Half-time analysis of the kinetics of irreversible enzyme inhibition by an unstable site-specific reagent

The half-time method for the determination of Michaelis parameters from enzyme progress-curve data (Wharton, C.W. and Szawelski, R.J. (1982) Biochem. J. 203, 351-360) has been adapted for analysis of the kinetics of irreversible enzyme inhibition by an unstable site-specific inhibitor. The method is applicable to a model in which a product (R) of the decomposition of the site-specific reagent, retaining the chemical moiety responsible for inhibitor specificity, binds reversibly to the enzyme with dissociation constant Kr: (formula; see text). Half-time plots of simulated enzyme inactivation time-course data are shown to be unbiased, and excellent estimates of the apparent second-order rate constant for inactivation (k +2/Ki) and Kr can be obtained from a series of experiments with varying initial concentrations of inhibitor. Reliable estimates of k +2 and Ki individually are dependent upon the relative magnitudes of the kinetic parameters describing inactivation. The special case, Kr = Ki, is considered in some detail, and the integrated rate equation describing enzyme inactivation shown to be analogous to that for a simple bimolecular reaction between enzyme and an unstable irreversible inhibitor without the formation of a reversible enzyme-inhibitor complex. The half-time method can be directly extended to the kinetics of enzyme inactivation by an unstable mechanism-based (suicide) inhibitor, provided that the inhibitor is not also a substrate for the enzyme.     

Mass transport in a microchannel enzyme reactor with a porous wall: Hydrodynamic modeling and applications

A two-dimensional flow model, incorporating mass transport, has been developed to simulate a microchannel enzyme reactor with a porous wall. A two-domain approach based on the finite volume method was implemented. Two parameters are defined to characterize the mass transports in the fluid and porous regions: the porous Damkohler number and the fluid Damkohler number. For reactions close to first-order type (enzyme reactor), the concentration results are found to be well correlated by the use of a reaction–convection distance parameter which incorporates the effects of axial distance, substrate consumption and convection. The reactor efficiency reduces with reaction–convection distance parameter because of reduced reaction (or flux) due to the lower concentration. Increased fluid convection improves the efficiency but it is limited by the diffusion in the fluid region. The correlated results can find applications for the design of enzyme reactors with a porous wall.     

Ill-conditioning associated with the "end-point" method for the determination of kinetic parameters describing irreversible enzyme inactivation by an unstable inhibitor

Study of the complete time-course of irreversible enzyme inhibition by an unstable inhibitor yields more information than can be obtained by recording data only at the end point of reaction. Time-course analysis of co-operative irreversible enzyme inhibition by an unstable inhibitor has been shown to be considerably less susceptible to ill-conditioning than the "end-point" method for the determination of kinetic parameters describing inactivation. As a result, mechanisms that cannot be distinguished by the "end-point" method are readily differentiated by time-course analysis without the need to isolate intermediate species.     

A computer program for enzyme kinetics that combines model discrimination, parameter refinement and sequential experimental design.

A method of model discrimination and parameter estimation in enzyme kinetics is proposed. The experimental design and analysis of the model are carried out simultaneously and the stopping rule for experimentation is deduced by the experimenter when the probabilities a posteriori indicate that one model is clearly superior to the rest. A FORTRAN77 program specifically developed for joint designs is given. The method is very powerful, as indicated by its usefulness in the discrimination between models. For example, it has been successfully applied to three cases of enzyme kinetics (a single-substrate Michaelian reaction with product inhibition, a single-substrate complex reaction and a two-substrate reaction). By using this method the most probable model and the estimates of the parameters can be obtained in one experimental session. The FORTRAN77 program is deposited as Supplementary Publication SUP 50134 (19 pages) at the British Library (Lending Division), Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1986) 233, 5.     

