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

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

A practical kinetic model that considers endproduct inhibition in anaerobic digestion processes by including the equilibrium constant

The classical Michaelis-Menten model is widely used as the basis for modeling of a number of biological systems. As the model does not consider the inhibitory effect of endproducts that accumulate in virtually all bioprocesses, it is often modified to prevent the overestimation of reaction rates when products have accumulated. Traditional approaches of model modification use the inclusion of irreversible, competitive, and noncompetitive inhibition factors. This article demonstrates that these inhibition factors are insufficient to predict product inhibition of reactions that are close the dynamic equilibrium. All models investigated were found to violate thermodynamic laws as they predicted positive reaction rates for reactions that were endergonic due to high endproduct concentrations. For modeling of biological processes that operate close to the dynamic equilibrium (e.g., anaerobic processes), it is critical to prevent the prediction of positive reaction rates when the reaction has already reached the dynamic equilibrium. This can be achieved by using a reversible kinetic model. However, the major drawback of the reversible kinetic model is the large number of empirical parameters it requires. These parameters are difficult to determine and prone to experimental error. For this reason, the reversible model is not practical in the modeling of biological processes.This article uses the fundamentals of steady-state kinetics and thermodynamics to establish an equation for the reversible kinetic model that is of practical use in bio-process modeling. The behavior of this equilibrium-based model is compared with Michaelis-Menten-based models that use traditional inhibition factors. The equilibrium-based model did not require any empirical inhibition factor to correctly predict when reaction rates must be zero due to the free energy change being zero. For highly exergonic reactions, the equilibrium-based model did not deviate significantly from the Michaelis-Menten model, whereas, for reactions close to equilibrium, the reaction rate was mainly controlled by the quotient of mass action ratio (concentration of all products over concentration of all substrates) over the equilibrium constant K. This quotient is a measure of the displacement of the reaction from its equilibrium. As the new equation takes into account all of the substrates and products, it was able to predict the inhibitor effect of multiple endproducts. The model described is designed to be a useful basis for a number of different model applications where reaction conditions are close to equilibrium.     

Kinetic modeling of omega-transamination for enzymatic kinetic resolution of alpha-methylbenzylamine

A kinetic model for omega-transaminase from Bacillus thuringiensis JS64 was developed by using the King-Altman method to simulate the kinetic resolution of alpha-methylbenzylamine (alpha-MBA). Starting from a ping-pong bi-bi mechanism, a complete kinetic model including substrate inhibition only in the reverse reaction (i.e., transamination between acetophenone and L-alanine) was developed. The asymmetric synthesis of (S)-alpha-MBA proved to be difficult due to a much lower maximum reverse reaction rate than the maximum forward reaction rate, thermodynamically exergonic forward reaction (i.e., transamination between (S)-alpha-MBA and pyruvate), and the severe product and substrate inhibition of the reverse reaction. Experimental values for kinetic parameters show that the product inhibition constant of (S)-alpha-MBA is the most important parameter on determining the resolution reaction rate, suggesting that the resolution reaction rate will be very low unless (S)-alpha-MBA strongly inhibits the reverse reaction. Using the kinetic model, the kinetic resolution of alpha-MBA in aqueous buffer was simulated, and the simulation results showed a high degree of consistency with experimental data over a range of reaction conditions. Various simulation results suggest that the crucial bottleneck in the kinetic resolution of alpha-MBA lies mainly in the accumulation of acetophenone in reaction media as the reaction proceeds, whereas L-alanine exerts a little inhibitory effect on the reaction. The model predicts that removing acetophenone produced during the reaction can enhance the reaction rate dramatically. Indeed, the biphasic reaction system is capable of extracting acetophenone from the aqueous phase, showing a much higher reaction rate compared to a monophasic reaction system. The kinetic model was also useful in predicting the properties of other, better enzymes as well as the optimal concentrations of amino acceptor and enzyme in the resolution reaction.     

