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.     

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

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

The analysis of enzyme progress curves by numerical differentiation, including competitive product inhibition and enzyme reactivation

A new method for analyzing steady-state enzyme kinetic data is presented. The technique, which is based on the numerical differentiation of the complete reaction curve, has several advantages over initial velocity and integrated Michaelis-Menten equation methods. The differentiated data are fit to the differential equation describing the appropriate kinetic scheme. This approach is particularly valuable in cases of strong competitive product inhibition and of changing concentrations of active enzyme. The method assumes a reversible reaction and is applicable to a very wide variety of steady-state kinetic schemes. A particular advantage of this approach over integrated methods is that it is independent of [S0] and hence of errors in [S0]. The combination of complete progress curve and computer analysis makes this approach very efficient with respect to both time and materials. Running on an IBM PC XT or equivalent microcomputer with an 8087 coprocessor, the analyses are very fast, the complete process usually being complete in a minute or two. The utility of the technique is demonstrated by application to both simulated and real data. We show that the differentiation of the progress curve for the ribonuclease-catalyzed hydrolysis of 2',3'-cyclic cytidine monophosphate reveals strong product inhibition by 3'-CMP, and this product inhibition accounts for the large discrepancies reported in the literature for the value of Km for this substrate. The method was also applied to determine the rate of reactivation of beta-lactamase which had been reversibly inactivated by cloxacillin. Since large numbers of data points are required for the numerical differentiation the method has become practical only with the advent of computer-acquired data systems.     

The kinetic effect of product instability in a Michaelis-Menten mechanism with competitive inhibition

In most kinetic studies it is assumed that both the reactant and the products are stable. However, under certain conditions spontaneous decomposition or deterioration caused by one of the participating species occurs. Studies, in which a species (the free enzyme, the enzyme-substrate complex, an inhibitor or the product of the reaction) is unstable, have appeared in the literature. However, to our knowledge, the enzymatic systems, in which a competitive inhibition and a decomposition or transformation of the products take place simultaneously, have not been studied so far. In this paper, we present a kinetic analysis of an enzyme reaction that follows a Michaelis-Menten mechanism, in which the free enzyme suffers a competitive inhibition simultaneously with the decomposition of the immediate product. In this study, we have linearised the differential equations that describe the kinetics of the process. Under the assumption of limiting concentration of enzyme, we have obtained and tested the explicit equation describing the time dependence of the product concentration using numerical calculus. With this equation and the experimental progress curve of the product, we constructed an easy procedure for the evaluation of the principal kinetic parameters of the process.     

Kinetic analysis of the michaelis-menten mechanism in which the substrate and the product are unstable

• 1.1. A kinetic analysis of the Michaelis-Menten mechanism for the case in which both the substrate and the product are unstable, either spontaneously or as the result of the addition of a reagent, has been made.
• 2.2. The explicit time course equations of the immediate product and the species into which it subsequently is transformed have been derived under the conditions of rapid equilibrium and limiting substrate concentration.
• 3.3. The validity of these equations has been checked using numerical simulations.
• 4.4. The kinetic data analysis which we suggest is based on the time progress curves of the product or, in the case in which the product accumulation cannot be monitored experimentally, on the time progress curve of the species into which the immediate product is transformed.
• 5.5. This analysis allows the determination of the rate and the equilibrium constants if adequate experimental results are available.
• 6.6. We have chosen a numerical example, with which we illustrate the procedure of the kinetic data analysis by simulating some curves with assumed experimental errors.

