Modelling of the enzymatic kinetically controlled synthesis of cephalexin: influence of diffusion limitation

In this study the influence of diffusion limitation on enzymatic kinetically controlled cephalexin synthesis from phenylglycine amide and 7-aminodeacetoxycephalosporinic acid (7-ADCA) was investigated systematically. It was found that if diffusion limitation occurred, both the synthesis/hydrolysis ratio (S/H ratio) and the yield decreased, resulting in lower product and higher by-product concentrations. The effect of pH, enzyme loading, and temperature was investigated, their influence on the course of the reaction was evaluated, and eventually diffusion limitation was minimised. It was found that at pH >or=7 the effect of diffusion limitation was eminent; the difference in S/H ratio and yield between free and immobilised enzyme was considerable. At lower pH, the influence of diffusion limitation was minimal. At low temperature, high yields and S/H ratios were found for all enzymes tested because the hydrolysis reactions were suppressed and the synthesis reaction was hardly influenced by temperature. The enzyme loading influenced the S/H ratio and yield, as expected for diffusion-limited particles. For Assemblase 3750 (the number refers to the degree of enzyme loading), it was proven that both cephalexin synthesis and hydrolysis were diffusion limited. For Assemblase 7500, which carries double the enzyme load of Assemblase 3750, these reactions were also proven to be diffusion limited, together with the binding-step of the substrate phenylglycine amide to the enzyme. For an actual process, the effects of diffusion limitation should preferably be minimised. This can be achieved at low temperature, low pH, and high substrate concentrations. An optimum in S/H ratio and yield was found at pH 7.5 and low temperature, where a relatively low reaction pH can be combined with a relatively high solubility of 7-ADCA. When comparing the different enzymes at these conditions, the free enzyme gave slightly better results than both immobilised biocatalysts, but the effect of diffusion limitation was minimal.     

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.     

Manometric transduction in enzyme biosensors

The combination of enzymatic recognition and manometric transduction is explored, using enzymes that consume or evolve a gas with low solubility in aqueous media. A design is discussed whereby change in partial pressure of a gas in the headspace is related to the turnover of analyte by the enzyme. Headspace and sample volume dimensions are considered, demonstrating the influence of flux at the air-water interface. The relative importance of diffusion and reaction for the enzyme solution is shown. When enzyme kinetics dominate, the concentration gradient is low and the overall kinetics are determined by the total amount of active enzyme, reducing either enzyme concentration or enzyme layer thickness will reduce the diffusion limitation. A Teflon-enzyme composite is presented to allow a reuseable immobilised enzyme preparation and a disc with stirring magnet identified as an efficient configuration. A glucose oxidase system was tested in the monitoring of glucose consumption during fermentation. Application to other enzyme systems is discussed.     

Temperature dependence of a diffusion-limited immobilized enzyme reaction.

The apparent activation energy of N-alpha-benzoyl-L-arginine-ethyl ester (BAEE) hydrolysis by immobilized trypsin varies with the bulk substrate concentration from its maximum value, comparable to that of the free enzyme, to considerably lower values. Thus, with a concentration change from 3 x 10(-2) to 10(-4) M the apparent activation energy diminishes from 9.5 to 4.5 kcal/mol. This experimental finding is interpreted to be due to Michaelis-type kinetics in a heterogeneous system, in one case reflecting the temperature dependence of the maximal enzyme reaction rate, in another case illustrating the diffusion limited overall reaction at low substrate concentrations. As a consequence it may not be feasible to operate a reaction at elevated temperatures in a high conversion range, since diffusion limitation may restrict the enhancement of the overall reaction rate. Some further data are given concerning the buffer effect on the reaction rate, which should occur due to its limitation by proton transfer in the buffer-free system.     

