A comprehensive kinetic model of laccase‐catalyzed oxidation of aqueous phenol

A comprehensive model was developed to describe the kinetics of the laccase‐catalyzed oxidation of phenol that incorporates enzyme kinetics, enzyme inactivation, variable reaction stoichiometry between substrate and oxygen, and oxygen mass‐transfer. The model was calibrated and validated against data obtained from experiments conducted in an open system, which allowed oxygen to transfer from air to the reacting mixture and phenol conversion to approach completion. Inactivation of laccase was observed over the course of the reaction and was found to be dependent on the rate of substrate transformation. A single kinetic expression was sufficient to describe laccase inactivation arising from interaction with reacting species over time. Excellent agreement was found between model predictions of phenol and oxygen concentrations and experimental data over time for a wide range of initial substrate concentrations and enzyme activities. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

Variable stoichiometry during the laccase-catalyzed oxidation of aqueous phenol

The oxidation of aqueous phenol through the catalytic action of laccase from Trametes versicolor was studied over a wide range of phenol concentrations and enzyme activities. The stoichiometric ratio, which is defined as the molar ratio of phenol transformed to oxygen consumed in the catalytic reaction, was found to increase with phenol concentration in the reaction mixture from a theoretical lower limit of 1 and to approach a theoretical upper limit of 4. A logistic equation was proposed to relate reaction stoichiometry to substrate concentration and was successfully used to relate these parameters over a range of phenol concentrations extending from approximately 0.15 to 8 mM. This expression was incorporated into two kinetic models in order to account for variations in reaction stoichiometry during the reaction and to extend the range over which the models may be accurately applied. The new models demonstrated an improved ability to predict concentrations of phenol and oxygen over time in a closed batch reaction system.     

Characterization of Trametes versicolor laccase for the transformation of aqueous phenol

Laccase (oxygen oxidoreductase, EC 1.10.3.2) from Trametes versicolor was thoroughly characterized in terms of its catalytic stability and its effectiveness as a biocatalyst under various reaction conditions when using phenol as a model substrate. This enzyme demonstrated high or moderate degrees of stability at pHs from 5 to 8 at 25 degrees C and at temperatures from 10 to 30 degrees C at pH 6. Exponential decay expressions were successfully used to model laccase inactivation when incubated under various conditions of pH and temperature. Phenol transformation was optimum at pH 6, but significant transformation was observed over a pH range of 4-7, provided that sufficient laccase was present in the reacting solution. Partial inactivation of laccase was observed during the oxidation of phenol, even under conditions of optimal stability (pH 6 and 25 degrees C).     

Kinetic analysis of the mechanism of Escherichia coli dihydrofolate reductase

A kinetic mechanism is presented for Escherichia coli dihydrofolate reductase which describes the full time course of the enzymatic reaction over a wide range of substrate and enzyme concentrations at pH 7.2 and 20 degrees C. Specific rate constants were estimated by computer simulation of the full time course of single turnover, burst, and steady-state experiments using both nondeuterated and deuterated NADPH. The mechanism involves the random addition of substrates, but the substrates and enzyme are not at equilibrium prior to the chemical transformation step. The rate-limiting step follows the chemical transformation, and the maximum velocity of the reaction is limited by the release of the product tetrahydrofolate. The full time course of the reaction is markedly affected by the formation of the enzyme-NADPH-tetrahydrofolate abortive complex, but not by the enzyme-NADP-dihydrofolate abortive complex.     

