Modeling, simulation, and kinetic analysis of a heterogeneous reaction system for the enzymatic conversion of poorly soluble substrate.

We developed a kinetic model that describes a heterogeneous reaction system consisting of a solid substrate suspension for the production of D-amino acid using D-hydantoinase. As a biocatalyst, mass-produced free and whole cell enzymes were used. The heterogeneous reaction system involves dissolution of a solid substrate, enzymatic conversion of the dissolved D-form substrate, spontaneous racemization of an L-form substrate to D-form, and deactivation of the enzyme. In the case of using whole cell enzymes, transfer of the dissolved substrate and product through the cell membrane was considered. The kinetic parameters were determined from experiments, literature data, and by using Marquardt's method of nonlinear regression analysis. The model was simulated using the kinetic parameters and compared with experimental data, and a good agreement was observed between the experimental results and the simulation ones. Factors affecting the kinetics of the heterogeneous reaction system were analyzed on the basis of the kinetic model, and the efficiency of the reaction systems using free and whole cell enzymes was also compared.     

Investigation of kinetics of immobilized liver esterase by flow calorimetry

Flow calorimetry (FC) was shown to be a powerful tool for investigation of the kinetics of phenyl acetate hydrolysis catalyzed by pig liver carboxyl esterase. The enzyme was immobilized in alginate gel particles that were placed in a calorimetric flow column and the heat effect of enzyme reaction was followed in single flow and total recirculation conditions. It was shown that the registered temperature change was proportional to molar amount of substrate transformed in the column. A mathematical model describing the enzyme reaction, mass transfer, and heat effects in the calorimetric system was developed and used for the kinetic data evaluation. By combining data from single flow and recirculation modes true kinetic parameters were evaluated by the proposed mathematical procedure based on the model solution and successive approximations.

The kinetic data for carboxyl esterase showed a slide substrate inhibition by phenyl acetate. The obtained kinetic parameters were as follows: Michaelis constant K_m=2 mmol dm⁻³ and substrate inhibition constant K_i=42 mmol dm⁻³. The method can be applied to kinetic study of immobilized enzymes directly in the flow calorimeter without any requirement of an independent analytical technique.     

Estimation of kinetic parameters for substrate and inhibitor in a reaction with an enzyme sample containing different types of inhibitor

The method of kinetic analysis is developed to obtain the maximum velocity (V_m), the Michaelis constant (K_m) and the parameters characterizing the inhibitors in an impure enzyme reaction, contaminated with one of four types of inhibitor (competitive, noncompetitive, uncompetitive and mixed-type). Although the reaction rate decreases with the increasing concentration of the enzyme sample containing an inhibitor, the double-reciprocal plot of the rate against the sample concentration becomes linear. The slopes of these linear plots at several different concentrations of substrate provide K_m and the specific enzyme activity, which is proportional to V_m, in the sample. These linear straight lines intersect in a point, of which the coordinates give the unique parameters for the inhibitor. To prove the validity of this kinetic method, the model experiments were carried out with acetylcholinesterase and its inhibitors, phenyltrimethylammonium and trimethylammonium. The present method was applied to the measurement of the specific activity of galactosylceramide galactosidase in the mouse cerebral homogenate. In addition, a kinetic method is indicated for the inhibition of an enzymatic reaction by a contaminant which binds the substrate to reduce the fraction available to the enzyme.     

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.     

Mathematical modelling and kinetic study for CD production catalysed by Toruzyme® and CGTase from Bacillus firmus strain 37

A new mathematical model was developed for the kinetics of α-, β- and γ-cyclodextrin production, expanding an existing model that only included the production of β- and γ-cyclodextrins, because a detailed kinetic modelling of the reactions involved allows the manipulation of the process yields. The kinetic behaviour of the commercial enzyme Toruzyme^® was studied with maltodextrin as substrate at different concentrations and for CGTase from Bacillus firmus strain 37 at a concentration of 100 g L⁻¹. The mathematical model showed a proper fit to the experimental data, within the 24-h period studied, confirming that the considered hypotheses represent the kinetic behaviour of the enzymes in the reaction medium. The kinetic parameters generated by the model allowed reproducing previous observed qualitative tendencies as it can be seen that changing experimental conditions in the reaction process such as enzyme and substrate concentrations results in large changes in the enzyme kinetics and using high substrate concentrations does not guarantee the highest conversion rates due to enzyme inhibition and reverse reactions. In addition, this new mathematical model complements previous qualitative observations enabling the manipulation of the direct and reverse reactions catalysed by the enzyme by adjusting the reaction conditions, to target quantitative results of increased productivity and better efficiency in the production of a desired cyclodextrin.

