Urokinase bound to fibrocollagenous tubes: an in vitro kinetic study

Urokinase (UK) has been immobilized to the inner surfaces of fibrocollagenous tubes (FCT) in an attempt to develop a fibrinolytic biomaterial which may be suitable for use as a small diameter vascular prosthesis. The enzyme was bound by adsorption followed by glutaraldehyde crosslinking. An in virto kinetic study of immobilized urokinase was conducted by employing the tubular material as a flow through reactor operated in a batch recycle mode in which the esterolysis of the model substrate, N-alpha-acetyl-L-lysine methyl ester (ALME), was monitored as a function of substrate concentration, recycle flow rate, and temperature. Results were compared with data from the soluble enzyme reaction, which was conducted in the presence and absence of 10% swine skin gelatin, in order to identify the specific effects of a collagenous microenvironment. Observed rates for the UK-FCT catalyzed reaction were observed to be dependent on recycle flow rates below 12 mL/min (Re = 107). Apparent Michaelis-Menten rate parameters were determined by a nonlinear search technique for two flow rates: one above the critical point for external diffusion effects (Re = 282) and one within the mass-transfer-limited region (Re = 71). When the latter data were corrected for external diffusion by applying the Graetz correlation for laminar flow in tubes to estimate themass transfer coefficient, the corrected K(m) of 6.45 +/- 0.38 mM agreed very closely with the diffusion free parameter (i.e. 6.13 +/- 0.63). Furthermore, this value was observed to be an order of magnitude higher than that of the soluble enzyme but approximately equal to the K(m) of the soluble enzyme in a 10% gelatin environment (8.13 +/- 1.53 mM). It is postulated that the difference in kinetic parameters between soluble and collagen immobilized UK is due to an inherent interaction between collagen and enzyme rather than to mass transfer effects. Such aninteraction is supported by the effects of collagen on thermal stability and energy of activation.     

Deactivation studies of immobilized glucose oxidase

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

Mass transfer studies on immobilized alpha-chymotrypsin biocatalysts prepared by deposition for use in organic medium

Mass transfer limitations were studied in enzyme preparations of alpha-chymotrypsin made by deposition on different porous support materials such as controlled pore glasses, Celite, and polyamides of different particle sizes. It is the onset of mass transfer limitations that determines the position of the activity optimum with respect to enzyme loading on each support. The evidence of various experiments indicates that internal diffusional limitations are the important mechanism for the observed mass transfer limitations. External diffusion was not found to play an important role under the conditions used, and it was also found that when immobilizing multilayers of enzyme the buried enzyme molecules are active to a large extent. An extreme situation is observed on Celite at very high loadings. Under these conditions, this support is expected to have its pores completely filled with packed enzyme molecules, and then it is the diffusion within the enzyme layer that determines the observed rate. As the enzyme loading increases, the area of contact between the deposited enzyme layers and the liquid solution inside the pores diminishes, causing a decrease on the observed rate of an intrinsically fast reaction which apparently is incongruous with the presence of more enzyme in the system. This work shows that mass transfer limitations can be an important factor when working with immobilized enzymes in organic media, and its study should be carried out in order to avoid undesired reduced enzyme activities and specificities.     

A unified model for signal transduction reactions in cellular membranes.

An analytical solution is obtained for the steady-state reaction rate of an intracellular enzyme, recruited to the plasma membrane by active receptors, acting upon a membrane-associated substrate. Influenced by physical and chemical effects, such interactions are encountered in numerous signal-transduction pathways. The generalized modeling framework is the first to combine reaction and diffusion limitations in enzyme action, the finite mean lifetime of receptor-enzyme complexes, reactions in the bulk membrane, and constitutive and receptor-mediated substrate insertion. The theory is compared with other analytical and numerical approaches, and it is used to model two different signaling pathway types. For two-state mechanisms, such as activation of the Ras GTPase, the diffusion-limited activation rate constant increases with enhanced substrate inactivation, dissociation of receptor-enzyme complexes, or crowding of neighboring complexes. The latter effect is only significant when nearly all of the substrate is in the activated state. For regulated supply and turnover pathways, such as phospholipase C-mediated lipid hydrolysis, an additional influence is receptor-mediated substrate delivery. When substrate consumption is rapid, this process significantly enhances the effective enzymatic rate constant, regardless of whether enzyme action is diffusion limited. Under these conditions, however, enhanced substrate delivery can result in a decrease in the average substrate concentration.     

