Enzyme kinetics: partial and complete uncompetitive inhibition

A graphical method for analysing enzyme data to obtain kinetic parameters, to identify the types of inhibition and the enzyme mechanisms is described. The method consists of plotting experimental data as v/(V(0)-v) versus 1/(I) at different substrate concentrations. I is the inhibitor concentration; V(0) and v are the initial rates of enzyme reaction attained by the system in the presence of a fixed amount of substrate and in the absence and presence of inhibitor respectively. Complete inhibition gives straight lines that pass through the origin while partial inhibition gives straight lines that converge on the 1/I-axis at a point away from the origin. With uncompetitive inhibition the slopes of the lines decrease with increasing substrate concentration. The kinetic parameters K(m), K'(i) and beta (degree of partiality) can best be determined from respective secondary plots of slope and intercept versus reciprocal of substrate concentration.     

A microcomputer method for designing optimal experiments for estimating enzyme kinetic parameters

A computer program, written in BASIC, for designing optimal experiments with the aim of evaluating estimates of the parameters for any enzyme kinetic model is given. This computer program can be run on any microcomputer with less than 32 Kbytes of random access memory. The program uses the termed D-optimization design criterion, which minimizes the determinant of the variance-covariance matrix. The user only supplies the rate equation, the maximum and minimum concentrations of substrates and inhibitors, the weighting pattern, and the best possible values of the parameters. The computer supplies the optimal substrate and inhibitor concentrations (one for each parameters), for estimating the parameter values, and the determinant of the variance-covariance matrix. Likewise, the microcomputer supplies the eigenvalues and eigenvectors of information and redundancy matrices, the sensitivity and the global redundancy.     

Mechanistic and kinetic studies of inhibition of enzymes

A graphical method for analyzing enzyme data to obtain kinetic parameters, and to identify the types of inhibition and the enzyme mechanisms, is described. The method consists of plotting experimental data as nu/(V0 - nu) vs 1/(I) at different substrate concentrations. I is the inhibitor concentration; V0 and nu are the rates of enzyme reaction attained by the system in the presence of a fixed amount of substrate, and in the absence and presence of inhibitor, respectively. Complete inhibition gives straight lines that go through the origin; partial inhibition gives straight lines that converge on the 1-I axis, at a point away from the origin. For competitive inhibition, the slopes of the lines increase with increasing-substrate concentration; with noncompetitive inhibition, the slopes are independent of substrate concentration; with uncompetitive inhibition, the slopes of the lines decrease with increasing substrate concentrations. The kinetic parameters, Km, Ki, Ki', and beta (degree of partiality) can best be determined from respective secondary plots of slope and intercept vs substrate concentration, for competitive and noncompetitive inhibition mechanism or slope and intercept vs reciprocal substrate concentration for uncompetitive inhibition mechanism. Functional consequencs of these analyses are represented in terms of specific enzyme-inhibitor systems.     

Inhibition of beta-lactamase of Bacillus licheniformis 749/C by compound PS-5, a new beta-lactam antibiotic.

By use of a new computer-assisted u.v.-spectrophotometric assay method, the kinetic parameters of the reaction catalysed by Bacillus licheniformis 749/C beta-lactamase were re-examined and the mode of inhibition of the enzyme by compound PS-5, a novel beta-lactam antibiotic, was studied with benzylpenicillin as substrate. (1) The fundamental assay conditions for the determination of Km and V were examined in detail with benzylpenicillin as substrate. In 0.1 M-sodium/potassium phosphate buffer, pH 6.8, at 30 degrees C, initial substrate concentrations of benzylpenicillin above 0.7 mM were very likely to lead to substrate inhibition. The Km value of the enzyme for benzylpenicillin at initial concentrations from 1.96 to 0.07 mM was calculated to be 97-108 microM. (2) The Km values of the enzyme for 6-aminopenicillanic acid, ampicillin and cephaloridine were found to be 25, 154-161 and 144-161 microM respectively. (3) Compound PS-5 was virtually unattacked by Bacillus licheniformis 749/C beta-lactamase. (4) The activity of the enzyme was diminished by compound PS-5, to extents depending on the duration of incubation and the concentration of the inhibitor. The rate of inactivation of the enzyme by compound PS-5 followed first-order kinetics. (5) In an Appendix, a new computer-assisted u.v.-spectrophotometric enzyme assay method, in which a single reaction progress curve of time-absorbance was analysed by the integrated Michaelis-Menten equation, was devised for the accurate and precise determination of the kinetic constants of beta-lactamase. For conversion of absorbance readings into molar substrate concentrations, the initial or final absorbance reading that was independent of the reaction time was used as the basis of calculation. In calculation of Km and V three systematic methods of data combination were employed for finer analysis of the reaction progress curve. A list of the computer program named YF6TAIM is obtainable from the author on request or as Supplementary Publication SUP 50100 (12 pages) from the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., on the terms indicated in Biochem. J. (1978) 169, 5.     