Kinetic implications of the occurrence of several relaxations in the conformational transition of mnemonical enzymes

If the conformational transition involved in enzyme memory occurs in several elementary steps, the time constant of the overall 'slow' relaxation is mostly determined by the individual values of the rate constants pertaining to the overall transconformation. The extent of kinetic co-operativity of the enzyme reaction, however, is mostly controlled by the degree of reversibility of the elementary steps of the conformational transition. There is then no simple relation between the time scale of the 'slow' transition and the extent of kinetic co-operativity of the enzyme reaction. A slow transition of about 10(-3) s-1 is therefore perfectly compatible with a strong positive or negative co-operativity and in particular with the negative co-operativity observed with wheat germ hexokinase LI. The relationship that has been established recently [Pettersson, G. (1986) Eur. J. Biochem. 154, 167-170] between the 'slow' enzyme relaxation and the extent of kinetic co-operativity holds only in the specific case where the transconformation occurs in one step. Owing to the possible occurrence of a multistep conformation change, the lack of this relationship means nothing as to the validity, or the invalidity, of the concept of mnemonical transition. More informative than the time scale of the 'slow' transition is its dependence with respect to glucose and glucose 6-phosphate, which both react with the enzyme. The effect of reaction products on the modulation of kinetic co-operativity is also of cardinal importance in the diagnosis of enzyme memory. Since an alternative model has been recently proposed by Pettersson (cited above) to explain the mechanistic origin of kinetic co-operativity of monomeric enzymes, the effect of products on the kinetic co-operativity predicted by this alternative model has been studied theoretically, in order to determine whether it is consistent with the experimental results obtained with wheat germ hexokinase LI. This analysis shows that the predictions of this model are in total disagreement with both the predictions of the mnemonical model and the experimental results obtained with wheat germ hexokinase LI, as well as with other enzymes. This alternative model cannot therefore be considered as a sensible explanation of the mechanistic origin of co-operativity of monomeric enzymes. It is therefore concluded that the mnemonical model which rests on numerous experimental results, obtained by different research groups, on different enzymes is the simplest and most likely explanation of the kinetic subtleties displayed by some monomeric enzymes, and in particular wheat germ hexokinase LI.     

A kinetic model for lipoxygenases based on experimental data with the lipoxygenase of reticulocytes

A comprehensive kinetic model for lipoxygenase catalysis is proposed which includes the simultaneous occurrence of dioxygenase and hydroperoxidase activities and is based on the assumption of a single binding site for substrate fatty acid and product. The aerobic reaction of purified lipoxygenase from rabbit reticulocytes with 9,12(Z,Z)-octadecadienoic acid (linoleic acid) as substrate was studied. The rate constants and the dissociation constants of this enzyme were calculated for the model from progress curves; the model describes correctly the experimental data. The following kinetic features of the reticulocyte enzyme are assumed to apply generally to lipoxygenases. (a) The enzyme shows autoactivation by its product. (b) The rate-limiting step is the hydrogen abstraction. (c) Both substrate fatty acid and its product are competitive inhibitors of the lipoxygenase. (d) Lowering the oxygen concentration enhances the degree of substrate inhibition, whereas product inhibition is not influenced. (e) If substrate is in excess the oxygen concentration determines the share of dioxygenase and hydroperoxidase activities of the enzyme. As predicted from the model it was found that at low concentrations of oxygen the regio- and stereo-specificities of the dioxygenation are diminished. During the autoactivation phase the steady-state approximation does not hold.     

Kinetic mechanism of choline oxidase from Arthrobacter globiformis

Choline oxidase catalyzes the four-electron oxidation of choline to glycine-betaine, with betaine-aldehyde as intermediate and molecular oxygen as primary electron acceptor. The enzyme is capable of accepting betaine-aldehyde as a substrate, allowing the investigation of the reaction mechanism for both the conversion of choline to the aldehyde intermediate and of betaine-aldehyde to glycine-betaine. The steady state kinetic mechanism has been determined at pH 7 with choline and betaine-aldehyde as substrate to be sequential, consistent with oxygen reacting with the reduced enzyme before release of betaine-aldehyde or glycine-betaine, respectively. A K(m) value < or =20 microM has been estimated for betaine-aldehyde based on the kinetic pattern with a y-intercept seen in a plot of 1/rate versus 1/[oxygen]. The kinetic data suggest that betaine-aldehyde predominantly remains bound at the active site during turnover of the enzyme with choline. In agreement with such a conclusion, less than 10% betaine-aldehyde has been found in the reaction mixture under enzymatic turnover with saturating concentrations of choline. The k(cat) values were 6.4+/-0.3 and 15.3+/-2.5 s(-1) for choline and betaine-aldehyde, respectively, suggesting that a kinetic step in the oxidation of choline to the aldehyde intermediate must be partially rate-limiting for catalysis. Cleavage of the CH bond of choline as being partially rate-limiting for catalysis is discussed.     