Study on the kinetics of enzymatic interesterification of triglycerides for biodiesel production with methyl acetate as the acyl acceptor

A new route for biodiesel production using methyl acetate instead of methanol as the acyl acceptor was proposed in our previous research, and it has been found that this novel route could enhance the stability of the immobilized lipase greatly. In this paper, the kinetics of lipase-catalyzed interesterification of triglycerides for biodiesel production with methyl acetate as the acyl acceptor was further studied. First, a simplified model based on Ping Pong Bi Bi with substrate competitive inhibition mechanism was proposed to describe the reaction kinetics of the interesterification. During our further study, it was observed that three consecutive and reversible reactions occurred in the interesterification of triglycerides and methyl acetate. So, a kinetic model based on mass balance of three second-order reversible reactions was developed and the reaction rate constant, k, was determined by solving the differential rate equations of the reaction system. The results showed that k_DG–MG (0.1124) and k_MG–TA (0.1129) were much higher than k_TG–DG (0.0311), which indicated that the first step reaction was the limit step for the overall interesterification.     

Enzymatic Separation and Resolution of Nucleophiles: A Predictive Kinetic Model

Analysis of nucleophile separation via lipase catalyzed reactions has been developed on the basis of competitive enzymatic kinetics. Ester synthesis as well as ester interchange reactions catalyzed by lipases in organic media have been analyzed according to a transfer reaction of the acyl group from/to the enzyme. The reversible reactions are conveniently simulated from the knowledge of the a competitive factor of the enzymatic system and of the final equilibrium conditions. The model which is proposed describes the reaction profile in a predictive way. Modelling of alcohol kinetic separation and resolution is given.     

The determination of specificity constants in enzyme-catalysed reactions.

A convenient and accurate procedure for determining the kinetic parameter Vmax./Km is described. This avoids the error in the usual method of taking the observed first-order rate constant of an enzymic reaction at low substrate concentration as Vmax./Km. A series of reactions is used in which the initial concentration of substrate is below Km (e.g. from 5% to 50% of Km). Measurements are taken over the same extent of reaction (e.g. 70%) for each member of the series, and treated as if the kinetics were truly first-order. The reciprocal of the observed first-order rate constant is then plotted against the initial concentration of substrate: the reciprocal of the ordinate intercept is Vmax./Km. The procedure, as well as being applicable to simple reactions, is shown to be valid when there is competitive inhibition by the product, or when the reaction is reversible, or when there is competitive or mixed inhibition. The hydrolysis of cephalosporin C by a beta-lactamase from Pseudomonas aeruginosa is used to illustrate the method.     

Role of substrate inhibition kinetics in enzymatic chemical oscillations.

Two chemical kinetic models are investigated using standard nonlinear dynamics techniques to determine the conditions under which substrate inhibition kinetics can lead to oscillations. The first model is a classical substrate inhibition scheme based on Michaelis-Menten kinetics and involves a single substrate. Only when this reaction takes place in a flow reactor (i.e., both substrate and product are taken to follow reversible flow terms) are oscillations observed; however, the range of parameter values over which such oscillations occur is so narrow it is experimentally unobservable. A second model based on a general mechanism applied to the kinetics of many pH-dependent enzymes is also studied. This second model includes both substrate inhibition kinetics as well as autocatalysis through the activation of the enzyme by hydrogen ion. We find that it is the autocatalysis that is always responsible for oscillatory behavior in this scheme. The substrate inhibition terms affect the steady-state behavior but do not lead to oscillations unless product inhibition or multiple substrates are present; this is a general conclusion we can draw from our studies of both the classical substrate inhibition scheme and the pH-dependent enzyme mechanism. Finally, an analysis of the nullclines for these two models allows us to prove that the nullcline slopes must have a negative value for oscillatory behavior to exist; this proof can explain our results. From our analysis, we conclude with a brief discussion of other enzymes that might be expected to produce oscillatory behavior based on a pH-dependent substrate inhibition mechanism.     

Lipase‐Catalyzed Kinetic Resolution of (±)‐1‐(2‐Furyl) Ethanol in Nonaqueous Media