Rational polynomial equation as an unbiased approach for the kinetic studies of Drosophila melanogaster acetylcholinesterase reaction mechanism

The hydrolysis of substrates by cholinesterases does not follow the Michaelis–Menten reaction mechanism. The well-known inhibition by excess substrate is often accompanied by an unexpectedly high activity at low substrate concentrations. It appears that these peculiarities are the consequence of an unusual architecture of the active site, which conducts the substrate molecule over many stages before it is cleaved and released. Structural and kinetic data also suggest that two substrate molecules can attach at the same time to the free, as well as to the acetylated, enzyme. We present a procedure which provides an unbiased framework for mathematical modelling of such complex reaction mechanisms. It is based on regression analysis of a rational polynomial using classical initial rate data. The determination of polynomial degree reveals the number of independent parameters that can be evaluated from the available information. Once determined, these parameters can substantially facilitate the construction and evaluation of a kinetic model reflecting the expected molecular events in an enzymic reaction. We also present practical suggestions for testing the postulated kinetic model, using an original thermodynamic approach and an isolated effect in a specifically mutated enzyme.     

Kinetic studies on the two common inherited forms of human erythrocyte adenylate kinase

1. The kinetic properties of two genetic variants of human erythrocyte adenylate kinase were studied at limiting concentrations of both ADP and MgADP(-) in the forward direction and at limiting concentrations of both AMP and MgATP(2-) in the reverse direction. 2. Primary reciprocal plots rule out the possibility of a Ping Pong mechanism for both forms of the enzyme. 3. Analysis of the kinetic data by an appropriate computer program gave the following K(m) values for the type 1 enzyme: AMP, 0.33mm+/-0.1; MgATP(2-), 0.95mm+/-0.13; ADP, 0.12mm+/-0.03; MgADP(-), 0.22mm+/-0.04. Values for the type 2 enzyme were: AMP, 0.27mm+/-0.03; MgATP(2-), 0.40mm+/-0.05; ADP, 0.08mm+/-0.07; MgADP(-), 0.20mm+/-0.04. 4. Product inhibition studies were done by studying the reverse reaction. With ADP as product inhibitor competitive inhibition patterns were obtained with AMP and/or MgATP(2-) as variable substrate. Similar results were obtained for product inhibition by MgADP(-) with AMP as variable substrate. The results are consistent with a Rapid Equilibrium Random mechanism. 5. Secondary plots of slope versus product concentration were linear. The data were fitted to the appropriate equation and analysed by computer to give values for the product inhibition constants. 6. Differences between the values of certain kinetic constants for the two forms of the enzyme were observed.     

A kinetic study of the suicide inactivation of an enzyme measured through coupling reactions. Application to the suicide inactivation of tyrosinase.

A systematic procedure for the kinetic study of reaction mechanisms with enzyme inactivation induced by a suicide substrate in the presence or in the absence of an auxiliary substrate, when the enzyme activity is measured through coupling reactions, enzymically catalysed or not, was developed and analysed by using the transient-phase approach. The methodology is established to determine the parameters and kinetic constants corresponding to the enzyme suicide inactivation and the coupling reactions. This approach is illustrated by a study of the suicide inactivation of tyrosinase by catechol in the presence of L-proline. Treatment of the experimental data was carried out by non-linear regression.     

Purine nucleoside phosphorylase of rabbit liver. Mechanism of catalysis.