Analysis and quantification of a mixed exo-acting and endo-acting polysaccharide depolymerization system

A new mathematical model has been proposed based on a model presented by Suga, van Dedem, and Moo-Young.(10) The model requires a separate differential equation for each polymeric species (differentiated by degree of polymerization) in the reaction mixture. The main contribution of this model is the incorporation of experimental molecular weight distributions as the initial conditions. These molecular weight distributional as the initial conditions were obtained using modern analytical equipment previouly unknown for this application. The equipment, SEC/LALLS, measures relative concentrations of specific molecular weight species along with the corresponding molecular weights, thus yielding (through some mathematical manipulation) the absolute concentration of each molecular weight species. The concentration at each molecular weight can then be incorporated as the initial condition for that equation. Theoretically, the system of differential equations can be solved to give a more realistic time course of reaction.Synergism between endo-acting and exo-acting enzymes was examined theoretically using the mathematical model. Through model predictions, it was found that synergy is based on two fundamental parameters: (1) each enzyme's activity relative to the sum of enzyme activities and, (2) overall substrate concentration relative to the exo-acting enzyme's Michaeiis kinetic constant K(m). Theoretically, synergism increases as a function of reaction time. Intermediate endo fractions (ratio of endo-acting enzyme activity to the sum of endo-acting and exo-acting enzyme activity) from 0.3 to 0.7 exhibit the most synergism. Values of k[log(K(m, exo)/S(0))] above about zero also exhibits the most synergism.An examination of experimental data obtained both by SEC/LALLS and by reducing sugar measurements shows that the model is inadequate for successfully predicting quantities associated with the substrate during reaction. This is especially true for synergism predictions. At short reaction times, the model predicts the data fairly well, but at longer times the predictions are inconsistent with experimental data. These inconsistencies may be due to complicating phenomena such as enzyme inhibitions.     

Transient response of rod outer segment cGMP phosphodiesterase to actinic light pulses. II. Detailed quantitative kinetic model

In the accompanying article (Schmidt, J.A., and Yguerabide, J. (1989) J. Biol. Chem. 264, 19790-19803), we presented a minimal quantitative kinetic model with one rate-limiting step for the transient response of rod outer segment (ROS) phosphodiesterase (PDE) to stimulating light pulses of low fractional bleach (linear response range) and showed that the model was in excellent quantitative agreement with experimental results. The model characterizes the PDE response in terms of the specific rate constant of the rate-limiting step, kL, the lifetime of photoactivated rhodopsin, tau R, and the lifetime of activated PDE, tau P, but makes no predictions on how these kinetic parameters should depend on the concentrations of the various reactive species involved in the PDE response to light and does not reveal the nature of the rate-limiting step. However, we established by curve fitting experimental data to theoretical expressions from the model that kL increases hyperbolically with [GTP], tau R decreases with [GTP], and tau P is independent of GTP. In this report we present three detailed kinetic models which make specific quantitative predictions on how the kinetic parameters of the minimal model should depend on nucleotide and G protein concentrations and test the models against experimental data. Each model consists of one rate-limiting step. The first detailed model postulates that the rate-limiting step is the dissociation of R*GT into R* and GT (T stands for GTP). The second model postulates that the rate-limiting step is the binding of GTP to R*G, and the third model postulates that the rate-limiting step is the encounter rate of R* and G on the ROS disc membrane. We find that only the first detailed model is consistent with the experimental results as characterized by the minimal model. Using this detailed model we (a) define kL and tau R in terms of more fundamental equilibrium and rate parameters, (b) develop a theory for the systematic evaluation of amplification or gain of the PDE light response from light-stimulated GTP-binding data as well as v(t) versus t graphs, and (c) clarify methods which have been used in the past to evaluate gain experimentally.     

