Starting D-optimal designs for batch kinetics studies of enzyme-catalyzed reactions in the presence of enzyme deactivation.

This paper describes a strategy for the starting experimental design of experiments required by general research in the field of biochemical kinetics. The type of experiments that qualify for this analysis involve batch reactions catalyzed by soluble enzymes where the activity of the enzyme decays with time. Assuming that the catalytic action of the enzyme obeys a Michaelis-Menten rate expression and that the deactivation of the enzyme follows a first-order decay, the present analysis employs the dimensionless, integrated form of the overall rate expression to obtain a criterion (based on the maximization of the determinant of the derivative matrix) that relates the a priori estimates of the parameters with the times at which samples should be withdrawn from the reacting mixture. The analysis indicates that the initial concentration of substrate should be as large as possible, and that the samples should be taken at times corresponding to substrate concentrations of approximately 2/3, 1/4, and I/epsilon of the initial concentration (where epsilon should be as large as possible).     

Optimum temperature policy for batch reactors performing biochemical reactions in the presence of enzyme deactivation

A necessary condition is found for the optimum temperature policy which leads to the minimum reaction time for a given final conversion of substrate in a well stirred, enzymatic batch reactor performing an enzyme-catalyzed reaction following Michaelis-Menten kinetics in the presence of first order enzyme decay. The reasoning, which is based on Euler's classical approach to variational calculus, is relevant for the predesign steps because it indicates in a simple fashion which temperature program should be followed in order to obtain the maximum advantage of existing enzyme using the type of reactor usually elected by technologists in the fine biochemistry field. In order to highlight the relevance and applicability of the work reported here, the case of optimality under isothermal operating conditions is considered and a practical example is worked out.List of Symbols C _E mol.m^–3 concentration of active enzyme - C _E ^* dimensionless counterpart of C_E - C _E,0 mol.m^–3 initial concentration of active enzyme - C _E,b mol.m^–3 final concentration of active enzyme - C _E,opt ^* optimal dimensionless counterpart of C_E - C _smol.m^–3 concentration of substrate - C _S ^Emphasis>/* dimensionless counterpart of C_S - C _S,0mol.m^–3 initial concentration of substrate - C _S,bmol.m^–3 final concentration of substrate - E enzyme in active form - E ₃ ^* dimensionless counterpart of E_a,3 - E _a,1J.mol^–1 activation energy associated with k₁ - E _a,3J.mol^–1 activation energy associated with k₃ - E _d enzyme in deactivated form - ES enzyme/substrate complex - k ₁ s^–1 kinetic constant associated with the enzyme-catalyzed transformation of substrate - k _1,0 s^–1 preexponential factor associated with k₁ - k ₂ mol^–1.m³s^–1 kinetic constant associated with the binding of substrate to the enzyme - k _–2 s^–1 kinetic constant associated with the dissociation of the enzyme/substrate complex - K _2,0 mol.m^–3 constant value of K₂ - K _2,0 ^* dimensionless counterpart of K_2,0 - k ₃ s^–1 kinetic constant associated with the deactivation of enzyme - k _3,0 s^–1 preexponential factor associated with k₃ - k _3,0 ^* dimensionless counterpart of k_3,0 - P product - R J.K^–1.mol^–1 ideal gas constant - S substrate - t s time since start-up of reaction - T K absolute temperature - T ^* dimensionless absolute temperature - T _i,opt ^* optimal dimensionless isothermal temperature of operation - T _opt ^* optimal dimensionless temperature of operation - t _b s time of a batch - t _b ^* dimensionless counterpart of t_b - t _b,min ^* minimum value of the dimensionless counterpart of t_b Greek Symbols dimensionless counterpart of C_E,0 - dimensionless counterpart of C_E,b - dummmy variable of integration - dummy variable of integration - auxiliary dimensionless variable - ^* dimensionless variation of k₁ with temperature - _i ^* dimensionless value of k₁ under isothermal conditions - _opt ^* optimal dimensionless variation of k₁ with temperature     

On the optimum distribution of enzyme feed in a cascade of CSTR's performing an enzyme-catalyzed reaction with deactivation

A search for the optimum fractional distribution of an enzyme-rich stream to the various reactors of a cascade of CSTR's was implemented. A theoretical analysis, laid out in dimensionless form and based on the assumptions that the system is operated under steady state conditions, the enzyme undergoes first order deactivation, and the reaction catalyzed by the enzyme follows Michaelis-Menten kinetics, is reported. The objective function utilised is the minimisation of the overall volume of the cascade, and analytical expressions are obtained for the concentration of active enzyme and substrate in the outlet stream from each reactor. It is found that the best option is to add the whole enzyme-rich stream to the first reactor in the cascade irrespective of the operating and kinetic parameters of the system.     