KINETICS OF PHOSPHATE TRANSPORT BY SYNECHOCOCCUS LEOPOLIENSIS (CYANOPHYTA): EVIDENCE FOR DIFFUSION LIMITATION OF PHOSPHATE UPTAKE1

The kinetics of phosphate transport by Synechococcus leopoliensis (Racih.) Komarek was investigated. Deviations from Michaelis-Menten kinetics were observed at law concentrations of phosphate and the deviations were consistent with diffusion limitation of transport. Activation energy analysis of the transport process at two concentrations, one at carrier saturation and the other at zero added phosphate yielded activation energies of 11.9 and 5.6 kcal/mole respectively at 25° C. The first is consistent with an enzyme limited process and the second with diffusion limitation through the unstirred layer.     

Cheaters, diffusion and nutrients constrain decomposition by microbial enzymes in spatially structured environments

Extracellular enzymes allow microbes to acquire carbon and nutrients from complex molecules and catalyse the rate-limiting step in nutrient mineralization. Because the factors regulating enzyme production are poorly understood, I used a simulation model to examine how competition, nutrient availability and spatial structure affect microbial growth and enzyme synthesis. In simulations where enzyme-producing microbes competed with cheaters (who do not synthesize enzymes but take-up product), higher enzyme costs favoured cheaters, while lower rates of enzyme diffusion favoured producers. Cheaters and producers coexisted in highly organized spatial patterns at intermediate enzyme costs and diffusion rates. Simulations with varying nutrient inputs showed that nitrogen supply can limit carbon mineralization, microbial growth and enzyme production because of the nitrogen-demanding stoichiometry of enzymes (C : N =  c. 3.5 : 1). These results suggest that competition from cheaters, slow diffusion and nitrogen limitation may constrain microbial foraging and the enzymatic decomposition of complex compounds in natural environments.     

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.     

Cytochrome P-450 for 11beta- and 18-hydroxylase activities of bovine adrenocortical mitochondria: one enzyme or two?

The 11beta- and 18-hydroxylase activities of a highly purified cytochrome P-450 from bovine adrenocortical mitochondria have been examined in detail with a view to determining whether the two activities are shown by a single protein or by two distinct proteins. The purified enzyme shows a single N-terminal residue (glutamic acid) and its amino acid composition is reported. Both enzyme activities decay considerably during storage at 4 degrees C for 11 days and the rates of decay are similar for the two activities. Metyrapone inhibits both activities competitively (Ki = 1.50 and 1.43 micrometer for 11beta- and 18-hydroxylase, respectively). Carbon monoxide inhibits both activities and the ratio CO:O2 for 50% inhibition is similar for the two activities (K = 1.69 and 1.53). A variety of nonspecific inhibitors produce approximately the same inhibition of both activities. Finally, antiserum produced by rabbits to the purified enzyme on double diffusion in agarose gels gives a single band with the purified enzyme. Increasing concentrations of antiserum added to the assay system produce increasing and proportionate inhibition of both activities. The evidence strongly supports earlier suggestions that the two hydroxylase activities occur in a single protein.     

A general solution for the steady-state kinetics of immobilized enzyme systems

A power series solution is presented which describes the steady-state concentration profiles for substrate and product molecules in immobilized enzyme systems. Diffusional effects and product inhibition are incorporated into this model. The kinetic consequences of diffusion limitation and product inhibition for immobilized enzymes are discussed and are compared to kinetic behavior characteristic of other types of effects, such as substrate inhibition and substrate activation.     

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.     

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.     

Parameters important in tuning the response of monolayer enzyme electrodes fabricated using self-assembled monolayers of alkanethiols

Enzyme electrodes were observed experimentally to have a broad dynamic range, high sensitivity and excellent reproducibility. The theoretically predicted response of the monolayer enzyme electrodes was in good agreement with that observed experimentally over the broad range of experimental conditions tested. The response is limited by the rate of enzyme turnover by a mediating species rather than mass transport. As a consequence of this limitation, the response was very sensitive to the enzyme loading and the concentration of mediator in the sample solution but insensitive to mass transport variables such as solution stirring or the diffusion coefficients of the substrate or cosubstrate.     

