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.     

Immobilized enzymes: electrokinetic effects on reaction rates in a porous medium

The effect of the internal diffusion and electrical surface charge on the overall rate of a reaction catalyzed by an enzyme immobilized on a porous medium are examined. Effectiveness factors have been calculated which compare the global reaction rate to that existing in the absence of the internal diffusion and/or the electrical field. The surface charge, assumed to arise from the dissociation equilibria of the acidic and basic surface groups of the enzyme, generates an electrical double layer at the pore surface. The double-layer potential is governed by the Poisson-Boltzmann equation. It is shown that the diffusion potential can be characterized by a modulus which depends upon the surface reaction rate, the charges and diffusivities of the substrate and products, the ionic strength, and the pore dimensions. The flux of a charged species in the pore occurs under the influences of the concentration gradient and the electrical potential gradient. The governing equations are solved by an iterative numerical method. The effects of pH, enzyme concentration, and substrate concentration on the rates of two different hydrolysis reactions catalyzed by immobilized papain are examined. The release of H(+) in one of the reactions causes the lowering of internal pH, and also a constancy of the internal pH when the external pH in creases beyond a certain value. The latter reaction also shows a maximum in the reaction rate with respect to enzyme concentration. The reaction not involving H(+) as a product shows a maximum in the reaction rate with respect to external pH, but a monotonic increase in the reaction rate as the enzyme concentration increases.     

Non-porous magnetic micro-particles: comparison to porous enzyme carriers for a diffusion rate-controlled enzymatic conversion

In this study the kinetics of conversion of a low-soluble substrate by an immobilized enzyme was investigated with respect to the diffusion limitation within porous and non-porous carriers. Non-porous micro-magnetic beads in comparison to conventional porous supports like Eupergit and Sepharose were tested. Due to their small diameters and their magnetic properties, micro-magnetic beads are especially applicable in diffusion rate-controlled processes in biological suspensions. The enzymatic reaction studied was the conversion of emulsified dirhamnolipid by immobilized Naringinase from Penicillium decumbens to monorhamnolipid and L-rhamnose. Taking into account mass transfer phenomena, the variation of the reaction effectiveness factor with increasing enzyme loading was estimated and compared with experimental efficiencies utilizing different enzyme loaded immobilized preparations. For comparison, carrier activities were also determined with the model substrate p-nitro-phenyl-rhamnoside. Intrinsic enzyme activities were thereby evaluated for porous supports. Highest specific activities were obtained with the micro-magnetic beads. These non-porous micro-beads demonstrated to be the most suitable carrier for bioconversion of a low-soluble substrate like rhamnolipids, where mass diffusional resistances in the three-phase reaction process are completely overcome. However, the smaller particle surface available limited the specific activity obtained at high protein loadings.     

Optimization of urease immobilization onto non-porous HEMA incorporated poly(EGDMA) microbeads and estimation of kinetic parameters.

Jack bean urease (urea aminohydrolase, EC 3.5.1.5) was immobilized onto modified non-porous poly(ethylene glycol dimethacrylate/2-hydroxy ethylene methacrylate), (poly(EGDMA/HEMA)), microbeads prepared by suspension copolymerization for the potential use in hemoperfusion columns, not previously reported. The conditions of immobilization; enzyme concentration, medium pH, substrate and ethylene diamine tetra acetic acid (EDTA) presence in the immobilization medium in different concentrations, enzyme loading ratio, processing time and immobilization temperature were investigated for highest apparent activity. Immobilized enzyme retained 73% of its original activity for 75 days of repeated use with a deactivation constant kd = 3.72 x 10(-3) day(-1). A canned non-linear regression program was used to estimate the intrinsic kinetic parameters of immobilized enzyme with a low value of observable Thiele modulus (phi < 0.3) and these parameters were compared with those of free urease. The best-fit kinetic parameters of a Michaelis-Menten model were estimated as Vm = 3.318 x 10(-4) micromol/s mg bound enzyme protein, Km = 15.94 mM for immobilized, and Vm = 1.074 micromol NH3/s mg enzyme protein, Km = 14.49 mM for free urease. The drastic decrease in Vm value was attributed to steric effects, conformational changes in enzyme structure or denaturation of the enzyme during immobilization. Nevertheless, the change in Km value was insignificant for the unchanged affinity of the substrate with immobilization. For higher immobilized urease activity, smaller particle size and concentrated urease with higher specific activity could be used in the immobilization process.     