Effect of immobilized enzyme deactivation in fixed- and fluid-bed reactors

A two-parameter theoretical model is developed to evaluate the effect of immobilized enzyme deactivation on substrate conversion in fixed- and fluid-bed reactors under diffusion-free conditions. The method describes a simple reaction in which three different immobilized enzyme deactivation forms are considered, and an expression is developed to evaluate the effect of immobilized enzyme deactivation on yield in a consecutive reaction. Comparison of reactor performances for the two reactor types reduces to a comparison of the appropriate dimensionless parameters. The practical implications of the development are illustrated through an example.     

酶促反应制备壳寡糖条件的研究

通过膜分离法从Microbacterium sp.OU01的发酵液中分离到内切壳聚糖酶ChiN,并对其酶解制备壳寡糖条件进行了优化,获得的酶解产物数均分子量为1200。经薄层层析与HPLC分析,降解产物中不含单糖,初步说明降解产物为壳寡糖。酶解制备壳寡糖反应条件温和,操作简便,为实现壳寡糖产业化奠定了基础。     

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.     

The pressure-induced inactivation of mammalian enolases is accompanied by dissociation of the dimeric enzyme

The effects of exposure to pressure on both the activity and the quaternary structure of rabbit brain enolases, forms alpha alpha, alpha gamma, and gamma gamma were studied in the pressure range of 1 to 3400 bar. Effects on quaternary structure were determined by subunit scrambling (the formation of alpha alpha and gamma gamma from alpha gamma or vice versa). All three dimers are stable up to pressures of 1200 bar. The dissociation of gamma gamma begins at 1200 bar, yielding a stable monomer; inactivation of gamma gamma does not begin until the pressure is greater than 2000 bar. Dissociation of gamma gamma is not accompanied by changes in the tryptophan fluorescence of the protein. However, the fluorescence does decrease when the pressure is greater than 2000 bar, the point at which inactivation of gamma gamma starts. The alpha monomer, on the other hand, is unstable in the pressure range that produces dissociation of alpha alpha. This process, which also begins at 1200 bar, is paralleled by inactivation. Crosslinking the enzyme with glutaraldehyde demonstrated that the inactive form of the enzyme is monomeric. The pressure-induced inactivation of these forms of enolase is thus clearly a two-step process, with both dissociation and inactivation occurring. The difference in pressure sensitivity of rabbit brain alpha alpha and gamma gamma is due to a difference in stability of the alpha and gamma monomers and not due to a difference in the pressures required for dissociation.     

Optimal control of an enzyme reaction subject to enzyme deactivation. I. Batch process

This paper is concerned with the study of an enzymatic system in a repeated batch process where the enzyme is subject to deactivation. The particular system studied was the enzymatic hydrolysis of Penicillin G to 6-aminopenicillanic acid. Utilizing standard optimization techniques, pH and temperature control policies were determined that would maximize the product yield.     

Determination of the optimum operating time for batch isothermal performance of enzyme-catalyzed multisubstrate reactions