Effect of microwave radiation on the permeability of carbonic anhydrase loaded unilamellar liposomes

The influence of 2.45 GHz microwave exposure (6 mW/g) on the diffusion processes in enzyme-loaded unilamellar liposomes as bioreactors was studied. The enzyme carbonic anhydrase (CA) was entrapped into cationic unilamellar vesicles. Previous kinetic experiments showed a very low self-diffusion rate of the substrate p-nitrophenyl acetate (PNPA) across intact liposome bilayer. A twofold increase in the diffusion rate of PNPA through the lipid bilayer was observed after 120 min of microwave radiation compared to temperature control samples. The microwave effect was time dependent. The enzyme activity, as a function of increased diffusion of PNPA, rises over 120 min from 22.3% to 80%. The increase in stearylamine concentration reduces the enzyme activity from 80% to 65% at 120 min. No enzyme leakage was observed. © 1994 Wiley-Liss, Inc.     

Effects of convective transport on chemical signal propagation in epithelia

We study effects of convective transport on a chemical front wave representing a signal propagation at a simple (single layer) epithelium by means of mathematical modeling. Plug flow and laminar flow regimes were considered. We observed a nonmonotonous dependence of the propagation velocity on the ligand receptor binding constant under influence of the convective transport. If the signal propagates downstream, the region of high velocities becomes much broader and spreads over several orders of magnitude of the binding constant. When the convective transport is oriented against the propagating signal, either velocity of the traveling front wave is slowed down or the traveling front wave can stop or reverse the direction of propagation. More importantly, chemical signal in epithelial systems influenced by the convective transport can propagate almost independently of the ligand-receptor binding constant in a broad range of this parameter. Furthermore, we found that the effects of the convective transport becomes more significant in systems where either the characteristic dimension of the extracellular space is larger/comparable with the spatial extent of the ligand diffusion trafficking or the ligand-receptor binding/ligand diffusion rate ratio is high.     

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.     

Diffusion control in reversible enzyme reactions. Applications to carbonic anhydrase.

The limit to the possible rate of reversible enzymatic reactions set by the diffusional motion has been considered. It is found that not only the diffusion of the reactants to the enzyme but also the diffusion away of the products can be rate limiting. To avoid assumptions about the detailed nature of the enzyme only diffusion in the bulk aqueous medium is treated. By such an approach one obtains an upper limit to the possible rate. In the latter half of the paper the derived general equations are applied to the possible suggested reaction schemes for the enzyme carbonic anhydrase. It is found that a scheme involving HCO3- as substrate for the dehydration process and a direct reaction between buffer and enzyme is comsistent with the limits set by the diffusional motion, while several other possibilities can be ruled out.     

Diffusional effects on the heterogeneous kinetics of two-substrate enzymic reactions.

When a two-substrate reaction is catalyzed by a surface bound enzyme, the diffusion of both substrates can considerably modify the kinetic properties of the reaction. According to this theoretical analysis, limitations in substrate diffusion yield very different effects depending whether the two substrates have similar or different affinities for the enzyme. With two substrates of comparable affinities the diffusion of the two substrates can be limiting, and similar activity dependences on the two substrate concentrations are obtained. Under these conditions, diffusional limitations may only slightly influence half-maximal-activity substrate concentrations. With two substrates of widely different affinities, on the contrary, the rate of the enzymic reaction can only be limited by the diffusion of the high-affinity substrate, used at the lower concentration. Under these conditions, in the presence of diffusional limitations the activity dependence on the two substrate concentrations are highly different, and the half-maximal-activity concentration is increased and decreased for the high- and low-affinity substrates, respectively. The theoretical results are verified by experimental data previously obtained with collagen-bound aspartate aminotransferase and sorbitol dehydrogenase.     

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.     