Acetic acid formation in Escherichia coli fermentation

Theoretical analysis of cellulase product inhibition (by cellobiose and glucose) has been performed in terms of the mathematical model for enzymatic cellulose hydrolysis. The analysis showed that even in those cases when consideration of multienzyme cellulase system as one enzyme (cellulase) or two enzymes (cellulase and beta-glucosidase) is valid, double-reciprocal plots, usually used in a product inhibition study, may be nonlinear, and different inhibition patterns (noncompetitive, competitive, or mixed type) may be observed. Inhibition pattern depends on the cellulase binding constant, enzyme concentration, maximum adsorption of the enzyme (cellulose surface area accessible to the enzyme), the range in which substrate concentration is varied, and beta-glucosidase activity. A limitation of cellulase adsorption by cellulose surface area that may occur at high enzyme/substrate ratio is the main reason for nonlinearity of double-reciprocal plots. Also, the results of calculations showed that material balance by substrate, which is usually neglected by researchers studying cellulase product inhibition, must be taken into account in kinetic analysis even in those cases when the enzyme concentration is rather low. (c) 1992 John Wiley & Sons, Inc.     

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.     

The kinetic mechanism and properties of the cytoplasmic acetoacetyl-coenzyme A thiolase from rat liver

1. Cytoplasmic acetoacetyl-CoA thiolase was highly purified in good yield from rat liver extracts. 2. Mg(2+) inhibits the rate of acetoacetyl-CoA thiolysis but not the rate of synthesis of acetoacetyl-CoA. Measurement of the velocity of thiolysis at varying Mg(2+) but fixed acetoacetyl-CoA concentrations gave evidence that the keto form of acetoacetyl-CoA is the true substrate. 3. Linear reciprocal plots of velocity of acetoacetyl-CoA synthesis against acetyl-CoA concentration in the presence or absence of desulpho-CoA (a competitive inhibitor) indicate that the kinetic mechanism is of the Ping Pong (Cleland, 1963) type involving an acetyl-enzyme covalent intermediate. In the presence of CoA the reciprocal plots are non-linear, becoming second order in acetyl-CoA (the Hill plot shows a slope of 1.7), but here this does not imply co-operative phenomena. 4. In the direction of acetoacetyl-CoA thiolysis CoA is a substrate inhibitor, competing with acetoacetyl-CoA, with a K(i) of 67mum. Linear reciprocal plots of initial velocity against concentration of mixtures of acetoacetyl-CoA plus CoA confirmed the Ping Pong mechanism for acetoacetyl-CoA thiolysis. This method of investigation also enabled the determination of all the kinetic constants without complication by substrate inhibition. When saturated with substrate the rate of acetoacetyl-CoA synthesis is 0.055 times the rate of acetoacetyl-CoA thiolysis. 5. Acetoacetyl-CoA thiolase was extremely susceptible to inhibition by an excess of iodoacetamide, but this inhibition was completely abolished after preincubation of the enzyme with a molar excess of acetoacetyl-CoA. This result was in keeping with the existence of an acetyl-enzyme. Acetyl-CoA, in whose presence the overall reaction could proceed, gave poor protection, presumably because of the continuous turnover of acetyl-enzyme in this case. 6. The kinetic mechanism of cytoplasmic thiolase is discussed in terms of its proposed role in steroid biosynthesis.     

Pore diffusion model for a two-substrate enzymatic reaction: Application to galactose oxidase immobilized on porous glass particles

An analysis of the pore diffusion model involving a two-substrate enzymatic reaction is presented. The resulting equations have been applied to the case of galactose oxidase catalyzed oxidation of galactose when the enzyme is immobilized on porous glass particles. The physical constants of the system were obtained by theoretical predictions and the enzyme concentration in the porous medium was derived from the experimental results. The calculations were performed with the assumption that the kinetic parameters of the enzyme remain unchanged upon immobilization. The theoretically calculated effectiveness factors were compared with the experimental effectiveness factors determined from the batch kinetic experiments and were found to be in agreement. The results are presented as effectiveness factor plots graphed as functions of bulk galactose and oxygen concentrations. The model was extended in order to study the effect of external mass transfer coefficients and pore enzyme concentrations on the effectiveness factors.     

