatment of hollow fibres with a protein was necessary to minimize enzyme inactivation. Residence time distribution studies indicated that the product of the reaction (ONP) was significantly adsorbed by the fibres, which resulted in the reactor taking 10–30 h to achieve steady-state. An equation based on Michaelis-Menten kinetics and a plug-flow model adequately described the performance of the reactor with regard to operating variables, even though some diffusion effects were observed.     

A re-examination of oxygen diffusion in a spherical cell with michaelis-menten oxygen uptake kinetics

Oxygen diffusion in a spherical cell with Michaelis-Menten oxygen uptake kinetics is re-examined and the results of a recent paper by Lin corrected. An extension of this model to include external diffusion is made and its effect is shown to be significant. A model which attempts to model the nucleus as a central sphere which does not consume any oxygen is also investigated. Finally, a perturbation solution for a small Michaelis constant is developed.     

Kinetic study of a hollow-fiber enzyme reactor

Enzymes, such as urease and uricase, were entrapped in three kinds of hollow fibers. The apparent Michaelis–Menten constants K_m(app) obtained for these enzyme reactors were always larger than K_m of free enzyme because of the permeation resistance of substrate across the hollow-fiber membrane. K_m(app) increased with increasing degree of permeation resistance across the membrane by the increase in enzyme concentration. The half-life of the entrapped urease in the continuous reaction system was 60–80% of that of free enzyme. Activation energies of hollow-fiber enzyme reactors were always smaller than that of the free enzyme, because the activation energy of permeation was smaller than that of the enzyme reaction.     

Production of lipolyzed butteroil by a calf pregastric esterase immobilized in a hollow fiber reactor: III. Effect of glycerol

Lipolysis of butter oil in a hollow fiber reactor containing an immobilized calf pregastric esterase was studied at 40 degrees C, a pH of 6.0, and glycerol concentrations of 0, 150, and 500 g/L in the buffer solution. The concentrations of 10 fatty acid species in the lipolyzed product were determined using high-performance liquid chromatography. The rate of loss of enzyme activity and the relative selectivities of this esterase depended on the glycerol concentration. By contrast, the overall rate of release of fatty acids was not affected by the glycerol concentration. Loss of enzyme activity was modeled using first-order kinetics. The models for deactivation and reaction kinetics were fit simultaneously to the data. The model was successful in describing the rates of release of all 10 fatty acid species for a range of space times from 0 to 25 h. The parameters of the model were tested for dependence on glycerol concentration.     

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.     

Enzyme reactions at the surface of living cells. I. Electric repulsion of charged ligands and recognition of signals from the external milieu

The dynamic behaviour of a polyelectrolyte-bound enzyme is studied when diffusion of substrate or diffusion of product is coupled to electric repulsion and to Michaelis-Menten enzyme reaction. The definition of the classical concepts of electric partition coefficients and Donnan potential of a polyelectrolyte membrane has been extended under global non-equilibrium conditions. This extension is permissible when a strong repulsion exists of substrate and product by the fixed negative charges of the membrane. Coupling between product diffusion, electric repulsion and enzyme reaction at constant advancement may result in a hysteresis loop of the partition coefficient as the product concentration is increased in the reservoir. This hysteresis loop vanishes as the rate of product diffusion increases. No hysteresis loop may occur when electric repulsion effects are coupled to substrate diffusion and reaction. The existence of multiple values of the partition coefficient for a fixed concentration of product implies that the membrane may store short-term memory of the former product concentration present in the external milieu. The occurrence of hysteresis generated by coupling enzyme reaction, product diffusion, electric partition effects at constant advancement of the reaction may be viewed as a sensing device of product concentration in the external milieu. Surprisingly, non-linearities required to generate this sensing device come from electrostatic effects and not from enzyme kinetics.     

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

The lipolysis of butter oil in a hollow-fiber reactor containing an immobilized calf pregastric esterase was studied at 40 degrees C and at pH values of 4.0, 5.0, 6.0, and 7.0. The concentrations of ten fatty acid species in the lipolyzed product were determined using high-performance liquid chromatography (HPLC). The relative specificity of this esterase depended on pH. Three mathematical models derived from a generalized Michaelis-Menten mechanism were tested for their ability to describe the rates of release of individual specific fatty acids. Loss of enzyme activity was modeled using first order kinetics. The models for deactivation and reaction kinetics were fit simultaneously to the data. The parameters of the model were also tested for dependence on pH. The model was successful in describing the rates of release of all ten fatty acid species for a range of space times and pH values.     

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.     

Immobilized glucoamylase on porous glass

A study was made to determine the controlling mass transfer resistance in the overall reaction rate for conversion of maltose to glucose, catalyzed by glucoamylase immobilized onto porous glass. For normal operation of a packed column and air-stirred batch reactor, the rate controlling step was found to be the internal resistance of simultaneous pore diffusion and chemical reaction. Experimental effectiveness factors were determined and are compared with those derived from a theoretical diffusion model based on Michaelis-Menten kinetics. Also given are temperature and pH relationships for the free and immobilized glucoamylase.     

Properties of urease immobilized on the functional organic silica surface

The paper deals with kinetics of the urea hydrolysis by microbial-origin urease dissolved and immobilized on the organic silica surface. It is shown that hydrolysis kinetics for soluble urease is described by the Michaelis-Menten equation until the concentration of urea reaches 1 M. Two fractions differing in the Michaelis constant are revealed for silochrome immobilized urease. The rate of urea hydrolysis by native and immobilized urease was studied depending on the pH value in presence of the substrate in the 1 M and 5 mM concentration. The hydrolysis rate of 1 M urea in the buffer-free solution by silochrome-immobilized urease is practically independent of pH within 4.5-6.5. Application of a 2.5 mM phosphate-citrate buffer as a solvent causes an increase in the hydrolysis rate within this pH range. For a soluble urease the 1 M urea hydrolysis rate dependence on pH is ordinary at pH 5.8-6.0. If the substrate concentration is 5 mM, the pH-dependences for the rate of the urea hydrolysis by silochrome- and aerosil-immobilized urease are close and at pH above 6.0 coincide with those for a soluble enzyme. The found differences in the properties of soluble and immobilized ureases are explained by the substrate and reaction products diffusion.     

An enzyme rate equation for the overall rate of reaction of gel-immobilized glucose oxidase particles under buffered conditions. I. Pseudo-one substrate conditions

The overall rate of reaction of buffered gel-immobilized glucose oxidase particles is described by means of an enzyme rate equation which relates the overall reaction rate of a particle to the free solution characteristics of the enzyme, the effective diffusivity of the limiting substrate in the gel, the characteristic particle size, and the limiting substrate concentration adjacent to the gel surface. This equation accounts quantitatively for the limitation of the overall rate of reaction by substrate diffusion, and it is used to illustrate the influence of the system parameters, i. e., particle size, enzyme concentration, and pH, on the extent of the diffusional resistance associated with gel-immobilized glucose oxidase particles. The enzyme rate equation is generally applicable to those enzymes whose kinetics approximately follow Michaelis-Menten form when in free solution.