     

Kinetic modeling of lipase‐catalyzed esterification reaction between oleic acid and trimethylolpropane: A simplified model for multi‐substrate multi‐product ping–pong mechanisms

Kinetic models are among the tools that can be used for optimization of biocatalytic reactions as well as for facilitating process design and upscaling in order to improve productivity and economy of these processes. Mechanism pathways for multi‐substrate multi‐product enzyme‐catalyzed reactions can become very complex and lead to kinetic models comprising several tens of terms. Hence the models comprise too many parameters, which are in general highly correlated and their estimations are often prone to huge errors. In this study, Novozym^®435 catalyzed esterification reaction between oleic acid (OA) and trimethylolpropane (TMP) with continuous removal of side‐product (water) was carried out as an example for reactions that follow multi‐substrate multi‐product ping‐pong mechanisms. A kinetic model was developed based on a simplified ping‐pong mechanism proposed for the reaction. The model considered both enzymatic and spontaneous reactions involved and also the effect of product removal during the reaction. The kinetic model parameters were estimated using nonlinear curve fitting through unconstrained optimization methodology and the model was verified by using empirical data from different experiments and showed good predictability of the reaction under different conditions. This approach can be applied to similar biocatalytic processes to facilitate their optimization and design. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 29:1422–1429, 2013     

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.     

Theoretical approach to the steady-state kinetics of a bi-substrate acyl-transfer enzyme reaction that follows a hydrolysable-acyl-enzyme-based mechanism. Application to the study of lysophosphatidylcholine:lysophosphatidylcholine acyltransferase from rabbit lung.

A kinetic model is proposed for catalysis by an enzyme that has several special characteristics: (i) it catalyses an acyl-transfer bi-substrate reaction between two identical molecules of substrate, (ii) the substrate is an amphiphilic molecule that can be present in two physical forms, namely monomers and micelles, and (iii) the reaction progresses through an acyl-enzyme-based mechanism and the covalent intermediate can react also with water to yield a secondary hydrolytic reaction. The theoretical kinetic equations for both reactions were deduced according to steady-state assumptions and the theoretical plots were predicted. The experimental kinetics of lysophosphatidylcholine:lysophosphatidylcholine acyltransferase from rabbit lung fitted the proposed equations with great accuracy. Also, kinetics of inhibition by products behaved as expected. It was concluded that the competition between two nucleophiles for the covalent acyl-enzyme intermediate, and not a different enzyme action depending on the physical state of the substrate, is responsible for the differences in kinetic pattern for the two activities of the enzyme. This conclusion, together with the fact that the kinetic equation for the transacylation is quadratic, generates a 'hysteretic' pattern that can provide the basis of self-regulatory properties for enzymes to which this model could be applied.     

Reaction kinetics of protease with substrate phage. Kinetic model developed using stromelysin

Peptide libraries generated using phage display have been widely applied to proteolytic enzymes for substrate selection and optimization, but the reaction kinetics between the enzyme and substrate phage are not well understood. Using a quantitative ELISA assay to monitor the disappearance of substrate, we have been able to follow the course of reaction between stromelysin, a metalloprotease, and its substrate phage. We found that under the proteolytic conditions where the enzyme was present in nanomolar concentration or higher, in excess over the substrate, the proteolysis of substrate phage was a single exponential event and the observed rate linear with respect to enzyme concentration. The enzyme concentration dependence could be described by pseudo first-order kinetic equations. Our data suggest that substrate binding is slow relative to the subsequent hydrolysis step, implying that the phage display selection process enriches clones that have high binding affinity to the protease, and the selection may not discriminate those of different chemical reactivity toward the enzyme. Considering that multiple substrate molecules may be present on a single phage particle, we regard the substrate phage reaction kinetic model as empirical. The validity of the model was ascertained when we successfully applied it to determine the binding affinity of a competitive inhibitor of stromelysin.     