Study of substrate-enzyme interaction between immobilized pyridoxamine and recombinant porcine pyridoxal kinase using surface plasmon resonance biosensor

Pyridoxal kinase (PK) is an important enzyme involved in bioactivation of vitamin B(6). Binding of PK with its substrate is the prerequisite step for the subsequent catalytic phosphorylation of the substrate. In the present study, a surface plasmon resonance biosensor (BIAcore) was employed to characterize the binding interaction between wild-type porcine PK and an immobilized substrate, pyridoxamine. Pyridoxamine was modified with 11-mercaptoundecanic acid and immobilized on a sensor chip through the formation of a self-assembled monolayer. The binding of PK to the immobilized pyridoxamine was followed in real time and the kinetic parameters were derived from non-linear analysis of the sensorgram. The effects of buffer pH, monovalent cations (Na(+), K(+)) and divalent cations (Mn(2+), Zn(2+), Mg(2+)) on the binding kinetics were determined. Optimal pH for PK-pyridoxamine interaction in the absence of divalent ions is at around 7.4. While K(+) increased and Na(+) decreased the binding affinity (K(A)) of PK to immobilized pyridoxamine, all divalent cations increased the K(A) of PK for pyridoxamine. Solution phase affinity measurement based on a competitive binding assay was used to determine the affinities of PK for different vitamin B(6) analogues. The order of affinity of PK for different analogues is: pyridoxal-oxime>pyridoxine>pyridoxamine>pyridoxal>pyridoxal phosphate. This is the first study to demonstrate that buffer conditions such as pH and concentration of monovalent and/or divalent ions can directly alter the binding of PK for its substrates. The quantitative kinetic and thermodynamic parameters obtained by SPR measurement provide the insight information into the catalytic activity of this enzyme.     

Effect of pore diffusion limitation on dextrin hydrolysis by immobilized glucoamylase

Data reported here and previously indicate that when dextrin is hydrolyzed in the presence of immobilized glucoamylase, use of a larger average molecular weight substrate leads to lower overall rates of hydrolysis, while the maltose concentration during the bulk of the reaction and the maximum glucose concentration are lower than when the soluble form of the enzyme is employed under the same conditions. Computer simulation of the system demonstrated that all three observations were caused by pore diffusion limitation: the first by slow diffusion of substrate, the second by slow diffusion of intermediates, and the third by slow diffusion of glucose. Follow-up experiments with glucoamylase immobilized to particles of different sizes confirmed this finding, as results with the smallest beads were identical to those with soluble glucoamylase.     

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.     

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.     

Analysis of the transient response of a CSTR containing immobilized enzyme particles: Part I. Model development and analysis of the influence of operating conditions and process parameters

The transient response of the bulk substrate concentration in a CSTR containing immobilized enzyme (IMEs) in porous solid supports and the possibilities of exploiting the minimum behavior for parameter estimation purposes are studied in this work. For that purpose, mathematical models have been developed for several kinetic expressions with parallel deactivation mechanisms and for two different particle shapes (cylindrical and spherical). The influence of a number of system variables and non-dimensional parameters, i.e., pellet radius, mass of particles, flow rate, effective diffusivity, mass transfer coefficient, Thiele modulus, Michaelis constant, and enzyme deactivation constant, is also reported in a systematic way. Simulations, using realistic data, show that the minimum bulk substrate concentration is sufficiently pronounced and the time scale for the minimum to occur is sufficiently practical, so that it can be used to extract several parameters of the immobilized enzyme system.     

Enhanced recombinant protein production and differential expression of molecular chaperones in sf-caspase-1-repressed stable cells after baculovirus infection

Background

Industrial-scale biocatalytic synthesis of fine chemicals occurs preferentially as continuous processes employing immobilized enzymes on insoluble porous carriers. Diffusional effects in these systems often create substrate and product concentration gradients between bulk liquid and the carrier. Moreover, some widely-used biotransformation processes induce changes in proton concentration. Unlike the bulk pH, which is usually controlled at a suitable value, the intraparticle pH of immobilized enzymes may deviate significantly from its activity and stability optima. The magnitude of the resulting pH gradient depends on the ratio of characteristic times for enzymatic reaction and on mass transfer (the latter is strongly influenced by geometrical features of the porous carrier). Design and selection of optimally performing enzyme immobilizates would therefore benefit largely from experimental studies of the intraparticle pH environment. Here, a simple and non-invasive method based on dual-lifetime referencing (DLR) for pH determination in immobilized enzymes is introduced. The technique is applicable to other systems in which particles are kept in suspension by agitation.