S‐1‐(2‐Furyl) ethanol serves as an important chiral building block for the preparation of various natural products, fine chemicals, and is widely used in the chemical and pharmaceutical industries. In this work, lipase‐catalyzed kinetic resolution of (R/S)‐1‐(2‐furyl) ethanol using different acyl donors was investigated. Vinyl esters are good acyl donors vis‐à‐vis alkyl esters for kinetic resolution. Among them, vinyl acetate was found to be the best acyl donor. Different immobilized lipases such as Rhizomucor miehei lipase, Thermomyces lanuginosus lipase, and Candida antarctica lipase B were evaluated for this reaction, among which C. antarctica lipase B, immobilized on acrylic resin (Novozym 435), was found to be the best catalyst in n‐heptane as solvent. The effect of various parameters was studied in a systematic manner. Maximum conversion of 47% and enantiomeric excess of the substrate (ee_s) of 89% were obtained in 2 h using 5 mg of enzyme loading with an equimolar ratio of alcohol to vinyl acetate at 60°C at a speed of 300 rpm in a batch reactor. From the analysis of progress curve and initial rate data, it was concluded that the reaction followed the ordered bi–bi mechanism with dead‐end ester inhibition. Kinetic parameters were obtained by using nonlinear regression. This process is more economical, green, and easily scalable than the chemical processes. Chirality 26:286–292, 2014. © 2014 Wiley Periodicals, Inc.     

Kinetic Analysis and Simulation Studies for Lipase-Catalysed Resolution of Racemic 2-Methyl-1-Pentanol

The lipase-catalysed optical resolution of a racemic mixture of 2-methyl-l-pentanol by transesterifica-tion using vinyl acetate as acyl donor has been studied experimentally. A mechanistic model has been developed for the double-substrate reaction sequence treating both enantiomers as competing substrates. The model is based upon a ping-pong mechanism with alternative substrates involving an acyl-enzyme intermediate. The kinetic constants of the model have been evaluated using initial rate experiments and nonlinear regression analysis. The model successfully predicts the evolution of the enantiomeric excess of substrate (ee_R) and the degree of conversion with time for batch experiments with various initial concentrations of vinyl acetate and (R,S)-2-methyl-1-pentanol. Furthermore, the rate equations have been used to theoretically study the dynamic progression of a continuous enzyme-catalysed resolution process. The enantiomeric excess as a function of conversion for different process configurations is discussed. It is found, that the maximum attainable ee_R is strongly dependent on the residence time distribution of the continuous reactor and is rather low for a continuous stirred tank reactor (CSTR) due to competitive inhibition effects.     

Optimum design of a series of CSTRs performing reversible Michaelis-Menten kinetics: a rigorous mathematical study

The optimum design of a given number of CSTRs in series performing reversible Michaelis-Menten kinetics in the liquid phase assuming constant activity of the enzyme is studied. In this study, the presence of product in the feed stream to the first reactor, as well as the effect of the product intermediate concentrations in the downstream reactors on the reaction rate are investigated. For a given number of N CSTRs required to perform a certain degree of substrate conversion and under steady state operation and constant volumetric flow rate, the reactor optimization problem is posed as a constrained nonlinear programming problem (NLP). The reactor optimization is based on the minimum overall residence time (volume) of N reactors in series. When all the reactors in series operate isothermally, the constrained NLP is solved as an unconstrained NLP. And an analytical expression for the optimum overall residence time is obtained. Also, the necessary and sufficient conditions for the minimum overall residence time of N CSTRs are derived analytically. In the presence of product in the feed stream, the reversible Michaelis-Menten kinetics shows competitive product inhibition. And this is, because of the increase in the apparent rate constant K^' _m that results in a reduction of the overall reaction rate. The optimum total residence time is found to increase as the ratio (‚₀) of product to substrate concentrations in the feed stream increases. The isomerization of glucose to fructose, which follows a reversible Michaelis-Menten kinetics, is chosen as a model for the numerical examples.     

Phosphorylation reaction of vertebrate smooth muscle myosin: an enzyme kinetic analysis

Phosphorylation of vertebrate smooth muscle myosin or its isolated 20 000-dalton light chains by myosin light-chain kinase (MLCK) was found to follow first-order kinetics not only at low ([M] much less than Km) but also at high ([M] greater than or equal to Km) substrate concentration. This observation can most simply be explained by a product inhibition for which the Michaelis constants (Km) of the enzyme for the substrate (dephosphorylated myosin) and for the product (phosphorylated myosin) are approximately the same. For such a case, integration of the kinetic velocity equation gives an exponential formula similar to that of a true first-order reaction, the only difference being that its rate constant (k) depends additionally on the initial substrate concentration ([M]0). The standard kinetic constants (k, Km, Vmax) have been calculated by using this pseudo-first-order relationship. Independent evidence for the validity of the derived kinetic relationship was obtained from binding studies with myosin and MLCK. These showed that MLCK binds to phosphorylated and dephosphorylated myosin with approximately equal affinity (Ks = 30 X 10(-9) M). The possible applicability of the same kinetic relationship to other enzyme systems is discussed.     