Initial velocity studies and product inhibition patterns for purine nucleoside phosphorylase from rabbit liver were examined in order to determine the predominant catalytic mechanism for the synthetic (forward) and phosphorolytic (reverse) reactions of the enzyme. Initial velocity studies in the absence of products gave intersecting or converging linear double reciprocal plots of the kinetic data for both the synthetic and phosphorolytic reactions of the enzyme. The observed kinetic pattern was consistent with a sequential mechanism, requiring that both substrates add to the enzyme before products may be released. The product inhibition patterns showed mutual competitive inhibition between guanine and guanosine as variable substrates and inhibitors. Ribose 1-phosphate and inorganic orthophosphate were also mutually competitive toward each other. Other combinations of substrates and products gave noncompetitive inhibition. Apparent inhibition constants calculated for guanine as competitive inhibitor and for ribose 1-phosphate as noncompetitive inhibitor of the enzyme, with guanosine as variable substrate, did not vary significantly with increasing concentrations of inorganic orthophosphate as fixed substrate. These results suggest that the mechanism was order and that substrates add to the enzyme in an obligatory order. Dead end inhibition studies carried out in the presence of the products guanine and ribose 1-phosphate, respectively, showed that the kinetically significant abortive ternary complexes of enzyme-guanine-inorganic orthophosphate (EQB) and enzyme-guanose-ribose 1-phosphate (EAP) are formed. The results of dead end inhibition studies are consistent with an obligatory order of substrate addition to the enzyme. The nucleoside or purine is probably the first substrate to form a binary complex with the enzyme, and with which inorganic orthophosphate or ribose 1-phosphate may interact as secondary substrates. The evidences presented in this investigation support an Ordered Theorell-Chance mechanism for the enzyme.     

A kinetic study of lipase-catalyzed reversible kinetic resolution involving verification at miniplant-scale

Lipase-catalyzed kinetic resolution of racemates is a popular method for synthesis of chiral synthons. Most of these resolutions are reversible equilibrium limited reactions. For the first time, an extensive kinetic model is proposed for kinetic resolution reactions, which takes into account the full reversibility of the reaction, substrate inhibition by an acyl donor and an acyl acceptor as well as alternative substrate inhibition by each enantiomer. For this purpose, the reversible enantioselective transesterification of (R/S)-1-methoxy-2-propanol with ethyl acetate catalyzed by Candida antarctica lipase B (CAL-B) is investigated. The detailed model presented here is valid for a wide range of substrate and product concentrations. Following model discrimination and the application of Haldane equations to reduce the degree of freedom in parameter estimation, the 11 free parameters are successfully identified. All parameters are fitted to the complete data set simultaneously. Six types of independent initial rate studies provide a solid data basis for the model. The effect of changes in substrate and product concentration on reaction kinetics is discussed. The developed model is used for simulations to study the behavior of reaction kinetics in a fixed bed reactor. The typical plot of enantiomeric excess versus conversion of substrate and product is evaluated at various initial substrate mixtures. The model is validated by comparison with experimental results obtained with a fixed bed reactor, which is part of a fully automated state-of-the-art miniplant.     

Yeast dipeptidase: active site mapping by kinetic studies with substrates and substrate analogs.

In order to characterize the active site of yeast dipeptidase in more detail, kinetic studies with a variety of dipeptide substrates and substrate analogs were performed. To analyze kinetic data, computer programs were developed which first calculate initial velocities from progress curves and then evaluate the kinetic parameters by nonlinear regression analysis. A free carboxyl group is a prerequisite for binding of dipeptidase substrates; its position relative to the peptide bond must not deviate from the normal L-dipeptide conformation. The spatial arrangement of the terminal ammonium ion seems to be less crucial. The enzyme's substrate specificity clearly reflects the interactions of the substrate amino acid side chains with complementary dipeptidase subsites. The domain of the enzyme in contact with the C-terminal substrate side chain seems to be an open structure of moderately hydrophobic character. In contrast, the binding site for the amino-terminal side chain is a more strongly hydrophobic "pocket" of limited dimensions. The kinetics of inhibition by free amino acids points to an ordered release of products from 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.     

Kinetic and inhibitor studies with arylsulfhydrolases A and B from avian and mammalian sources

Arylsulfhydrolases A and B from chicken and from bovine liver have been isolated and their reactions with a range of synthetic arylsulfates examined using kinetic methods. Some differences of Michaelis-Menten parameters were observed in comparing the A with the B forms from the two sources at the level of individual substrates. At that level also, interspecies comparisons of A forms and B forms similarly showed differences. However, for none of the four enzymes examined was there consistent correlations of kinetic values with electronic, hydrophobicity, or steric properties of the substrates. The bovine A enzyme displayed the well-documented “anomalous” kinetic behavior at high substrate concentrations; at low concentrations conventional hydrolysis of p-nitrocatechol sulfate occurred, except that there was evidence with this substrate and others of product inhibition. The avian A enzyme reacted normally over all substrate concentrations examined, but again product inhibition occurred. The mammalian but not the avian B enzyme was also clearly subject to product inhibition.     