This communication consists of a mathematical analysis encompassing the maximization of the average rate of monomer production in a batch reactor performing an enzymatic reaction in a system consisting of a multiplicity of polymeric substrates which compete with one another for the active site of a soluble enzyme, under the assumption that the form of the rate expression is consistent with the Michaelis-Menten mechanism. The general form for the functional dependence of the various substrate concentrations on time is obtained in dimensionless form using matrix terminology; the optimum batch time is found for a simpler situation and the effect of various process and system variables thereon is discussed. The reasoning developed here emphasizes, in a quantitative fashion, the fact that the commonly used lumped substrate approaches lead to nonconservative decisions in industrial practice, and hence should be avoided when searching for trustworthy estimates of optimum operation.List of Symbols O 1/s row vector of zeros - a 1/s row vector of rate constants k _i(i = 2,...,N) - A 1/s matrix of rate constants k _i and k_–i (i=2,...,N) - b 1/s row vector of rate constant k ₂ and zeros - C mol/m³ molar concentration of S - C mol/m³ vector of molar concentrations of C _i (i=0, 1, 2, ..., N) - C ₀ mol/m³ column vector of initial molar concentrations of C _i(i=0, 1, 2,.., N) - C _–01 mol/m³ column vector of initial molar concentrations of C _i(i=2,..., N) - C _{E, tot} mol/m³ total molar concentration of enzyme molecules - C _i mol/m³ molar concentration of S _i (i=0,1,2,...,N) - C _{i, o} mol/m³ initial molar concentration of S _i(i=0, 1, 2, ..., N) - E enzyme molecule - I identity matrix - K 1/s matrix of lumped rate constants - k _i 1/s pseudo-first order lumped rate constant associated with the formation of S _i -1 (i=1, 2, ...,N) - k _{cat, i} 1/s first order rate constant associated with the formation of S _i-1 (i=1, 2, ..., N) - K _m mol/m³ Michaelis-Menten constant - L number of distinct eigenvalues - M _i multiplicity of the i-th eigenvalue - N maximum number of monomer residues in a single polymeric molecule - r ₁ mol/m³ s rate of formation of S ₀ - r _i mol/m³ s rate of release of S _i -1 - r _opt maximum average dimensionless rate of production of monomer S₀ - S lumped, pseudo substrate - S₁ inert moiety - S _i substrate containing i monomer residues, each labile to detachment as - S₀ by enzymatic action (i=1,2,...,N) - t s time elapsed since startup of batch reaction - t _lag s time interval required for cleaning, loading, and unloading the batch reactor - t _opt s time interval leading to the maximum average rate of monomer production - v _ij s^1-j eigenvectors associated with eigenvalue imi (i=1, 2, ..., L; j =1, 2, ..., M_i) Greek Symbols _ij mol/m³ arbitrary constant associated with eigenvalue _i (i=1, 2, ..., L; j=1, 2, ..., M _i ) - 1/s generic eigenvalue - _i 1/s i-th eigenvalue     

Nitrification in activated sludge batch reactors is linked to protozoan grazing of the bacterial population

Protozoa feed upon free-swimming bacteria and suspended particles inducing flocculation and increasing the turnover rate of nutrients in complex mixed communities. In this study, the effect of protozoan grazing on nitrification was examined in activated sludge in batch cultures maintained over a 14-day period. A reduction in the protozoan grazing pressure was accomplished by using either a dilution series or the protozoan inhibitor cycloheximide. As the dilutions increased, the nitrification rate showed a decline, suggesting that a reduction in protozoan or bacterial concentration may cause a decrease in nitrification potential. In the presence of cycloheximide, where the bacterial concentration was not altered, the rates of production of ammonia, nitrite, and nitrate all were significantly lower in the absence of active protozoans. These results suggest that a reduction in the number or activity of the protozoans reduces nitrification, possibly by limiting the availability of nutrients for slow-growing ammonia and nitrite oxidizers through excretion products. Furthermore, the ability of protozoans to groom the heterotrophic bacterial population in such systems may also play a role in reducing interspecies competition for nitrification substrates and thereby augment nitrification rates.     

Technical aspects of separation and simultaneous enzymatic reaction in multiphase enzyme membrane reactors

The technical aspects of the membrane extraction of a compound either from aqueous phase into apolar organic solvent phase or from the apolar phase to the aqueous one and the enzymatic conversion of the solute in a multiphase enzyme membrane reactor are considered. The application possibilities, the selection aspects of membrane material as well as the solvent phase, the water content and its control, the method of the enzyme immobilisation and the operation of the extraction/reaction system are discussed.     

An experimental method to determine the substrate protection of enzyme against deactivation in a reversible reaction.

The substrate protection effect on an enzyme in a reversible reaction was studied by using glucose isomerase immobilized in small particles (radius less than 100 micron). Deactivation of the enzyme at various substrate concentrations in Tris buffer, pH 8.25, at 62.1 degrees C was studied in eight-column reactor sets. At set times the immobilized enzyme in one of the eight reactors was taken out and rinsed thoroughly, and then its residual activity was determined. The conclusions are, first, that the protection by the reactant is equal to the protection by the product, and, secondly, that the half-life of the enzyme increases slowly at high sugar concentrations. Thus the experimental method described here appears to be a useful one for the determination of substrate protection of enzyme deactivation in reversible reactions.     