Venom exonuclease — kinetics and specificity towards different nucleotide substrates

The steady-state kinetics of the reactions catalyzed by the exonuclease from Crotalus adamanteus venom were studied by the titrigraphic method. The kinetic parameters of the enzyme reactions were determined for the hydrolysis of a number of different substrates with phosphodiester and prophosphate bonds. When low molecular weeight substrates were hydrolysed, a relative base specificity was observed. The hydrolysis of polymeric substrates showed an increase in the reaction rate of the consecutive liberation of the mononucleotide product, parallel with the decrease of the substrate chain length. A strict correlation of the kinetic parameters of the hydrolysis of the first phosphodiester bond of oligomeric substrates with the degree of polymerization of these substrates was obtained. On the basis of the determined kinetic parameters of hydrolysis for the different substrates under study, some thermodynamic parameters of the enzyme reactions were calculated. A hypothetical model is put forward for the active site of the venom exonuclease.     

Evaluation of intrinsic immobilized kinetics in hollow fiber reactor systems.

Immobilized cell and enzyme hollow fiber reactors have been developed for a variety of biochemical and biomedical applications. Reported mathematical models for predicting substrate conversion in these reactors have been limited in accuracy because of the use of free-solution kinetic parameters. This paper describes a method for determining the intrinsic kinetics of enzymes immobilized in hollow fiber reactor systems using a mathematical model for diffusion and reaction in porous media and an optimization procedure to fit intrinsic kinetic parameters to experimental data. Two enzymes, a thermophilic beta-galactosidase that exhibits product inhibition and L-lysine alpha-oxidase, were used in the analysis. The intrinsic kinetic parameters show that immobilization enhanced the activity of the beta-galactosidase while decreasing the activity of L-lysine alpha-oxidase. Both immobilized enzymes had higher Km values than did the soluble enzyme, indicating less affinity for the substrate. These results are used to illustrate the significant improvement in the ability to predict substrate conversion in hollow fiber reactors.     

Isothermal titration calorimetry uncovers substrate promiscuity of bicupin oxalate oxidase from Ceriporiopsis subvermispora

Isothermal titration calorimetry (ITC) may be used to determine the kinetic parameters of enzyme-catalyzed reactions when neither products nor reactants are spectrophotometrically visible and when the reaction products are unknown. We report here the use of the multiple injection method of ITC to characterize the catalytic properties of oxalate oxidase (OxOx) from Ceriporiopsis subvermispora (CsOxOx), a manganese dependent enzyme that catalyzes the oxygen-dependent oxidation of oxalate to carbon dioxide in a reaction coupled with the formation of hydrogen peroxide. CsOxOx is the first bicupin enzyme identified that catalyzes this reaction. The multiple injection ITC method of measuring OxOx activity involves continuous, real-time detection of the amount of heat generated (dQ) during catalysis, which is equal to the number of moles of product produced times the enthalpy of the reaction (ΔH_app). Steady-state kinetic constants using oxalate as the substrate determined by multiple injection ITC are comparable to those obtained by a continuous spectrophotometric assay in which H₂O₂ production is coupled to the horseradish peroxidase-catalyzed oxidation of 2,2′-azinobis-(3-ethylbenzthiazoline-6-sulfonic acid) and by membrane inlet mass spectrometry. Additionally, we used multiple injection ITC to identify mesoxalate as a substrate for the CsOxOx-catalyzed reaction, with a kinetic parameters comparable to that of oxalate, and to identify a number of small molecule carboxylic acid compounds that also serve as substrates for the enzyme.     