The computation of hyperbolic dependences in enzyme kinetics.

A computer program aimed at analysing results following Michaelis-Menten kinetics can be used unmodified in the treatment of other kinetic results provided that the kinetic equations in these cases can be written in the form of the Michaelis-Menten equation. A list is presented of the parameters to be set instead of substrate concentration and reaction rate, and of constants replacing Km and V, if such a program is applied in analysing enzyme inhibitions, activations and pH-dependences.     

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.     

Computer program for the expression of the kinetic equations of enzyme reactions as functions of the rate constants and the initial concentrations.

A versatile computer program with an easy input method has been developed for the construction of the terms in kinetic equations of enzyme reactions. It allows the expression of the time-dependence of the concentrations of all of the species involved as functions of the kinetic parameters. The mathematical theory used in this paper, the program and examples of its use have been deposited as Supplementary Publication SUP 50159 (41 pages) at the British Library Document Supply Centre, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1990) 265, 5.     

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.     

Optimization of urease immobilization onto non-porous HEMA incorporated poly(EGDMA) microbeads and estimation of kinetic parameters.

Jack bean urease (urea aminohydrolase, EC 3.5.1.5) was immobilized onto modified non-porous poly(ethylene glycol dimethacrylate/2-hydroxy ethylene methacrylate), (poly(EGDMA/HEMA)), microbeads prepared by suspension copolymerization for the potential use in hemoperfusion columns, not previously reported. The conditions of immobilization; enzyme concentration, medium pH, substrate and ethylene diamine tetra acetic acid (EDTA) presence in the immobilization medium in different concentrations, enzyme loading ratio, processing time and immobilization temperature were investigated for highest apparent activity. Immobilized enzyme retained 73% of its original activity for 75 days of repeated use with a deactivation constant kd = 3.72 x 10(-3) day(-1). A canned non-linear regression program was used to estimate the intrinsic kinetic parameters of immobilized enzyme with a low value of observable Thiele modulus (phi < 0.3) and these parameters were compared with those of free urease. The best-fit kinetic parameters of a Michaelis-Menten model were estimated as Vm = 3.318 x 10(-4) micromol/s mg bound enzyme protein, Km = 15.94 mM for immobilized, and Vm = 1.074 micromol NH3/s mg enzyme protein, Km = 14.49 mM for free urease. The drastic decrease in Vm value was attributed to steric effects, conformational changes in enzyme structure or denaturation of the enzyme during immobilization. Nevertheless, the change in Km value was insignificant for the unchanged affinity of the substrate with immobilization. For higher immobilized urease activity, smaller particle size and concentrated urease with higher specific activity could be used in the immobilization process.     

Pig heart lipoamide dehydrogenase: solvent equilibrium and kinetic isotope effects.

Lipoamide dehydrogenase is a flavoprotein which catalyzes the reversible oxidation of dihydrolipoamide, Lip(SH)2, by NAD+. The ping-pong kinetic mechanism involves stable oxidized and two-electron-reduced forms. We have investigated the rate-limiting nature of proton transfer steps in both the forward and reverse reactions catalyzed by the pig heart enzyme by using a combination of alternate substrates and solvent kinetic isotope effect studies. With NAD+ as the variable substrate, and at a fixed, saturating concentration of either Lip(SH)2 or DTT, inverse solvent kinetic isotope effects of 0.68 +/- 0.05 and 0.71 +/- 0.05, respectively, were observed on V/K. Solvent kinetic isotope effects on V of 0.91 +/- 0.07 and 0.69 +/- 0.02 were determined when Lip(SH)2 or DTT, respectively, was used as reductant. When Lip(SH)2 or DTT was used as the variable substrate, at a fixed concentration of NAD+, solvent kinetic isotope effects of 0.74 +/- 0.06 and 0.51 +/- 0.04, respectively, were observed on V/K for these substrates. Plots of the kinetic parameters versus mole fraction D2O (proton inventories) were linear in all cases. Solvent kinetic isotope effect measurements performed in the reverse direction using NADH as the variable substrate showed equivalent, normal solvent kinetic isotope effects on V/KNADH when oxidized lipoamide, lipoic acid, or DTT were present at fixed, saturating concentrations. Solvent kinetic isotope effects on V were equal to 1.5-2.1. When solvent kinetic isotope effect measurements were performed using the disulfide substrates lipoamide, lipoic acid, or DTT as the variable substrates, normal kinetic isotope effects on V/K of 1.3-1.7 were observed.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.