Abortion of infection during the Rhizobium meliloti—alfalfa symbiotic interaction is accompanied by a hypersensitive reaction

Nodulation, the organogenetic process resulting from the symbiotic interaction between Rhizobium and legumes, is under the feedback control of the plant. However, the autoregulatory mechanisms controlling root nodule formation are poorly understood. In this paper it is shown that alfalfa can react to infection by its symbiont Rhizobium meliloti by eliciting a defence mechanism similar to the hypersensitive reaction (HR) observed in incompatible plant-pathogen interactions. After the first nodule primordia have been induced, an increasing proportion of infection threads abort in a single or a few root cortical cells in which both symbionts simultaneously undergo necrosis. Autofluorescent, cytochemical and immunolocalization assays revealed that phenolic compounds and proteins associated with defence mechanisms in plants have accumulated in the necrotic cells. These results lead to the proposition that the elicitation of a HR is part of the mechanism by which the plant controls infection and, therefore, regulates nodulation.     

Cometabolic biodegradation of 4-chlorophenol by sequencing batch reactors at different temperatures

The simultaneous removal of 4-chlorophenol (4-CP) and phenol in lab-scale sequencing batch reactors at different temperatures has been studied. Phenol feed concentration was fixed at 525 mg/L and 4-CP concentration was increased from 105 to 2100 mg/L at a constant hydraulic residence time (HRT) of 10.5 d. Complete phenol and 4-CP biodegradation was achieved during the aerobic stage working with 4-CP concentrations up to 1470 mg/L in the feed. Both 4-CP and phenol specific initial removal rates were strongly affected by 4-CP feed concentration and temperature. Only at the highest temperature tested (35 °C) it was possible to increase the maximum assimilative 4-CP concentration by the biological sludge up to 2100 mg/L, and a significant reduction of the ecotoxicity of the effluents was observed. 4-chlorocatechol (4-CC) was identified as the major intermediate in the aerobic cometabolic 4-CP degradation, being the ecotoxicity of that species substantially lower than that of 4-CP.     

Biodegradative threonine dehydratase. Reduction of ferricyanide by an intermediate of the enzyme-catalyzed reaction.

The threonine-dependent reduction of ferricyanide catalyzed by the purified biodegradative threonine dehydratase of Escherichia coli has been studied. The rate of production of 2-oxobutyrate in the presence of ferricyanide was lower than that found in the absence of ferricyanide. The concentrations of threonine required for half-maximal effects for the reduction of ferricyanide and, in the presence of the dye, for 2-oxobutyrate production, were 3 mM and 9mM, respectively. Reduction of ferricyanide was accompanied by evolution of CO2, and even within a very short incubation time with the enzyme, the ratio of ferricyanide reduced over CO2 evolved was approximately 7. Stopping the enzyme activity after a brief exposure to threonine at pH 9.7 resulted in the accumulation of an intermediate (with a half-life of 4 min at 25 degrees C) which formed an adduct with N-ethylmaleimide; the accumulated intermediate, in the absence of N-ethylmaleimide, reduced ferricyanide with concomitant evolution of CO2. We conclude from these results that 2-aminocrotonate is the intermediate which serves as a source of reducing equivalent for ferricyanide, and nonstoichiometric amount of ferricyanide reduction may be attributed to some secondary reactions of ferricyanide with compounds derived from the oxidation product of 2-aminocrotonate.     

Advantages of continuous over batch reactors for the kinetic analysis of enzymes inhibited by an unknown substrate impurity

A new experimental technique, employing a continuous stirred-tank reactor, for studying enzyme kinetics in the presence of inhibitor-contaminated substrate is described. The proposed method is simulated mathematically for competitive, uncompetitive, and mixed-type noncompetitive inhibition. The step-by-step experimental procedure is described, as is the necessary data analysis for determining the kinetic parameters. Differences in system response for enzyme inhibition by excess substrate and by an impurity are illustrated, and a stability analysis of the system is performed.