Transient-phase kinetics of enzyme inactivation induced by suicide substrates

This paper deals with the kinetic study of reaction mechanisms with enzyme inactivation induced by a suicide substrate in the presence or absence of an auxiliary substrate and in conditions of excess of substrates in relation to the enzyme concentration and vice versa. A transient-phase approach has been developed that enables explicit equations with one or two significant exponentials to be obtained, thereby showing the dependence of product concentration on time. The validity of these equations has been checked, and a comparison made with those previously obtained by other authors. We propose an experimental design to determine the corresponding parameters and kinetic constants. The simplicity of our method allows a systematic application to more complex mechanisms.     

Ethanolaminephosphate cytidylyltransferase. Purification and characterization of the enzyme from rat liver.

Ethanolaminephosphate cytidylyltransferase (EC 2.7.7.14), which catalyzes a central step in phosphatidylethanolamine synthesis, has been purified 1000-fold from a postmicrosomal supernatant from rat liver. The enzyme, which requires a reducing agent, like dithiothreitol, for activity, is stable for weeks at 0-4 degrees when stored in the presence of dithiothreitol and in the pH range 7.5 to 9.0. A molecular weight of 100 to 120 X 10(3) was estimated by gel chromatography on Sephadex G-200. Gel electrophoresis in the presence of sodium dodecyl sulfate gave only one protein band with an apparent molecular weight of 49 to 50 X 10(3). The reaction catalyzed by the enzyme is reversible with a Keq for the forward reaction of 0.46 under the assay conditions. Michaelis constants of 53 and 65 muM were determined for CTP and ethanolaminephosphate, respectively. From the product inhibition pattern an ordered sequential reaction mechanism is proposed, in which CTP is the first substrate to add to the enzyme and CDP-ethanolamine is the last product to be released. The possible role of this reaction in the regulation of phosphatidylethanolamine synthesis in liver is discussed.     

Studies on prephenoloxidase-activating enzyme from cuticle of the silkworm Bombyx mori. I. Activation reaction by the enzyme

Prephenoloxidase-activating enzyme from larval cuticle of the silkworm catalyzes the activation reaction of hemolymphal prephenoloxidase to the active enzyme. The activation reaction of prephenoloxidase by the enzyme has been analyzed with respect to effect of salts, dependency on pH and substrate concentration, and susceptibility to inhibitors. It has been demonstrated that the reaction is highly sensitive to specific inhibitors for “serine enzyme.”Difference in substrate specificity of phenoloxidase preparations, produced by two enzyme fractions which can be separated by chromatography on DEAE-cellulose, is also described.     

Kinetics of bovine milk lipoprotein lipase and the mechanism of enzyme activation by apolipoprotein C-II

The kinetics of bovine milk lipoprotein lipase (LPL) were studied in order to determine the reaction mechanism of this enzyme. Reaction velocities were determined at varying concentrations of emulsified trioleoylglycerol (TG) and different fixed concentrations of apolipoprotein C-II (C-II) or at varying C-II concentrations and different fixed concentrations of TG. Neither the apparent Km(TG) nor the apparent Km(C-II) was affected by varying the concentrations of C-II or TG, respectively. However, C-II increased the apparent Vmax for the enzyme about 20-fold. The following kinetic parameters were calculated from Lineweaver-Burk plots: Km(C-II) = 2.5 X 10(-8) M and Km (TG) = 2.5 X 10(-3) M. The dissociation constant (KS) of the enzyme-TG binary complex was determined from Scatchard plots to be 7.6 X 10(-8) M. Heparin was found to be a competitive dead-end inhibitor against both TG and C-II. Tricapryloylglycerol represented a competitive inhibitor against TG but a noncompetitive inhibitor against C-II. C-II was shown to interact with dansylated bovine milk LPL, increasing its fluorescent emission by inducing a conformational change in the enzyme. Based on these studies, it was concluded that the LPL-catalyzed reaction follows a random, bireactant, rapid-equilibrium mechanism and the role of C-II in the activation process involves an increase in the catalytic rate constant (Kp) resulting from conformational changes of LPL induced by C-II.     

