New insights into activation and substrate recognition of polyhydroxyalkanoate synthase from Ralstonia eutropha

The polyhydroxyalkanoate synthase of Ralstonia eutropha (PhaC_Re) shows a lag time for the start of its polymerization reaction, which complicates kinetic analysis of PhaC_Re. In this study, we found that the lag can be virtually eliminated by addition of 50 mg/L TritonX-100 detergent into the reaction mixture, as well as addition of 2.5 g/L Hecameg detergent as previously reported by Gerngross and Martin (Proc Natl Sci USA 92: 6279–6283, 1995). TritonX-100 is an effective lag eliminator working at much lower concentration than Hecameg. Kinetic analysis of PhaC_Re was conducted in the presence of TritonX-100, and PhaC_Re obeyed Michaelis–Menten kinetics for (R)-3-hydroxybutyryl-CoA substrate. In inhibitory assays using various compounds such as adenosine derivatives and CoA derivatives, CoA free acid showed competitive inhibition but other compounds including 3′-dephospho CoA had no inhibitory effect. Furthermore, PhaC_Re showed a considerably reduced reaction rate for 3′-dephospho (R)-3-hydroxybutyryl CoA substrate and did not follow typical Michaelis–Menten kinetics. These results suggest that the 3′-phosphate group of CoA plays a critical role in substrate recognition by PhaC_Re.     

Catechol Oxidase and SOD Mimicking by Copper(II) Complexes of Multihistidine Peptides

Copper(II) complexes of five peptide ligands containing at least three histidine residues have been tested as catalysts in catechol oxidation and superoxide dismutation. All systems exhibit considerable catechol oxidase-like activity, and the Michaelis–Menten enzyme kinetic model is applicable in all cases. Beside the Michaelis–Menten parameters, the effects of pH, catalyst and dioxygen concentration on the reaction rates are also reported. Considering the rather different sequences, the observed oxidase activity seems to be a general behavior of copper(II) complexes with multihistidine peptides. Interestingly, in all cases {N_im/2N_im,2N^?} coordinated complexes are the pre-active species, the bound amide nitrogens were proposed to be an acid/base site for facilitating substrate binding. The studied copper(II)-peptide complexes are also able to effectively dismutate superoxide radical in the neutral pH range.     

Mathematical model for the fluidized bed biofilm reactor

A mathematical model is proposed for the fluidized bed biofilm reactor (FBBR). For individual biofilm-covered particles (bioparticles) within the reactor, an analysis of intrabiofilm mass transfer and simultaneous intrinsic zero order reaction yields an effectiveness factor expression which is a function of the modified, zero order Thiele modulus, Φ_0,m. This expression is linked to a one-dimensional reactor flow model and a fluidization model to yield an overall reactor model describing convective transport and simultaneous biochemical conversion of substrate within a FBBR. For Φ_0,m<1.15, FBBR is mass transfer limited and 0.45 order kinetics are observed. For Φ_0,m<1.15, mass transfer limitations are insignificant and intrinsic zero order kinetics are observed. A sensitivity analysis using the proposed mathematical model indicates that biofilm thickness and media size are the two most important operating parameters. These two parameters can be optimized simultaneously for a specific application. The proposed model provides a rational approach for FBBR design.     

Occurrence of dead core in catalytic particles containing immobilized enzymes: analysis for the Michaelis–Menten kinetics and assessment of numerical methods

In this article, the occurrence of dead core in catalytic particles containing immobilized enzymes is analyzed for the Michaelis–Menten kinetics. An assessment of numerical methods is performed to solve the boundary value problem generated by the mathematical modeling of diffusion and reaction processes under steady state and isothermal conditions. Two classes of numerical methods were employed: shooting and collocation. The shooting method used the ode function from Scilab software. The collocation methods included: that implemented by the bvode function of Scilab, the orthogonal collocation, and the orthogonal collocation on finite elements. The methods were validated for simplified forms of the Michaelis–Menten equation (zero-order and first-order kinetics), for which analytical solutions are available. Among the methods covered in this article, the orthogonal collocation on finite elements proved to be the most robust and efficient method to solve the boundary value problem concerning Michaelis–Menten kinetics. For this enzyme kinetics, it was found that the dead core can occur when verified certain conditions of diffusion–reaction within the catalytic particle. The application of the concepts and methods presented in this study will allow for a more generalized analysis and more accurate designs of heterogeneous enzymatic reactors.     