Limitations on the Analysis of Acetylene Reduction by Soybean at Low Levels of Acetylene

The analysis of acetylene reduction at low concentrations ofacetylene involves a number of assumptions and both technicaland kinetic complexities. The major difficulty in convertingacetylene reduction rates to apparent N₂ reduction rates isdetermining the K_m for acetylene in the presence of N₂. Thissubstrate competition is dominant over diffusion limitationeffects, but both introduce equivalent deviations in the observedK_m. Because N₂ is a non-linear partial competitive inhibitorof acetylene reduction, correction for its presence is difficult.Two further complications are introduced by the non-linear responseof nitrogenase to acetylene concentration even in the absenceof N₂, and changes in the apparent K_m of acetylene and K₁ ofN₂ as a function of other variables in the enzyme assay. Itis proposed that transient analysis may be used for measurementof diffusion coefficients and calculations of possible diffusionlimitations. It is demonstrated that one proposed model forestimating diffusion limitation (Denison et al., 1983, PlantPhysiology 73, 648–51) confounds substrate competitionwith diffusion limitation. Acetylene reduction, nitrogen fixation, diffusion limitation     

Mathematical modeling of a single-cell enzyme assay

A quantitative assay of beta-galactosidase activity in single cells of Saccharomyces cerevisiae has been developed using a fluorogenic substrate and flow cytometry [reported in Wittrup & Bailey, Cytometry, 9,394 (1988)]. The beta-galactosidase activity is expressed in yeast from the Escherichia coli lacZ gene under the control of the yeast GAL10 promoter, and is used as a marker for multicopy plasmid content. A nonfluorescent fluorogenic substrate is enzymatically cleaved by intracellular beta-galactosidase to form a fluorescent product. The accumulation of fluorescent product in single cells was found to depend on bulk substrate concentration and single-cell enzyme activity in a fashion that could not be described by a Michaelis-Menten kinetic rate form. It has been demonstrated that diffusion limitation rather than enzyme activity can determine the level of single-cell fluorescence under certain assay conditions, and a mathematical model has; been formulated which accounts for substrate and product diffusion. Guided by the mathematical model, the assay conditions were modified to allow measurement of single-cell enzyme activity rather than diffusion rates.     

Multiple gas washout during jet ventilation

Simultaneous washouts of He, N2, and SF6 were monitored during jet ventilation with tidal volumes of 50-200 ml and rates of 1-2 Hz. Gas concentrations were measured from the trachea and from a lower lobe bronchus in six baboons by mass spectrometry. Washouts using large tidal volumes approximated single exponential decays with the relative exponential rates of decay being He fastest, SF4 slowest, and N2 intermediate. Washouts using smaller tidal volumes demonstrated a two-phase exponential decay pattern. During the fast phase, the relative exponential rates of decay were He slowest, SF6 fastest, and N2 intermediate, the reverse order seen during large-volume washouts. During the slow phase, the relative exponential rates of decay were He fastest, SF4 slowest, and N2 intermediate, the same order seen during large-volume washouts. The magnitude of the first phase observed from the lower lobe bronchus was less than that observed from the trachea. These data are consistent with a serial two-compartment transport model incorporating a limitation of molecular diffusion between the peripheral and proximal compartments. The more rapid clearance of less diffusible gases from the central airways during the first phase of washout was due to slower transport from the alveoli to the central airways rather than faster transport from the central airways to the airway opening.     

Dynamic depolarization of interacting fluorophores. Effect of internal rotation and energy transfer.