     

Kinetic analysis of the general modifier mechanism of Botts and Morales involving a suicide substrate

Suicide substrates are widely used in enzymology for studying enzyme mechanisms and designing potential drugs. The presence of a reversible modifier decreases or increases the rate of substrate-induced inactivation, with evident physiological and experimental consequences. To date, only the action of a competitive or uncompetitive inhibitor of an enzyme system involving suicide substrate has been reported. In this paper, we analyse the kinetics of enzyme-catalysed reactions which evolve in accordance with the general modifier mechanisms of Botts and Morales in which enzyme inactivation is induced by suicide substrate. Rapid equilibrium of all of the reversible reaction steps involved is assumed and the time course equations for the residual enzyme activity, the inactive enzyme forms and the reaction product are derived. Partition ratios giving the relative weight of the product and inactive enzyme concentrations, and the relative contribution to the product formation of each of the unmodified and modified catalytic routes, are studied. New indices pointing to the conditions under which the modifier acts as inhibitor or as activator are suggested. The goodness of the analytical solutions is tested by comparison with the simulated curves obtained by numerical integration. An experimental design and kinetic data analysis to evaluate the kinetic parameters from the time progress curves of the product are proposed. From these results, those corresponding to several reaction mechanisms involving both a suicide substrate and a modifier, and which can be regarded as particular cases of the general case analysed here, can be directly and easily derived.     

Exact and user-friendly kinetic analysis of the two-step rapid equilibrium Michaelis-Menten mechanism

Most enzyme kinetic experiments are carried out under pseudo-first-order conditions, that is, when one of the reactant species (the enzyme or the substrate) is in a large excess of the other species. More accurate kinetic information about the system can be gained without the restrictions of the pseudo-first-order conditions. We present a practical and general method of analysis of the common two-step rapid equilibrium Michaelis-Menten mechanism. The formalism is exact in that it does not involve any other approximations such as the steady-state, limitations on the reactant concentrations or on reaction times. We apply this method to the global analysis of kinetic progress curves for bovine alkaline phosphatase assays carried out under both pseudo-first-order and pseudo-second-order conditions.     

Analysis of progress curves for a highly concentrated Michaelian enzyme in the presence or absence of product inhibition.

Methods are given for analysing the time course of an enzyme-catalysed reaction when the concentration of the enzyme itself is high, a situation which is often found in vivo. (1) The integrated form of the kinetic equation for a concentrated Michaelian enzyme in absence of product inhibition is given. Parameters are shown to be calculated easily using non-linear fitting procedures. (2) A general algorithm to analyse progress-curve data in more complex cases (i.e. when the analytical form of the integrated rate equation is not known or is exceedingly complex) is proposed. This algorithm may be used for any enzyme mechanism for which the differential form of the kinetic equation may be written analytically. We show that the method allows differentiation between the main types of product inhibition which may occur in the case of a highly concentrated Michaelian enzyme.     

Polyphosphate kinase from M. tuberculosis: an interconnect between the genetic and biochemical role

The enzyme Polyphosphate Kinase (PPK) catalyses the reversible transfer of the terminal γ-Pi of ATP to form a long chain Polyphosphate (PolyP). Using an IPTG inducible mycobacterial vector, the vulnerability of this gene has been evaluated by antisense knockdown experiments in M. tuberculosis. Expression profiling studies point to the fact that down regulation of PPK caused cidality during the late phase in contrast to its bacteriostatic mode immediately following antisense expression. PPK thus seems to be a suitable anti-tubercular drug target. The enzyme which is a tetramer has been cloned in E. coli and purified to homogeneity. An enzyme assay suitable for High Throughput Screening was optimized by using the statistical Taguchi protocol and the kinetic parameters determined. The enzyme displayed a strong product inhibition by ADP. In order to accurately estimate the product inhibition, progress curve analysis of the enzyme reaction was monitored. The kinetic equation describing the progress curve was suitably modified by taking into account the product inhibition. The reversible nature of the enzyme indicated a possibility of a two way ATP↔ADP switch operating in the bacteria as a response to its growth requirement.     