Lipase-catalyzed esterification of rutin and naringin with fatty acids of medium carbon chain

Flavonoids rutin and naringin were acylated with fatty acids of medium carbon chain (with 8–12 carbon atoms on their molecule) in a reaction catalyzed by immobilized lipase from Candida antarctica (Novozyme) in various solvent systems. The reaction parameters affecting the acylation rate and the conversion of the enzymatic process, such as the nature of the organic solvent and acyl donor used, the water activity (a_w) of the system, as well as the kinetic of the reaction have been investigated. In all cases studied, only flavonoid monoester is identified as the product, which indicates that this lipase-catalyzed esterification is regioselective. The enzymatic acylation of flavonoids seems to follow Michaelis–Menten kinetics.     

Perturbation Theory in the Catalytic Rate Constant of the Henri–Michaelis–Menten Enzymatic Reaction

The Henry–Michaelis–Menten (HMM) mechanism of enzymatic reaction is studied by means of perturbation theory in the reaction rate constant k ₂ of product formation. We present analytical solutions that provide the concentrations of the enzyme (E), the substrate (S), as well as those of the enzyme-substrate complex (C), and the product (P) as functions of time. For k ₂ small compared to k _?1, we properly describe the entire enzymatic activity from the beginning of the reaction up to longer times without imposing extra conditions on the initial concentrations E _o and?S _o , which can be comparable or much different.     

A detailed biochemical characterization of phosphopantothenate synthetase, a novel enzyme involved in coenzyme A biosynthesis in the Archaea

We have previously reported that the majority of the archaea utilize a novel pathway for coenzyme A biosynthesis (CoA). Bacteria/eukaryotes commonly use pantothenate synthetase and pantothenate kinase to convert pantoate to 4′-phosphopantothenate. However, in the hyperthermophilic archaeon Thermococcus kodakarensis, two novel enzymes specific to the archaea, pantoate kinase and phosphopantothenate synthetase, are responsible for this conversion. Here, we examined the enzymatic properties of the archaeal phosphopantothenate synthetase, which catalyzes the ATP-dependent condensation of 4-phosphopantoate and β-alanine. The activation energy of the phosphopantothenate synthetase reaction was 82.3?kJ?mol^?1. In terms of substrate specificity toward nucleoside triphosphates, the enzyme displayed a strict preference for ATP. Among several amine substrates, activity was detected with β-alanine, but not with γ-aminobutyrate, glycine nor aspartate. The phosphopantothenate synthetase reaction followed Michaelis–Menten kinetics toward β-alanine, whereas substrate inhibition was observed with 4-phosphopantoate and ATP. Feedback inhibition by CoA/acetyl-CoA and product inhibition by 4′-phosphopantothenate were not observed. By contrast, the other archaeal enzyme pantoate kinase displayed product inhibition by 4-phosphopantoate in a non-competitive manner. Based on our results, we discuss the regulation of CoA biosynthesis in the archaea.     

A Kinetic Analysis of Coupled (or Auxiliary) Enzyme Reactions

As a case study, we consider a coupled (or auxiliary) enzyme assay of two reactions obeying the Michaelis–Menten mechanism. The coupled reaction consists of a single-substrate, single-enzyme non-observable reaction followed by another single-substrate, single-enzyme observable reaction (indicator reaction). In this assay, the product of the non-observable reaction is the substrate of the indicator reaction. A mathematical analysis of the reaction kinetics is performed, and it is found that after an initial fast transient, the coupled reaction is described by a pair of interacting Michaelis–Menten equations. Moreover, we show that when the indicator reaction is fast, the quasi-steady-state dynamics are governed by three fast variables and one slow variable. Timescales that approximate the respective lengths of the indicator and non-observable reactions, as well as conditions for the validity of the Michaelis–Menten equations, are derived. The theory can be extended to deal with more complex sequences of enzyme-catalyzed reactions.     