Influence of mass transfer limitations on the enzymatic synthesis of β-lactam antibiotics catalyzed by penicillin G acylase immobilized on glioxil-agarose

Mass transfer effects were investigated for the synthesis of ampicillin and amoxicillin, at pH 6.5 and 25 degrees C, catalyzed by penicillin G acylase immobilized on agarose. The influence of external mass transfer was analysed using different stirring rates, ranging form 200 to 800 rpm. Above 400 rpm, the film resistance may be neglected. Intra-particle diffusion limitation was investigated using biocatalysts prepared with different enzyme loads and agarose with different mean pore diameters. When agarose with 6, 8 and 10% of crosslinking were used, for the same enzyme load, substrates and products concentration profiles presented no expressive differences, suggesting pore diameter is not important parameter. An increase on enzyme load showed that when more than 90 IU of enzyme activity were used per mL of support, the system was influenced by intra-particle mass transfer. A reactive-diffusive model was used to estimate effective diffusivities of substrates and products.     

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.     

Role of the electrostatic loop charged residues in Cu,Zn superoxide dismutase.

We have expressed and characterized a mutant of Xenopus laevis Cu,Zn superoxide dismutase in which four highly conserved charged residues belonging to the electrostatic loop have been replaced by neutral side chains: Lys120 --> Leu, Asp130 --> Gln, Glu131 --> Gln, and Lys134 --> Thr. At low ionic strength, the mutant enzyme is one of the fastest superoxide dismutases ever assayed (k = 6.7 x 10(9) M(-1) s(-1), at pH 7 and mu = 0.02 M). Brownian dynamics simulations give rise to identical enzyme-substrate association rates for both wild-type and mutant enzymes, ruling out the possibility that enhancement of the activity is due to pure electrostatic factors. Comparative analysis of the experimental catalytic rate of the quadruple and single mutants reveals the nonadditivity of the mutation effects, indicating that the hyperefficiency of the mutant is due to a decrease of the energy barrier and/or to an alternative pathway for the diffusion of superoxide within the active site channel. At physiological ionic strength the catalytic rate of the mutant at neutral pH is similar to that of the wild-type enzyme as it is to the catalytic rate pH dependence. Moreover, mutation effects are additive. These results show that, at physiological salt conditions, electrostatic loop charged residues do not influence the diffusion pathway of the substrate and, if concomitantly neutralized, are not essential for high catalytic efficiency of the enzyme, pointing out the role of the metal cluster and of the invariant Arg141 in determining the local electrostatic forces facilitating the diffusion of the substrate towards the active site.     

Immobilization of glucose oxidase in thin polypyrrole films: influence of polymerization conditions and film thickness on the activity and stability of the immobilized enzyme

Using monomers that polymerize to form electrically conducting polymers, one can control the thickness of the polymer film and the amount of enzyme that can be immobilized in the films. First, an investigation of the major variables that influence the immobilization of glucose oxidase by entrapment in polypyrrole films, prepared by electropolymerization from aqueous solutions containing the enzyme and monomer, was carried out. Then the optimized conditions were used to assess the effects of film thickness on the activity and stability of immobilized enzyme. For the films ranged in thickness from 0.1 mum to 1.6 mum, the resulting apparent activity and stability of the immobilized enzyme were found to be a strong function of the polymer film thickness. Above a thickness of 1.0 mum, the apparent activity of the immobilized enzyme increases linearly with increasing film thickness. The nonlinearity observed for films of thickness less than 1.0 mum can be attributed to the changes observed in the morphology of the resulting polypyrrole films. Furthermore, it was noted that when the glucose oxidase/polypyrrole films are stored in phosphate buffer, at 4 degrees C, the observed rate of loss in apparent activity of the immobilized enzyme is highest for the first few days, also being higher for the thinner films. However, after the loosely entrapped enzyme is leached from the polymer film, the rate of loss in activity is very low indicating that the well-entrapped enzyme, as well as the polypyrrole films, exhibit good stability. Finally, the reproducibility of the immobilization technique is excellent. (c) 1993 John Wiley & Sons, Inc.     

Mechanism of Carboxypeptidase Y Catalyzed Hydrolysis and Aminolysis Reactions

The reaction mechanism of carboxypeptidase Y catalyzed reactions is investigated. Presteady state and steady state kinetic measurements are performed on the hydrolysis and aminolysis of an ester and an amide substrate. It is found that deacylation is the rate determining step in hydrolysis of the ester, pivalic acid 4-nitrophenol and acylation in that of the amide, succinyl-L-alanyl-L-alalyl-L-propyl-L-phenylalanine 4-nitroanilide.