Synthesis of chromophoric, spin label enzyme substrates useful for cryoenzymology.

The spin label nitroxide derivative 3-(2,2,5,5-tetramethylpyrroline-1-oxyl)-propen-2-oic acid has been synthesized and characterized by chemical methods. It is a useful intermediate in the preparation of a new class of chromophoric spin label substrates for enzyme studies, as shown by the synthesis of O-3-(2,2,5,5-tetramethylpyrroline-1-oxyl)-propen-2-oyl-L-beta-phenyllactic acid, a specific ester substrate of bovine pancreatic carboxypeptidase A (peptidyl-L-amino acid hydrolase; EC 3.4.12.2). Kinetic parameters of the esterolytic reaction are conveniently determined by UV spectrophotometric methods, and a reaction intermediate can be stabilized in fluid cryosolvent mixtures at subzero temperatures. Results are presented of preliminary electron spin resonance studies to demonstrate that structural relationships of the spin label substrate in a catalytically active configuration to active site residues can be determined for this low temperature-stabilized reaction intermediate. This substrate thus demonstrates the utility of this new class of spin label derivatives for characterization of enzyme reaction intermediates stabilized by cryoenzymologic techniques.     

Effect of water activity on enzyme hydration and enzyme reaction rate in organic solvents

The effects of water on enzyme (protein) hydration and catalytic efficiency of enzyme molecules in organic solvents have been analyzed in terms of the thermodynamic activity of water, which has been estimated by the NRTL or UNIFAC equations. When the amount of water bound to the enzyme was plotted as a function of water activity, the water adsorption isotherms obtained from the water-solvent liquid mixtures were similar to the reported water-vapor adsorption isotherms of proteins. The water adsorption of proteins from the organic media was not significantly dependent on the properties of the solvents or the nature of the proteins. It is also shown that there is a linear relationship between the logarithm of the enzyme reaction rate and water activity. However, the dependence of the enzyme reaction rate on water activity was found to be different depending on the properties of the solvent. The relationship between water activity and other solvent parameters such as solvent hydrophobicity and the solubility of water in the solvent is also discussed.     

Evaluation method for the drying performance of enzyme containing formulations

A method is presented for fast and cheap evaluation of the performance of enzyme containing formulations in terms of preserving the highest enzyme activity during spray drying. The method is based on modeling the kinetics of the thermal inactivation reaction which occurs during the drying process. Relevant kinetic parameters are determined from differential scanning calorimeter (DSC) experiments and the model is used to simulate the severity of the inactivation reaction for temperatures and moisture levels relevant for spray drying. After conducting experiments and subsequent simulations for a number of different formulations it may be deduced which formulation performs best. This is illustrated by a formulation design study where 4 different enzyme containing formulations are evaluated. The method is validated by comparison to pilot scale spray dryer experiments.     

Comparison of two experimental methods for the determination of Michaelis-Menten kinetics of an immobilized enzyme

For the application of immobilized enzymes, the influence of immobilization on the activity of the enzyme should be Known. This influence can be obtained by determining the intrinsic kinetic parameters of the immobilized enzyme, and by comparing them with the kinetic parameters of the suspended enzyme. This article deals with the determination of the intrinsic kinetic parameters of an agarose-gel bead immobilized oxygen-consuming enzyme: L-lactate 2-monooxygenase. The reaction rate of the enzyme can be described by Michaelis-Menten kinetics. Batch conversion experiments using a biological oxygen monitor, as well as steady-state profile measurements within the biocatalyst particles using an oxygen microsensor, were performed. Two different mathematical methods were used for the batch conversion experiments, both assuming a pseudosteady-state situation with respect to the shape of the profile inside the bead. One of the methods used an approximate relation for the effectiveness factor for Michaelis-Menten kinetics which interpolates between the analytical solutions for zero- and first-order kinetics. The other mathematical method was based on a numerical solution and combined a mass balance over the reactor with a mass balance over the bead. The main difference in the application of the two methods is the computer calculation time; the completely numerical calculation procedure was about 20 times slower than the other calculation procedure.The intrinsic kinetic parameters resulting from both experimental methods were compared to check the reliability of the methods. There was no significant difference in the intrinsic kinetic parameters obtained from the two experimental methods. By comparison of the kinetic parameters for the suspended enzyme with the intrinsic kinetic parameters for the immobilized enzyme, it appeared that immobilization caused a decrease in the value of V(m) by a factor of 2, but there was no significant difference in the values obtained for K(m).     