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.     

Immobilization of enzymes on activated carbon: Properties of immobilized glucoamylase,glucose oxidase,and gluconolactonase

Apparent kinetics and pH–activity relationships have been determined for glucoamylase and glucose oxidase immobilized on activated carbon using a diimide method. Reaction rate expressions of Michaelis–Menten form adequately approximate the observed kinetics for both enzyme preparations over the ranges of substrate concentrations considered. Influences of external mass transfer as well as substrate and product adsorption on interpretation of the experimental data have been examined. Immobilization of a glucose oxidase–gluconolactonase enzyme mixture has been found to increase substantially the ratio of gluconolactonase to glucose oxidase activities compared to the corresponding activity ratio for these enzymes in solution.     

Effect of biocatalyst swelling on the operation of packed-bed immobilized enzyme bioreactor

A general mathematical model was developed for predicting the performance and simulation of a packed-bed immobilized enzyme reactor performing a reaction that follows Michaelis–Menten kinetics with competitive product inhibition. The performance of a packed-bed immobilized enzyme reactor was analyzed taking into account the effect of bed swelling on various diffusional phenomena such as axial dispersion, internal and external mass transfer limitations. The numerical solutions were compared with experimental data obtained for a packed-bed reactor operating with β-galactosidase entrapped in Ca-alginate-K-κ-carrageenan gels for lactose hydrolysis.     

Kinetic characteristics of L-lysine α- oxidase from Trichoderma cf. aureoviride Rifai VKM F-4268D: Substrate specificity and allosteric effects

The present work aims to investigate the kinetic characteristics of homodimer enzyme L-lysine α-oxidase from Trichoderma cf. aureoviride Rifai VKM F-4268D, taking into account allosteric effects. The enzyme was first shown to reveal positive cooperativeness, h=2.05±0.15. Using additional opportunities of Hill coefficient the value of the Michaelis–Menten constant has been estimated, K_m=1.015?10^?5М, indicating high strength of substrate binding to the active site of each subunit. High selectivity and absolute L-stereospecificity of the enzyme were shown. The inhibition of L-lysine conversion by non-cleavable lysine analogs as well as the reaction product was found out to take place. These effects have been evaluated only as the inhibition coefficients (%). A more detailed study of these inhibition effects was complicated because of the cooperativeness of enzyme subunits mentioned above. The kinetic scheme of L-lysine α-oxidase was proposed involving parallel-subsequent action of each of two subunits in the catalytic act.We think that the results obtained will be useful for studying the kinetic properties of other multi-subunit enzymes and improve understanding of the mechanisms of their action.     

Yeast glutathione reductase. Steady-state kinetic studies of its transhydrogenase activity.

Yeast glutathione reductase catalyzes a pyridine nucleotide transhydrogenase reaction using either NADPH or NADH as the electron donor and thionicotinamideadenine dinucleotide phosphate as the electron acceptor. Competitive substrate inhibition of the transhydrogenase reaction by NADPH (K_i = 11 μM) is observed when NADPH is the electron donor. Competitive substrate inhibition by thionicotinamide-adenine dinucleotide phosphate (K_i = 58 μM) is observed with NADH as the electron donor. The turnover numbers of the two transhydrogenase reactions are similar and are equal to about 1% of the turnover number for the NADPH-dependent reduction of oxidized glutathione catalyzed by the enzyme. The transhydrogenase kinetics are analyzed in terms of a pingpong mechanism. It is concluded that the substrate inhibition results from formation of abortive complexes of NADPH with the reduced form of the enzyme and of thionicotinamide-adenine dinucleotide phosphate with the oxidized form of the enzyme. With NADPH as the electron donor, the apparent Michaelis constant for thionicotinamide-adenine dinucleotide phosphate is sensitive to the ionic composition of the assay medium. The data are interpreted to support the existence of a general pyridine nucleotide-binding site at the active site of the enzyme and separate from the binding site for oxidized glutathione.     