Modeling and kinetic analysis of the reaction system using whole cells with separately and co-expressed D-hydantoinase and N-carbamoylase

We developed a kinetic model that describes a heterogeneous reaction system for the production of D-p-hydroxyphenylglycine from D,L-p-hydroxyphenyl-hydantoin using D-hydantoinase of Bacillus stearothermophilus SD1 and N-carbamoylase of Agrobacterium tumefaciens NRRL B11291. As a biocatalyst, whole cells with separately or co-expressed enzymes were used. The reaction system involves dissolution of substrate particles, enzymatic conversion, racemization of the L-form substrate, and transfer of the dissolved substrate, intermediate, and product through the cell membrane. Because the two enzymes have different pH optimum, kinetic parameters were evaluated at different pH for the reaction systems. The model was simulated using the kinetic parameters and compared with experimental data, and it was found that the kinetic model well describes the behavior of the reaction systems using whole cells with separately and co-expressed enzymes. Factors affecting the kinetics of the reaction systems were analyzed on the basis of the kinetic model. In the reaction system with separately expressed enzymes, racemization rate and transport of the reaction intermediate (N-carbamoyl-D-p-hydroxyphenylglycine) were revealed to be the limiting factors at neutral pH, resulting in accumulation of intermediate in the reaction medium. At alkaline condition, on the other hand, inhibition of N-carbamoylase by ammonia was severe, and thereby the reaction rate significantly reduced. In the co-expressed enzyme system, accumulation of intermediate was negligible in the reaction medium, and the improved performance was observed compared to that with separately expressed enzymes. The present model might be applied for the optimization and development of the reaction system using two sequential enzymes.     

Continuous hydrolysis of oil by immobilized lipase in a countercurrent reactor

Lipase from Pseudomonas fluorescens biotype I was immobilized by adsorption of anion exchange resin using glutaraldehyde to enhance the adsorption. The activity yield of the immobilized lipase was very low (below 1%) when lipase activity was measured using emulsion substrate. The activity yield was 10-70% when lipase activity was measured using non-emulsion substrate. Countercurrent reactors for hydrolysis of oil using non-emulsion substrate were studied. A fluidized bed reactor was found to be superior to a fixed bed one since in a fixed bed reactor the separation rate of the two layers was slow and the flow rate of the reactor had to be slower than the separation rate. A fluidized bed reactor system equipped with settling compartments and stirring compartments was devised. Continuous lipolysis at 60 degrees C and continuous separation of oily product and water soluble product were performed. After continuous operation for more than 3 months, 70% of the initial activity of the immobilized lipase was observed at the end of the reaction.     

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.     

Kinetic analysis of enzyme systems with suicide substrate in the presence of a reversible, uncompetitive inhibitor.

We present a general kinetic analysis of enzyme catalyzed reactions evolving according to a Michaelis-Menten mechanism, in which an uncompetitive, reversible inhibitor acts. Simultaneously, enzyme inactivation is induced by an unstable suicide substrate, i.e. it is a Michaelis-Menten mechanism with double inhibition: one originating from the substrate and another originating from the reversible inhibitor. Rapid equilibrium of the reversible reaction steps involved is assumed and the time course equations for the reaction product have been derived under the assumption of limiting enzyme. The goodness of the analytical solutions has been tested by comparison with simulated curves obtained by numerical integration. A kinetic data analysis to determine the corresponding kinetic parameters from the time progress curve of the product is suggested.     

Homoserine kinase of Escherichia coli: kinetic mechanism and inhibition by L-aspartate semialdehyde