On the use of apparent kinetic parameters for immobilized enzyme with noncompetitive substrate inhibition

The use of a simple rate equation with apparent parameters to describe the kinetic behavior of an immobilized enzyme with noncompetitive substrate inhibition was assessed. To do so, the reaction rate was calculated as a function of the interfacial substrate concentration, and the results were used to identify the apparent kinetic parameters by nonlinear regression. This procedure was repeated for different values of the diffusional constraints and of the inhibition constant. The equation using apparent parameters can describe the global kinetic behavior, provided that the diffusional and inhibitory constraints are not too high. When the constraints are high, a Michaelis-Menten equation can be used to model the kinetics for interfacial concentrations lower than the concentration leading to the maximum reaction rate.     

Systematic Construction of Kinetic Models from Genome-Scale Metabolic Networks

The quantitative effects of environmental and genetic perturbations on metabolism can be studied in silico using kinetic models. We present a strategy for large-scale model construction based on a logical layering of data such as reaction fluxes, metabolite concentrations, and kinetic constants. The resulting models contain realistic standard rate laws and plausible parameters, adhere to the laws of thermodynamics, and reproduce a predefined steady state. These features have not been simultaneously achieved by previous workflows. We demonstrate the advantages and limitations of the workflow by translating the yeast consensus metabolic network into a kinetic model. Despite crudely selected data, the model shows realistic control behaviour, a stable dynamic, and realistic response to perturbations in extracellular glucose concentrations. The paper concludes by outlining how new data can continuously be fed into the workflow and how iterative model building can assist in directing experiments.     

Determination of the Catalytic Mechanism for Mitochondrial Malate Dehydrogenase

The kinetics of malate dehydrogenase (MDH) catalyzed oxidation/reduction of L-malate/oxaloacetate is pH-dependent due to the proton generated/taken up during the reaction. Previous kinetic studies on the mitochondrial MDH did not yield a consensus kinetic model that explains both substrate and pH dependency of the initial velocity. In this study, we propose, to our knowledge, a new kinetic mechanism to explain kinetic data acquired over a range of pH and substrate concentrations. Progress curves in the forward and reverse reaction directions were obtained under a variety of reactant concentrations to identify associated kinetic parameters. Experiments were conducted at physiologically relevant ionic strength of 0.17 M, pH ranging between 6.5 and 9.0, and at 25°C. The developed model was built on the prior observation of proton uptake upon binding of NADH to MDH, and that the MDH-catalyzed oxidation of NADH may follow an ordered bi-bi mechanism with NADH/NAD binding to the enzyme first, followed by the binding of oxaloacetate/L-malate. This basic mechanism was expanded to account for additional ionic states to explain the pH dependency of the kinetic behavior, resulting in what we believe to be the first kinetic model explaining both substrate and pH dependency of the reaction velocity.     

Kinetic analysis of enzyme systems with suicide substrate in the presence of a reversible competitive inhibitor, tested by simulated progress curves

The use of suicide substrates remains a very important and useful method in enzymology for studying enzyme mechanisms and designing potential drugs. Suicide substrates act as modified substrates for the target enzymes and bind to the active site. Therefore the presence of a competitive reversible inhibitor decreases the rate of substrate-induced inactivation and protects the enzyme from this inactivation. This lowering on the inactivation rate has evident physiological advantages, since it allows the easy acquisition of experimental data and facilitates kinetic data analysis by providing another variable (inhibitor concentration). However despite the importance of the simultaneous action of a suicide substrate and a competitive reversible inhibition, to date no corresponding kinetic analysis has been carried out. Therefore we present a general kinetic analysis of a Michaelis-Menten reaction mechanism with double inhibition caused by both, a suicide substrate and a competitive reversible inhibitor. We assume rapid equilibrium of the reversible reaction steps involved, while the time course equations for the reaction product have been derived with the assumption of a limiting enzyme. The goodness of the analytical solutions has been tested by comparison with the 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. In conclusion, we present a complete kinetic analysis of an enzyme reaction mechanism as described above in an attempt to fill a gap in the theoretical treatment of this type of system.     