A new asymptotic analysis of the nth order reaction-diffusion problem: analytical and numerical studies

We present a new formulation of the steady state, isothermal, nonlinear reaction-diffusion problem involving nth order reaction kinetics for slab geometry. This results in tractable expressions for the effectiveness factor as a function of the Thiele modulus, the Thiele modulus as a function of the centerline concentration, and the concentration profiles in the slab. The expressions are valid asymptotically in the limit of large orders n. We compare these results with the exact numerical solutions obtained by transforming the nonlinear differential equation into an integral form, using Green's function methods, and solving by successive approximations. The formulation for a membrane is also given, and the nature of the asymmetrical solution discussed. The analysis is facilitated through the introduction of pseudo-reaction orders. A comparison of the asymptotic Thiele modulus obtained herein with a previously given expression shows the present theory to be an improvement.     

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.     

Kinetic model for DBT desulphurization by resting whole cells of Pseudomonas putida CECT5279

Bio-desulphurization kinetics of dibenzothiophene (DBT) using Pseudomonas putida CECT 5279, a genetically modified micro-organism (GMO), is studied. A kinetic model describing the 4S route of DBT desulphurization is proposed. Bio-desulphurization experiments have been carried out using resting whole cells of P. putida CECT 5279 obtained at different growth times as biocatalysts. The kinetic equations proposed for each reaction have been previously checked by studying each reaction of the 4S route individually, employing different substrates in different experiments. Finally, simple Michaelis–Menten kinetic equations for the three first reactions catalyzed by two mono-oxygenases (DszC and DszA) and a kinetic equation taking into account competitive inhibition due to product for the final reaction catalyzed by a desulfinase (DszB) have been adopted. DBT has been desulphurized using cells obtained at different growth times (5, 10, 23, 30 and 45 h). The overall kinetic model proposed involving the four reactions of the 4S route was fitted to all the experimental data yielding a set of kinetic parameters able to describe the system evolution. Cell age has influence on the rates of all the reactions: reactions (1), (2) and (3) present maximum rates for cell grown during 30 h, while reaction (4) shows a maximum rate for cells with around 10 h of growth time. However, affinities of each substrate and the inhibition constant of the last reaction are not influenced by the time of growth.     

Kinetic Analyses of the Substrate Inhibition of <Emphasis Type="Italic">Paramecium</Emphasis> Arginine Kinase

Paramecium tetraurelia expresses four types of arginine kinase (AK1–AK4). In a previous study, we showed that AK3 is characterized by typical arginine substrate inhibition, where enzymatic activity markedly decreases near a concentration of 1 mM of arginine substrate. This is in sharp contrast to the three other AK types, which obey the Michaelis–Menten reaction curve. Since cellular arginine concentration in another ciliate Tetrahymena is estimated to be 3–15 mM in vivo, Paramecium AK3 likely functions in conditions that are strongly affected by substrate inhibition. The purpose of this work is to find some novel aspect on the kinetic mechanism of the substrate inhibition of Paramecium AK3 enzyme. Substrate inhibition kinetics for AK3 were analyzed using three models and their validity were evaluated with three static parameters (R², AICc, and Sy.x). The most accurate model indicated that not only ES but also the SES complex reacts to form products, the latter being the complex with two substrates in the active center. The maximum reaction rate for the SES complex, V_max^SES?=?30.4 µmol Pi/min/mg protein, was one-eighth of the ES complex, V_max^ES?=?241.7. The dissociation constant for the SES complex (K_i^SES: 0.34 mM) was two times smaller than that of the ES complex (K_s^ES: 0.61 mM), suggesting that after the primary binding of the arginine substrate (ES complex formation), the binding of a second arginine to the secondarily induced inhibitory site is accelerated to form an SES complex with a lower V_max^SES. The same kinetics were used for the S79A, S80A, and V81A mutants. The results indicate that the S79 residue is significantly involved in the process of binding the second arginine substrate. Herein, the K_i^SES value was ten times (3.62 mM) the value for the wild-type (0.34 mM), weakening substrate inhibition. In contrast, V_max^ES and V_max^SES values for the mutants decreased by one-third, except for the V_max^SES of the S79A mutant, which had a value that was comparable with the value for the wild-type.     