The kinetic mechanism of homoserine kinase, purified to homogeneity from Escherichia coli, was examined by initial velocity techniques at pH 7.6. Whereas ATP displayed normal Michaelis-Menten saturation kinetics (Km = 0.2 mM), L-homoserine showed hyperbolic saturation kinetics only up to a concentration of 0.75 mM (Km = 0.15 mM). Above this concentration, L-homoserine caused marked but partial inhibition (Ki approximately 2 mM). The kinetic data indicated that the addition of substrates to homoserine kinase occurs by a preferred order random mechanism, with ATP preferentially binding before L-homoserine. When the ATP concentration was varied at several fixed inhibitory concentrations of L-homoserine, the resulting inhibition pattern indicated hyperbolic mixed inhibition. This suggested a second binding site for L-homoserine. L-Aspartate semialdehyde, an amino acid analog of L-homoserine, proved to be an alternative substrate of homoserine kinase (Km = 0.68 mM), and was subsequently used as a probe of its kinetic mechanism. In aqueous solution, at pH 7.5, this analog was found to exist predominantly (ca 85%) as its hydrated species. When examined as an inhibitor of the physiological reaction, L-aspartate semialdehyde showed mixed inhibition versus both L-homoserine and ATP. Although the pH profiles for the binding of L-homoserine as a substrate (Km) and as an inhibitor (Ki) were identical, the kinetic data were best fit to a two-site model, with separate catalytic and inhibitory sites for L-homoserine.     

Kinetics of acetophenone reduction to (R)-1-phenylethanol by a whole-cell Pichia capsulata biocatalyst

(R)-1-phenylethanol is an important substance in fragrance and flavor industry. In this work, the reduction of acetophenone to (R)-1-phenylethanol in an aqueous medium was examined using Pichia capsulata as a whole-cell biocatalyst. Progress curve and initial rate measurements were used to obtain kinetic data. The experiments were carried out at pH 5, temperature of 25?°C, and in the presence of glucose to maintain in vivo regeneration of NADH. A model of the reversible reaction kinetics considering the substrate inhibition of the forward reaction was developed. Five kinetic parameters of this model were determined by a simultaneous fit of a reaction rate dependence on substrate concentration and 18 substrate and product concentration progress curves with very good accuracy. Equilibrium constant of the reaction and equilibrium conversion of acetophenone to (R)-1-phenylethanol were 13.7 and 93%, respectively.     

Modeling and kinetic parameter estimation of alcohol dehydrogenase‐catalyzed hexanol oxidation in a microreactor

A mathematical model for hexanol oxidation catalyzed by NAD⁺‐dependent alcohol dehydrogenase from baker's yeast in a microreactor was developed and compared with the model when the reaction takes place in a macroscopic reactor. The enzyme kinetics was modeled as a pseudo‐homogeneous process with the double substrate Michaelis–Menten rate expression. In comparison with the kinetic parameters estimated in the cuvette, a 30‐fold higher maximum reaction rate and a relatively small change in the saturation constants are observed for the kinetic parameters estimated in the continuously operated tubular microreactor (V_m1=197.275 U/mg, K_m^hexanol=9.420 mmol/L, and K_m1^NAD+=0.187 mmol/L). Kinetic measurements performed in the microreactor, estimated from the initial reaction rate experiments at the residence time of 36 s, showed no product inhibition, which could be explained by hydrodynamic effects and the continuous removal of inhibiting products. The Fourier amplitude sensitivity test method was applied for global kinetic parameter analysis, which shows a significant increase in the sensitivity of K_m1^NAD+ in the microreactor. Independent experiments performed in the microreactor were used to validate and to verify the developed mathematical model.     

A new mechanism and kinetic model for the enzymatic synthesis of short-chain fructooligosaccharides from sucrose

A kinetic model based on a ping-pong mechanism was developed under the steady-state hypothesis to account for the short-chain fructooligosaccharides (sc-FOS) synthesis using the commercial cellulolytic enzyme preparation, Rohapect CM. This new mechanism takes into account the interactions between the enzyme species and potential substrates (sucrose and sc-FOS) as a single complex reaction, allowing a better understanding of the reaction kinetics.The initial reaction rate laws appropriately describe the kinetic profiles of the examined substrates. Whereas sucrose exhibited Michaelis–Menten behavior with substrate inhibition, 1-kestose and nystose followed Michaelis–Menten and sigmoid enzyme kinetics. In addition, the enzyme was competitively inhibited by glucose and exhibited significant hydrolytic activity in the presence of nystose.The overall model was simultaneously fitted to experimental data from three initial sucrose concentrations (0.5, 1.5 and 2.1 M) using a multi-response regression with kinetic parameters that have biochemical relevance and are independent of the enzyme concentration. According to the model, sucrose acts almost exclusively as a fructosyl donor substrate. The mathematical development described herein is expected to be suitable for modeling similar enzymatic reaction systems.