Results

The DLR method employs fluorescein as pH-sensitive luminophore and Ru(II) tris(4,7-diphenyl-1,10-phenantroline), abbreviated Ru(dpp), as the reference luminophore. Luminescence intensities of the two luminophores are converted into an overall phase shift suitable for pH determination in the range 5.0-8.0. Sepabeads EC-EP were labeled by physically incorporating lipophilic variants of the two luminophores into their polymeric matrix. These beads were employed as carriers for immobilization of cephalosporin C amidase (a model enzyme of industrial relevance). The luminophores did not interfere with the enzyme immobilization characteristics. Analytical intraparticle pH determination was optimized for sensitivity, reproducibility and signal stability under conditions of continuous measurement. During hydrolysis of cephalosporin C by the immobilizate in a stirred reactor with bulk pH maintained at 8.0, the intraparticle pH dropped initially by about 1 pH unit and gradually returned to the bulk pH, reflecting the depletion of substrate from solution. These results support measurement of intraparticle pH as a potential analytical processing tool for proton-forming/consuming biotransformations catalyzed by carrier-bound immobilized enzymes.

Conclusions

Fluorescein and Ru(dpp) constitute a useful pair of luminophores in by DLR-based intraparticle pH monitoring. The pH range accessible by the chosen DLR system overlaps favorably with the pH ranges at which enzymes are optimally active and stable. DLR removes the restriction of working with static immobilized enzyme particles, enabling suspensions of particles to be characterized also. The pH gradient developed between particle and bulk liquid during reaction steady state is an important carrier selection parameter for enzyme immobilization and optimization of biocatalytic conversion processes. Determination of this parameter was rendered possible by the presented DLR method.     

Consecutive immobilized enzymatic reactions with and without enzyme denaturation

Consecutive biochemical reactions in an immobilized enzyme particle under the effects of internal and external diffusional resistances are analyzed. A rigorous nonlinear reaction kinetics is employed and the steady state effectiveness factor with negligible enzyme denaturation compared with the previous prediction by the first-order kinetics. It is found that the difference between them is rather substantial under most circumstances. The cases with significant enzyme denaturation are also investigated by using an unsteady state model. The substrate concentration responses to variation of the physical and kinetic parameters reveal many interesting characteristics of the reaction system.     

A Fortran Program for Evaluation of the Effectiveness Factor of Biocatalysts in the Presence of External and Internal Diffusional Limitations

A Fortran program called SPEFF for evaluation of the effectiveness factor of immobilized enzyme preparations of spherical form in the presence of external and internal mass transfer resistances is described, and a listing of the program is given. Enzyme distribution in the bioparticle may be uniform or nonuniform. In the latter case the enzyme distribution is approximated by fifth-order polynomial. In the program differential equations are replaced by the system of non-linear algebraic equations, and the latter are solved by Newton iteration technique. The program is developed for Michaelis-Menten kinetics with allowance for competitive product inhibition and substrate inhibition. After slight modifications the program can be used for computation of the effectiveness factor of a membrane with an immobilized enzyme, or in the case when the enzyme kinetics are more complex. A typical run on a PDP-11/45 computer took 10-20 seconds. A typical computation time in the case of IBM-compatible TURBO PC was 15-30 seconds.     

A linear equation that describes the steady-state kinetics of enzymes and subcellular particles interacting with tightly bound inhibitors

When an enzyme exhibits a high affinity for an inhibitor, the steady-state analysis of the mechanism is complicated by the non-linearity of normal dose-response plots or of reciprocal replots. It is shown here that dose-response measurements generate a linear plot of inhibitor concentration divided by degree of inhibition against velocity without inhibitor divided by velocity with inhibitor; the concentration of enzyme may be derived from the extrapolated intercept of such plots, and the mechanism of inhibition from replots of the variation of the slope with substrate concentration. The limiting cases where virtually all inhibitor molecules are bound or virtually all are free are described, together with the situation when a significant proportion of the substrate becomes bound. This type of analysis indicates that the inhibitors of oxidative phosphorylation, rutamycin and bongkrekic acid, are tightly bound to rat liver mitochondria.     