ADP Is a Competitive Inhibitor of ATP-Dependent H Transport in Microsomal Membranes from Zea mays L. Coleoptiles

An anion-sensitive ATP-dependent H⁺ transport in microsomal membranes from Zea mays L. coleoptiles was partially characterized using the pH gradient-dependent decrease of unprotonated neutral red. The following criteria strongly suggest a tonoplast origin of the H⁺ transport observed: strict dependence on Cl⁻; inhibition by SO₄²⁻ and NO₃⁻; insensitivity against vanadate, molybdate, and azide; reversible inhibition by CaCl₂ (H⁺/Ca²⁺ antiport); inhibition by diethylstilbestrol. The substrate kinetics revealed simple Michaelis Menten kinetics for ATP in the presence of 1 millimolar MgCl₂ with a K_m value of 0.56 millimolar (0.38 millimolar for MgATP). AMP and c-AMP did not influence H⁺ transport significantly. However, ADP was a potent competitive inhibitor with a K_i value of 0.18 millimolar. The same inhibition type was found for membranes prepared from primary roots by the same procedure.     

Discrimination between rival laccase inhibition models from data sets with one inhibitor concentration using a penalized likelihood analysis and Akaike weights

Laccase from the white-rot fungus Fomes fomentarius was used for the biodegradation of ferulic acid (FA) in the presence of chloride anions. The initial reaction rates of substrate depletion were obtained by reverse-phase HPLC determination of remaining FA since substrate and reaction products have absorption peaks at similar wavelengths. Modelling of time-course data was accomplished by discrimination of the best enzyme inhibition equation from an initial set of seven different models based on Michaelis–Menten kinetics: competitive; uncompetitive; non-competitive; mixed; mixed hyperbolic; mixed parabolic; mixed hyperbolic and parabolic. Corrected Akaike information criterion was used to evaluate the relative merit of each kinetic model in order to rank them and find the more likely one. The discrimination results showed that the models with higher probabilities were the competitive and mixed inhibition types, but Akaike weights supported the selection of competitive inhibition (CI). After optimization by nonlinear regression, laccase kinetic parameters of FA biodegradation in the presence of chloride anions were: V_max?=?0.11?μmol?min^?1?mg^?1, K_m?=?44?μmol?L^?1 and a CI constant K_ic?=?14?mmol?L^?1.     

Yeast alcohol dehydrogenase immobilized in a glutaraldehyde–albumin matrix: Kinetics and cofactor diffusional effects*

This study was carried out to define how the overall rate of reaction would be influenced by different degrees of diffusional resistance to cofactor transport within an oxidoreductase membrane matrix. To accomplish this, 0.7–6.6μM yeast alcohol dehydrogenase was immobilized in an albumin matrix crosslinked with 2.5 or 5.0% glutaraldehyde to give 102–1685 μM thick membranes. The enzyme half-life was at least doubled at pH 7.5 or 8.8 on immobilization. Values of the kinetic constants for the soluble and immobilized enzyme were determined at 25°C and pH 8.8 over the range of 0.01–1.0M bulk solution concentration of ethanol as substrate and 140–1000μM bulk solution concentration of nicotinamide adenine dinucleotide (NAD⁺) as cofactor, to give essentially single substrate kinetics in NAD⁺. Equilibrium partitioning of ethanol and NAD⁺ between the solution and membrane was measured and used in the data analysis. The four kinetic constants for the soluble enzyme agreed with literature values; and all increased with immobilization of the enzyme. The Michaelis constants for NAD⁺ and for ethanol were greater for the immobilized enzyme. The diffusional resistance to NAD⁺ transport, presented in terms of the Thiele modulus, showed that the overall rate of reaction was decreased by about 50% even at values of the modulus as low as 2.0.