Pore diffusion model for a two-substrate enzymatic reaction: Application to galactose oxidase immobilized on porous glass particles

An analysis of the pore diffusion model involving a two-substrate enzymatic reaction is presented. The resulting equations have been applied to the case of galactose oxidase catalyzed oxidation of galactose when the enzyme is immobilized on porous glass particles. The physical constants of the system were obtained by theoretical predictions and the enzyme concentration in the porous medium was derived from the experimental results. The calculations were performed with the assumption that the kinetic parameters of the enzyme remain unchanged upon immobilization. The theoretically calculated effectiveness factors were compared with the experimental effectiveness factors determined from the batch kinetic experiments and were found to be in agreement. The results are presented as effectiveness factor plots graphed as functions of bulk galactose and oxygen concentrations. The model was extended in order to study the effect of external mass transfer coefficients and pore enzyme concentrations on the effectiveness factors.     

Effects of substrate branching characteristics on kinetics of enzymatic depolymerization of mixed linear and branched polysaccharides: II. Amylose/glycogen alpha-amylolysis

Enzymatic depolymerization of polysaccharides with alpha-amylase has been studied in mixed aqueous dimethylsulfoxide (DMSO)/water solvents. Polysaccharide substrate chemical compositions, configurational structures, and bonding pattersn are known to affect observed enzymatic reaction kinetics. The branching structures of polysaccharides and their effects on the kinetic mechanisms of depolymerization reactions via endo-acting hydrolyzing enzyme was studied via size exclusion chromatography coupled to low angle laser light scattering (SEC/LALLS). The glycogen branching structure is a heterogeneously distributed "cluster" structure rather than a homogeneously distributed "treelike" structure. The action pattern of alpha-amylase on glycogen, which is composed of highly branched clusters, as end-products, has a "pseudo-exo-attack" in contrast to an expected "endoattack" as seen in the hydrolysis of amylose or amylopectin substrates. These effects of branched substrates for mixed amylose/glycogen alpha-amylolysis have been predicted and demonstrated by both experimental and theoretical analysis using the kinetic model presented in this report. The "lumped" kinetic model employed, assumes that the enzyme simultaneously attacks both linear and branched substrates. In general, excellent agreement between the model predictions and the experimental observations, both qualitatively and quantitatively, was obtained. (c) 1995 John Wiley & Sons, Inc.     

Dynamic modeling and optimal fed-batch feeding strategies for a two-phase partitioning bioreactor

A dynamic model for the degradation of phenol in a two-phase partitioning bioreactor has been developed based on mechanistic balances around the bioreactor. The key process characteristics including substrate transfer between the organic and aqueous phases, substrate inhibition, oxygen limitation, and cell entrainment were incorporated into the model. The model predictions were validated against existing experimental data obtained for a 2-L bioreactor, and good correlation was observed for the time frames of the simulations, as well as for trends in cell and substrate concentrations. Optimal fed-batch, phenol feeding strategies were then developed based on two approaches: (1) maximization of phenol consumption in a fixed time interval and (2) consumption of a fixed amount of phenol in minimal time. The optimal feeding policies, determined using the Iterative Dynamic Programming algorithm, provided substantial improvements in the amount of phenol consumed when compared to a typical experimental heuristic approach. For example, 45.73 g of phenol was predicted to be consumed in 50 h (not including lag phase) using the optimal feeding profile compared to 10.26 g of phenol consumed in the simulated experimental approach. Oxygen limitation was predicted to be a recurring operational challenge in the partitioning bioreactor, and had a strong impact on the optimization results.     

The kinetics of reoxidation of reduced benzylamine oxidase.