Specific ligand-induced association of an enzyme. A new model of dissociating allosteric enzyme

The kinetic behavior of dissociative enzyme system of the type inactive monomer in equilibrium active dimer where dimeric form is stabilized by specific ligand (in particular by substrate) which is bound in the region of the contact of monomers has been analysed. It is assumed that the dissociation of dimer results in formation of monomers which retain the subsites for specific ligand binding. The shape of the dependences of enzyme reaction rate (v) on substrate concentration (S) has been characterized using the order of enzyme reaction rate with respect to substrate concentration: ns = d ln v/d ln [S]. When the substrate concentrations are low the dependences of v on [S] have S-shaped form (the maximum value of ns exceeds the unity) at the definite values of the parameters of the enzyme system. The value of ns approaches--2 at sufficiently high substrate concentrations (in the region where the substrate reveals the inhibitory effect due to blocking the association of inactive monomers into active dimer). The methods of calculation of the parameters of the dissociative enzyme system under discussion have been elaborated on the basis of the analysis of the experimental dependences of specific enzyme activity on enzyme concentration obtained at various fixed substrate concentrations.     

5-Methylthioribose kinase. A new enzyme involved in the formation of methionine from 5-methylthioribose.

The presence of a previously unidentified enzyme, tentatively designated 5-methylthioribose kinase, has been demonstrated in cell-free extracts of Enterobacter aerogenes. The enzyme catalyzes the ATP-dependent phosphorylation of 5-methylthioribose. ADP is one of the products of the reaction and, based on functional group analyses, the other product is 5-methylthioribose 1-phosphate. A 40-fold purified enzyme preparation has been obtained from a cell-free extract of E. aerogenes. Activity of the partially purified enzyme is totally dependent on the presence of a divalent cation and a sulfhydryl reagent. The substrate specificity of the enzyme is quite narrow, and the Km values for ATP and 5-methylthioribose are 7.4 X 10(-5) M and 8.1 X 10(-6) M, respectively. These results suggest that 5-methylthioribose kinase may be a primary enzyme involved in the recycling of the methylthio group of 5-methylthioribose back into methionine.     

A new multi-wavelength model-based method for determination of enzyme kinetic parameters

Lineweaver-Burk plot analysis is the most widely used method to determine enzyme kinetic parameters. In the spectrophotometric determination of enzyme activity using the Lineweaver-Burk plot, it is necessary to find a wavelength at which only the substrate or the product has absorbance without any spectroscopic interference of the other reaction components. Moreover, in this method, different initial concentrations of the substrate should be used to obtain the initial velocities required for Lineweaver-Burk plot analysis. In the present work, a multi-wavelength model-based method has been developed and validated to determine Michaelis-Menten constants for some enzyme reactions. In this method, a selective wavelength region and several experiments with different initial concentrations of the substrate are not required. The absorbance data of the kinetic assays are fitted by non-linear regression coupled to the numeric integration of the related differential equation. To indicate the applicability of the proposed method, the Michaelis-Menten constants for the oxidation of phenanthridine, 6-deoxypenciclovir and xanthine by molybdenum hydroxylases were determined using only a single initial concentration of the substrate, regardless of any spectral overlap.     