A Model for the Interfacial Kinetics of Phospholipase D Activity on Long-Chain Lipids

The membrane-active enzyme phospholipase D (PLD) catalyzes the hydrolysis of the phosphodiester bond in phospholipids and plays a critical role in cell signaling. This catalytic reaction proceeds on lipid-water interfaces and is an example of heterogeneous catalysis in biology. Recently we showed that planar lipid bilayers, a previously unexplored model membrane for these kinetic studies, can be used for monitoring interfacial catalytic reactions under well-defined experimental conditions with chemical and electrical access to both sides of the lipid membrane. Employing an assay that relies on the conductance of the pore-forming peptide gramicidin A to monitor PLD activity, the work presented here reveals the kinetics of hydrolysis of long-chain phosphatidylcholine lipids in situ. We have developed an extension of a basic kinetic model for interfacial catalysis that includes product activation and substrate depletion. This model describes the kinetic behavior very well and reveals two kinetic parameters, the specificity constant and the interfacial quality constant. This approach results in a simple and general model to account for product accumulation in interfacial enzyme kinetics.     

Glyceraldehyde-3-phosphate dehydrogenase from human erythrocyte membranes. Kinetic mechanism and competitive substrate inhibition by glyceraldehyde 3-phosphate

Glyceraldehyde-3-phosphate dehydrogenase (GAPD) was isolated from human erythrocyte ghosts by a simple procedure utilizing ammonium sulfate precipitation and affinity chromatography on NAD⁺-Sepharose 4B. The purified enzyme had a specific activity of 98 units/mg protein. The kinetic mechanism of GAPD was studied by product and deadend inhibition using NADH, α-glycerophosphate, nitrate, and 2,3-diphosphoglycerate. The results indicated that the human erythrocyte GAPD-catalyzed reaction follows an ordered ter bi mechanism characterized by the sequential addition of NAD⁺, glyceraldehyde 3-phosphate (GAP), and phosphate to the enzyme and the sequential release of 1,3-diphosphoglycerate and NADH from the enzyme. This contrasts with the mechanism (rapid equilibrium random ter bi) proposed by Oguchi (1970, J. Biochem. (Tokyo)68, 427–439) who based his conclusion on the initial rate data alone. Since the Michaelis-Menten kinetics were not applicable to this enzyme because of the competitive substrate inhibition by GAP, we devised a new kinetic approach for determining the parameters of the GAPD-catalyzed reaction. Results of this study indicate that the GAPD-catalyzed reaction is regulated by both ATP and GAP. We propose that GAP acts as an “amplifier” for the feedback inhibition effect of ATP. We discuss the effect this may have played in causing controversy over the regulatory role of this enzyme in glycolysis.     

Mathematical modelling of dynamics and control in metabolic networks. V. Static bifurcations in single biochemical control loops

Here we expand an earlier study of feedback activation in simple linear reaction sequences by searching the parameter space of biologically realistic rate laws for multiple stable steady states. The impetus for this work is to seek the origin of decision making strategies at the metabolic level, with particular emphasis on the switching between the operating conditions needed to meet changing substrate availability and organism requirements. The control loop considered herein is a linear reaction chain in which the end product of the reaction sequence feedback activates the first reaction in the sequence to produce feedback control. It has been found that the criteria for the existence of multiple steady state solutions in such loops involve only the kinetics of the regulatory enzyme controlling the first reaction and that of end product removal. The effects of these kinetics are examined here using two representative models for the regulatory enzyme: the lumped controller, based on Hill-type kinetics, and the symmetry model. The behavior of these two models is qualitatively similar, and both show the characteristics needed for switching between low and high substrate utilization. The removal rate is assumed to be of the Michaelis-Menten type. Judicious scaling of the governing equations permits separation of genetically determined kinetic parameters from concentration dependent ones. This allows us to conclude that, for a fixed set of kinetic parameters, the steady state flux through the loop can be switched between stable steady states by merely varying metabolite or enzyme concentrations. In particular, when the initial substrate exceeds a certain critical level, the loop can be "switched on" (by a discontinuous increase in the flux through the chain), and similarly, when it falls below a critical level, the pathway is shut down. Similar effects can be realized by varying the ratios of enzyme concentrations. It is proposed that by identifying these critical points one can gain significant insight into the objectives of decision making at the metabolic level.