Degradation of ribonucleic acid by immobilized ribonuclease.

An immobilized enzyme (pancreatic ribonuclease bound to porous titania) was investigated for the degradation of purified yeast ribonucleic acid as a substrate. The immobilized enzyme is active and stable in the pH range 4--8. Dependence of enzymatic activity on ionic strength, pH, temperature, fluid flow rate, and substrate concentration were investigated. A cumulative fluid residence time of 6 sec is sufficient for 50% substrate conversion at 25 degrees C and pH 7.0. The critical flow rate (i.e., the fluid flow rate necessary to remove film diffusion resistance) approximately doubles with each 10 degree C rise in reaction temperature. The critical flow rates obtained in this study are about 40 times greater than those obtained for a similar study on immobilized glucose oxidase. Arrhenius plots gave activation energies of -9.6 and -7.1 kcal/g mol at pH 4.6 and 7.0, respectively. The work reported herein is a bench-scale investigation of an immobilized enzyme with primary emphasis on the mass transfer and kinetic characteristics of the system. The rapid reaction rates obtainable at relatively low temperatures offer a potential alternative method of purifying yeast single cell protein (SCP) with miminum loss of desired protein. The key questions are how such a system would react in a yeast homogenate, what conditions in such a system must be controlled, and what type of immobilized reactor should be utilized, if such further work continued to show promise.     

Development of sensors for direct detection of organophosphates. Part I: Immobilization, characterization and stabilization of acetylcholinesterase and organophosphate hydrolase on silica supports

Biosensors for organophosphates in solution may be constructed by monitoring the activity of acetylcholinesterase (AChE) or organophosphate hydrolase (OPH) immobilized to a variety of microsensor platforms. The area available for enzyme immobilization is small (< 1 mm2) for microsensors. In order to construct microsensors with increased surface area for enzyme immobilization, we used a sol-gel process to create highly porous and stable silica matrices. Surface porosity of sol-gel coated surfaces was characterized using scanning electron microscopy; pore structure was found to be very similar to that of commercially available porous silica supports. Based upon this analysis, porous and non-porous silica beads were used as model substrates of sol-gel coated and uncoated sensor surfaces. Two different covalent chemistries were used to immobilize AChE and OPH to these porous and non-porous silica beads. The first chemistry used amine-silanization of silica followed by enzyme attachment using the homobifunctional linker glutaraldehyde. The second chemistry used sulfhydryl-silanization followed by enzyme attachment using the heterobifunctional linker N-gamma-maleimidobutyryloxy succinimide ester (GMBS). Surfaces were characterized in terms of total enzyme immobilized, total and specific enzyme activity, and long term stability of enzyme activity. Amine derivitization followed by glutaraldehyde linking yielded supports with greater amounts of immobilized enzyme and activity. Use of porous supports not only yielded greater amounts of immobilized enzyme and activity, but also significantly improved long term stability of enzyme activity. Enzyme was also immobilized to sol-gel coated glass slides. The mass of immobilized enzyme increased linearly with thickness of coating. However, immobilized enzyme activity saturated at a porous silica thickness of approximately 800 nm.     

Ca2+ and calmodulin antagonists inhibit the proton gradients associated with non-cyclic and cyclic photophosphorylation in spinach chloroplasts

The synthesis of benzylpenicillin (BP) after mixing phenyl-acetyl-glycine(PAG), 6-aminopenicillanic acid (6-APA) and free or immobilized penicillin amidase (E.C.3.5.1.11.) was studied as a function of pH and ionic strength. Before the final equilibrium was reached a kinetically controlled synthesis of BP was observed. Then a transient maximum concentration in BP much larger than the final equilibrium content was synthesized in the acyl-transfer process. The factors influencing this maximum have been analyzed. Increasing ionic strength markedly decreased the maximum in BP and the rate of deacylation of phenyl-acetyl-penicillin amidase by 6-APA. The change was largest when the enzyme was immobilized in a positively charged support, where at low ionic strength the concentration of 6-APA around the enzyme is larger than the bulk concentration due to the partitioning of charged solutes.