1. The mechanism of reoxidation of reduced benzylamine oxidase has been investigated at different pH between 6 and 10 by steady-state and transient-state kinetic methods. 2. The reoxidation process involves minimally a second-order interaction between reduced enzyme and oxygen leading to the formation of a spectrally modified enzyme intermediate, and a subsequent first-order step converting this intermediate into free enzyme. The variation with pH of rate constants according to such a reaction scheme is reported. 3. Under aerobic conditions the oxygen-independent reaction represents the main rate-limiting step in the catalytic process at alkaline pH. At neutral or acid pH the interaction between reduced enzyme and oxygen becomes mainly rate-limiting, indicating that the concentration of oxygen may be a critical factor controlling enzyme activity under physiological conditions. 4. The spectrally modified intermediate formed during the reoxidation process exhibits a difference-absorption band centered around 290 nm in comparison to free enzyme, and an additional difference-absorption band at 470 nm in comparison to reduced enzyme. These data indicate that formation of the intermediate, besides leading to a reappearance of the 470-nm absorption band disappearing on reduction of the enzyme, results in a spectral perturbation of one or several aromatic amino-acid residues in the protein. This perturbation could possibly reflect a conformational change of the enzymes.     

Kinetics of the sequential dechlorination of 2,4,6-trichlorophenol by an anaerobic microbial population

Summary A mathematical model was developed to describe the sequential dechlorination of 2,4,6-trichlorophenol to 2,4-dichlorophenol, 4-chlorophenol and phenol. Each compound was assumed to be degraded according a Michaelis-Menten expression. Experimental data were used to obtain the model kinetic constants and to test its validity. Good agreement between the model predictions and the experimental data was obtained.     

Kinetic cutinase-catalyzed esterification of caproic acid in organic solvent system

Practical application of any chemical reaction requires the knowledge of its kinetics; in particular if one wishes to be able to describe a chemical reactor over an extended range of reaction conditions or if one intends to optimize the reaction conditions, a suitable kinetic model must be obtained. In order to ensure that the model is applicable over a wide range of experimental conditions it should be based on a mechanistic scheme describing the fundamental steps involved in the reaction; the development of these kind of models can also be used to provide insight into the processes that are taking place.A kinetic study, using experiments carried out in a batch stirred reactor, has been made for the enzymatic esterification of caproic acid with ethyl alcohol catalyzed by Fusarium solani pisi cutinase. Different acid and alcohol concentrations (whilst also varying the acid/alcohol molar ratio) were tested and the results were used to identify the best reaction scheme to describe the results obtained over an extended range of conditions. Several different approaches were used to identify the most adequate mechanistic model, namely by resorting to the quasi stationary state and the rate-limiting hypothesis. The main kinetic characteristics observed in esterification reaction were found to follow an ordered Ping-Pong Bi–Bi mechanism but different modifications were used o ensure that the kinetic model was applicable over the entire range of experimental conditions that were covered.     

Kinetic analysis of cephalosporin biosynthesis in Streptomyces clavuligerus

A kinetic model describing the cephalosporin biosynthesis in Streptomyces clavuligerus was developed. Using previously reported kinetic data of biosynthetic enzymes, we examined the kinetics of cephalosporin production. The predicted time profile of the specific production rate during a batch culture parallels that of experimental observation. Sensitivity analysis reveals that delta-(L-alpha-aminoadipyl)-L-cysteinyl-D-valine (ACV) synthetase is the rate-limiting enzyme. The effect of amplifying ACV synthetase on the specific production rate was analyzed theoretically. Increasing ACV synthetase enhances the production rate initially until ACV synthetase enhances the production rate initially until deacetocycephalosporin C hydroxylase becomes rate-limiting. Such kinetic analysis can provide a rational basis for modifying the biosynthetic machinery of cephalosporin through gene cloning.     