Screening for enzyme activity in turbid suspensions with scattered light

New screening techniques for improved enzyme variants in turbid media are urgently required in many industries such as the detergent and food industry. Here, a new method is presented to measure enzyme activity in different types of substrate suspensions. This method allows a semiquantitative determination of protease activity using native protein substrates. Unlike conventional techniques for measurement of enzyme activity, the BioLector technology enables online monitoring of scattered light intensity and fluorescence signals during the continuous shaking of samples in microtiter plates. The BioLector technique is hereby used to monitor the hydrolysis of an insoluble protein substrate by measuring the decrease of scattered light. The kinetic parameters for the enzyme reaction (V(max,app) and K(m,app)) are determined from the scattered light curves. Moreover, the influence of pH on the protease activity is investigated. The optimal pH value for protease activity was determined to be between pH 8 to 11 and the activities of five subtilisin serine proteases with variations in the amino acid sequence were compared. The presented method enables proteases from genetically modified strains to be easily characterized and compared. Moreover, this method can be applied to other enzyme systems that catalyze various reactions such as cellulose decomposition.     

Kinetics of coupled enzyme reactions

A theory has been developed for the kinetics of coupled enzyme reactions. This theory does not assume that the first reaction is irreversible. The validity of this theory is confirmed by a model system consisting of enoyl-CoA hydratase (EC 4.2.1.17) and 3-hydroxyacyl-CoA dehydrogenase (EC 1.1.1.35) with 2,4-decadienoyl coenzyme A (CoA) as a substrate. This theory, in contrast to the conventional theory, proves to be indispensible for dealing with coupled enzyme systems where the equilibrium constant of the first reaction is small and/or the concentration of the coupling enzyme is higher than that of the intermediate. Equations derived on the basis of this theory can be used to calculate steady-state velocities of coupled enzyme reactions and to predict the time course of coupled enzyme reactions during the pre steady state.     

Dynamic properties of in vitro enzyme systems containing phosphofructokinase.

The dynamic properties of a series of in vitro reaction systems with increasing complexity and containing phosphofructokinase as central enzyme have been investigated. An experimental strategy and a principal mathematical treatment was elaborated to search for the minimum requirements with respect to the enzyme composition of a reaction system for generating limit cycle behaviour. As a criterion, such models have been developed which permit experimental realization by application of a specially designed flow-through equipment. In addition to phosphofructokinase, the following enzymes have been stepwise included into the reaction systems composing the Models 1 through 6: pyruvate kinase, adenylate kinase, hexokinase, and glucose 6-phosphate isomerase. It turned out that only a minimum dynamic system containing phosphofructokinase and pyruvate kinase as well as excesses of adenylate kinase and glucose 6-phosphate isomerase for maintaining equilibrium conditions between the respective reacting species, acquires the property of limit cycle behaviour and, hence, to generate sustained self-oscillations. The approach permits to compute the region of the experimentally variable parameters (influx rates of fructose 6-phosphate and ATP, maximum rate of pyruvate kianse) for which self-oscillatory behaviour can be predicted.     

An isothermal titration calorimetric method to determine the kinetic parameters of enzyme catalytic reaction by employing the product inhibition as probe.

An isothermal titration calorimetric (ITC) method was developed to measure the kinetic parameters of ribonuclease A catalytic hydrolysis of cytidine 2',3'-cyclic monophosphate. Employing the inhibition of product as a probe, the K(m), K(i), k(c), and DeltaH(m) can be determined by two simple calorimetric measurements. First, the substrate was titrated into the cell containing high concentration of enzyme. The molar reaction heat was calculated from the titration peak area divided by substrate moles per titration, and the initial catalytic reaction rate in the presence of various concentrations of product can be calculated from the peak height and the molar reaction heat. From Michaelis-Menten function in the presence of inhibitors, the relationship between K(m) and K(i) can be obtained. Then, the dissociation constant, which is equal to K(i), was measured by a regular ITC experiment. Thus, K(m) and k(c) can be calculated. The method developed here can be applied in other enzyme catalytic systems with inhibitive products.