The kinetic effects observed in the presence of a nucleophile, L-valine amide, where aminolysis occurs in parallel to the hydrolysis reaction are analysed in details. The results are described satisfactorily by a reaction scheme which involves the binding of the added nucleophile, (i) to the free enzyme, resulting in a simple competitive effect, and (ii) to the acyl-enzyme with the formation of a complex between the enzyme and the aminolysis product, the dissociation of which is rate determining. That scheme can account for both increases and decreases of kinetic parameter values as a function of the nucleophile concentration. There is no indication of binding of the nucleophile to the enzyme-substrate complex before acylation takes place.     

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.     

Mass transport in a microchannel enzyme reactor with a porous wall: Hydrodynamic modeling and applications

A two-dimensional flow model, incorporating mass transport, has been developed to simulate a microchannel enzyme reactor with a porous wall. A two-domain approach based on the finite volume method was implemented. Two parameters are defined to characterize the mass transports in the fluid and porous regions: the porous Damkohler number and the fluid Damkohler number. For reactions close to first-order type (enzyme reactor), the concentration results are found to be well correlated by the use of a reaction–convection distance parameter which incorporates the effects of axial distance, substrate consumption and convection. The reactor efficiency reduces with reaction–convection distance parameter because of reduced reaction (or flux) due to the lower concentration. Increased fluid convection improves the efficiency but it is limited by the diffusion in the fluid region. The correlated results can find applications for the design of enzyme reactors with a porous wall.     

Analysis of acetylene reduction rates of soybean nodules at low acetylene concentrations

It has been previously proposed that acetylene reduction data at subsaturating acetylene concentrations could be interpreted by use of the Michaelis-Menten equation, based on the acetylene concentration external to the nodules. One difficulty of this view is that the assumption that the system is not diffusion limited is violated when studying intact nodules. The presence of a gas diffusion barrier in the nodule cortex leads to an alternate expression for the gas exchange rates at subsaturating gas concentrations. A theoretical comparison of the `apparent' Michaelis-Menten model and diffusion model illustrated the difficulties observed in the former model of overestimating the Michaelis-Menten coefficient and yielding a correlation between the Michaelis-Menten coefficient and the maximum rate. On the other hand, use of a diffusion model resulted in (a) estimates of the Michaelis-Menten coefficient consistent with enzyme studies, (b) stability of the estimates of the Michaelis-Menten coefficient independent of treatment, and (c) a sensitivity of the diffusion barrier conductance to plant drought stress. It was concluded that all studies of nodule gas exchange need to consider possible effects caused by the presence of a diffusion barrier.     

Bose-Einstein condensation in biological systems

A theoretical model is presented for describing a previously untreated effect of viscosity on the apparent decomposition rate of enzyme-ligand complexes.Since the translational diffusion is hindered by the viscosity, its increased value results in an enlarged portion of ligands which can be rebound by the enzyme immediately after the dissociation of the complex.The model accounts for the experimentally observed decrease in maximal velocity of enzymic reactions at high viscosity. At the same time, it serves as a tool to obtain new information about the energetic processes of enzyme action.     

Kinetic model of the effects of electrogenic enzymes on the membrane potential

Electrogenic enzymes contribute to the electrical field existing across biological membranes by using a source of free energy to generate an ionic current. The model introduced here permits one to evaluate this contribution. Since the model incorporates the electrogenic enzyme in the form of a sequential kinetic diagram, it permits one to study the kinetic effects of the concentration of the enzyme, the substrates and the different ligands on the membrane potential. Ionic electrodiffusion is expressed in terms of a chemical reaction; ionic permeabilities are thus treated as voltage-dependent rate constants. We use the condition of global electroneutrality to obtain an expression for the electrical potential difference across the membrane; such expression constitutes an extension of the Goldman-Hodgkin-Katz equation. The enzyme-related terms appear in the equation as functions of the rate constants and the diverse concentrations. The model is used to analyze the case of a cell membrane traversed by Na+ and K+ by simple diffusion, and by electrogenic transport mediated by a Na+-K+ ATPase. The enzyme reaction is represented by the six-step scheme proposed by Chapman et al. (1983, J. membr. Biol. 74, 139-153). The main results of the numerical calculations are that, within a certain interval, the membrane potential difference depends linearly on the enzyme density and hyperbolically on the ATP concentration. A similar behavior has been experimentally observed for the electrogenic proton pump of Neurospora crassa. Thus, the model here can be useful in the explanation and prediction of effects of electrogenic enzymes on the membrane potential.