Inhibitory kinetics of phenol on the enzyme activity of beta-N-acetyl-D-glucosaminidase from green crab (Scylla serrata)

Chemical pollution such as chromium and phenol in the sea water has been increasing in recent years in China sea. At the same time, marine shellfish such as prawn and crab are sensitive to this pollution. beta-N-acetyl-D-glucosaminidase (NAGase, EC.3.2.1.52) catalyzes the cleavage the oligomers of N-acetylglucosamine (NAG) into the monomer. In this paper, the effects of phenol on the enzyme activity from green crab (Scylla serrata) for the hydrolysis of p-nitrophenyl-N-acetyl-beta-D-glucosaminide (pNP-NAG) have been studied. The results showed that appropriate concentrations of phenol could lead to reversible inhibition on the enzyme and the inhibitor concentration leading to 50% activity lost, IC(50), was estimated to be 75.0+/-2.0 mM. The inhibitory kinetics of phenol on the enzyme in the appropriate concentrations of phenol has been studied using the kinetic method of substrate reaction. The time course of the enzyme for the hydrolysis of pNP-NAG in the presence of different concentrations of phenol showed that at each phenol concentration, the rate decreased with increasing time until a straight line was approached. The results show that the inhibition of the enzyme by phenol is a slow, reversible reaction with fractional remaining activity. The microscopic rate constants are determined for the reaction on phenol with the enzyme.     

The reversible inhibition of carbonic anhydrase II: Computer simulations of a proposed mechanism of action

A mechanism of action for carbonic anhydrase II involving a rate-limiting intramolecular proton transfer, originally proposed by Steineret al., has been reexamined totally in steady state form using a digital computer. It is found that the mechanism is sufficient to account for all of the extant kinetic data, including the participation of external buffer as a second substrate in the hydration/dehydration reaction. The model of Steineret al. has been expanded to include the inhibitory effects of monovalent anions, phenol, and Cu(II) ion, and is able to account for the experimentally observed kinetics within a chemically reasonable framework. It is concluded that the proposed mechanism is a good working model for carbonic anhydrase II catalysis, and its ability to reconcile such a wide body of kinetic data solidifies the notion of a rate-limiting intramolecular proton transfer in the catalytic pathway.     

Detailed kinetic model describing new oligosaccharides synthesis using different β-galactosidases

The production of prebiotic galactooligosaccharides (GOS) from lactose has been widely studied whereas the synthesis of new prebiotic oligosaccharides with improved properties as those derived from lactulose is receiving an increasing interest. Understanding the mechanism of enzymatic oligosaccharides synthesis from lactulose would help to improve the quality of the products in a rational way as well as to increase the production efficiency by optimally selecting the operating conditions. A detailed kinetic model describing the enzymatic transgalactosylation reaction during lactulose hydrolysis is presented here for the first time. The model was calibrated with the experimental data obtained in batch assays with two different β-galactosidases at various temperatures and concentrations of substrate. A complete system identification loop, including model selection, robust estimation of the parameters by means of a global optimization method and computation of confidence intervals was performed. The kinetic model showed a good agreement between experimental data and predictions for lactulose conversion and provided important insights into the mechanism of formation of new oligosaccharides with potential prebiotic properties.     

Effect of mass transfer limitations on the enzymatic kinetic resolution of epoxides in a two-liquid-phase system

Optically active epoxides can be obtained by kinetic resolution of racemic mixtures using enantioselective epoxide hydrolases. To increase the productivity of the conversion of sparingly aqueous soluble epoxides, we investigated the use of a two-phase aqueous/organic system. A kinetic model which takes into account interphase mass transfer, enzymatic reaction, and enzyme inactivation was developed to describe epoxide conversion in the system by the epoxide hydrolase from Agrobacterium radiobacter. A Lewis cell was used to determine model parameters and results from resolutions carried out in the Lewis cell were compared to model predictions to validate the model. It was found that n-octane is a biocompatible immiscible solvent suitable for use as the organic phase. Good agreement between the model predictions and experimental data was found when the enzyme inactivation rate was fitted. Simulations showed that mass transfer limitations have to be avoided in order to maximize the yield of enantiomerically pure epoxide. Resolution of a 39 g/L solution of racemic styrene oxide in octane was successfully carried out in an emulsion batch reactor to obtain (S)-styrene oxide in high enantiomeric excess (>95% e.e.) with a yield of 30%.