Effects of internal rotation on the fluorescence decay functions and time-dependent anisotropies of fluorophores bound to a spherical macromolecule are theoretically investigated in the presence of the intramolecular energy transfer interaction by solving relevant rotational diffusion equations. The model system examined is one in which the energy donor is internally rotating around an axis fixed at the macromolecule and the acceptor is fixed at a definite position in the macromolecule. The effect of internal rotation in the system is described by Hill's functions with two cosine terms. The fluorescence decay function and anisotropy decay are functions of the ratio of energy-transfer probability averaged over the internal rotation angle to the rotary diffusion co-efficient. When the internal rotation is much faster than energy transfer, the decay function of the donor is predicted to be a single exponential, and the anisotropy decay is essentially described by the expression derived by Gotlieb and Wahl (1963. J. Chim. Phys. 60:849-856). However, deviation from it becomes pronounced as the rotation becomes slower. Methods of numerical analysis are presented for decay function and anisotropy decay, as well as relative quantum yield and polarization anisotropy under steady-state excitation, and examined for a simplified system under the variation of the diffusion coefficient.     

Biosensors based on acrylic microgels: a comparative study of immobilized glucose oxidase and tyrosinase

Acrylic microgels are proposed as enzyme immobilizing support in amperometric biosensors. Two enzymes, glucose oxidase and tyrosinase, were entrapped in this matrix and their behaviour is compared. The optimum cross-linking of the polymeric matrix required to retain the enzyme, and to allow the diffusion of the substrate is different for each enzyme, 3.2% for glucose oxidase and 4.5% for tyrosinase. The effect of pH and temperature on the biosensor responses has been studied by experimental design methodology and predictions have been compared with independently performed experimental measurements. A quadratic effect of the variables studied (pH and T) on the biosensor response and the small or null interaction between them was confirmed. The pH results obtained with both methods are coincident revealing an reversible effect on the enzyme. However, the temperature optimum value obtained by experimental design was 10 degrees C lower as a result of an activity decay due to irreversible thermal denaturation of both enzymes.     

Pilot plant production of glucose with glucoamylase immobilized to porous silica.

Glucoamylase was immobilized to porous silica and its kinetics and stability were observed with acid- and alpha-amylase-hydrolyzed dextrin as feed. The enzyme was found to be extremely stable in both laboratory and pilot plant operations. When the feed had been previously only lightly hydrolyzed, pore diffusion limitation caused appreciable decreases in glucose production rate. The severity of starch hydrolysis to dextrin markedly affected ultimate glucose yields. The diffusional gradients present in the carrier pores caused the immobilized enzyme to yield lower glucose concentrations than the free enzyme at similar feed conditions.     

The association reaction of yeast alcohol dehydrogenase with coenzyme is partly diffusion-controlled in solvents of increased viscosity

The steady-state kinetics of the yeast and liver alcohol dehydrogenase catalyzed reduction of aldehydes were examined in solvent mixtures of increased viscosity. This was done to investigate the effects of diffusion control on the fast association of NADH with the enzymes. Both glycerol and sucrose were unsatisfactory as viscosogens, as they inhibited the enzyme, but poly(ethylene glycol)/water mixtures were satisfactory. The 5-fold faster reaction of yeast alcohol dehydrogenase with NADH is partly diffusion controlled, whereas the slower liver alcohol dehydrogenase reaction showed no diffusion effects. These results are consistent with a yeast alcohol dehydrogenase active site that has relatively little steric hindrance to NADH binding. It is estimated that contributions to this association reaction from diffusion control and chemical activation control are equal at a solvent viscosity of 10 cP. Thus, under physiological conditions of increased viscocity the NADH association may be significantly affected by diffusion effects. In order to estimate accurately the maximum diffusion-controlled rate constant from diffusion theory, the diffusion coefficients of NADH were measured in poly(ethylene glycol)/water mixtures and were found to vary inversely as the solvent viscosity raised to the power of 0.5. The non-Stokesian behaviour of molecules as large as NADH in polymer/water mixtures may be a serious limitation to the routine use of poly(ethylene glycol) as a viscosogen for diffusion studies.