Defining a kinetic mechanism for l-DOPA 2,3 dioxygenase,a single-domain type I extradiol dioxygenase from Streptomyces lincolnensis

l-DOPA-2,3-dioxygenase from Streptomyces lincolnensis is a single domain type I extradiol dioxygenase of the vicinal oxygen chelate superfamily and catalyzes the second step in the metabolism of the propylhygric acid moiety of the antibiotic, lincomycin. In this report, the kinetic mechanism of l-DOPA dioxygenase is interrogated using stopped-flow in order to determine microscopic rate constants. Pre-steady state, progress curve and steady-state data were combined in a global kinetic analysis using KinTek Explorer in order to define and constrain a kinetic model for the type I l-DOPA dioxygenase. The data are best described by a four step mechanism, in which the cyclization of the enzymatic product is not enzyme catalyzed.     

Kinetics of suicide substrates. Practical procedures for determining parameters.

Many clinically important or mechanistically interesting inhibitors react with enzymes by a branched pathway in which inactivation of the enzyme and formation of product are competing reactions. The steady-state kinetics for this pathway [Waley (1980) Biochem. J. 185, 771-773] gave equations for progress curves that were cumbersome. A convenient linear plot is now described. The time (t1/2) for 50% inactivation of the enzyme (this is also the time for 50% formation of product), or for 50% loss of substrate, is measured in a series of experiments in which the concentration of inhibitor, [I]0, is varied; in these experiments the ratio of the concentration of enzyme to the concentration of inhibitor is kept fixed. Then a plot of [I]0 X t1/2 against [I]0 is linear, and the kinetic parameters can be found from the slope and intercept. Furthermore, simplifications of the equations for progress curves are described that are valid when the concentration of inhibitors is high, or is low, or when the extent of reaction is low. The use of simulated data has shown that the recommended methods are not unduly sensitive to experimental error.     

Progress curves analysis as an alternative for exploration of activation-inhibition phenomena in cholinesterases

The kinetic behaviour of insect acetylcholinesterases deviates from the Michaelis-Menten pattern. These deviations are known as activation or inhibition at various substrate concentrations and can be more or less observable depending on mutations around the active site of the enzyme. Most kinetic studies on these enzymes still rely on initial rate measurements. It is demonstrated here that according to this method one of the deviations can be overlooked. We attempt to point out that in such cases a detailed step-by-step progress curves analysis is successful. The study is focused on two different methods of analysing progress curves: (i) the first one is based on an integrated initial rate equation which can sufficiently fit truncated progress curves under corresponding conditions; and (ii) the other one precludes the algebraic formulae, but uses numerical integration for searching a non analytical solution of ordinary differential equations describing a kinetic model. All methods are tested on three different acetylcholinesterase mutants from Drosophila melanogaster. The results indicate that kinetic parameters for the E107K mutant with highly expressive activation and inhibition can be well evaluated applying any analysis method. It is quite different for E107W and E107Y mutants where latent activation is present, but discovered only using one or the other progress curves analysis methods.     

Kinetic studies on the enzyme (S)-hydroxynitrile lyase from hevea brasiliensis using initial rate methods and progress curve analysis

(S)-Hydroxynitrile lyase (EC 4.1.2.39) from Hevea brasiliensis(rubber tree) catalyzes the reversible cleavage of cyanohydrins to aldehydes or ketones and prussic acid (HCN). Enzyme kinetics in both directions was studied on a model system with mandelonitrile, benzaldehyde, and HCN using two different methods-initial rate measurements and progress curve analysis. To discriminate between possible mechanisms with the initial rate method, product inhibition was studied. Benzaldehyde acts as a linear competitive inhibitor against mandelonitrile whereas HCN shows S-linear I-parabolic mixed-type inhibition. These results indicate an Ordered Uni Bi mechanism with the formation of a dead-end complex of enzyme, (S)-mandelonitrile and HCN. Prussic acid is the first product released from the enzyme followed by benzaldehyde. For progress curve analysis, a kinetic model of an Ordered Uni Bi mechanism including a dead-end complex, enzyme inactivation, and the chemical parallel reaction was set up, which described the experimental values very well. From the reaction rates obtained the kinetic constants were calculated and compared with the ones obtained from the initial rate method. Good agreement could be achieved between the two methods supporting the suggested mechanism. Copyright 1999 John Wiley & Sons, Inc.     

Progress Curves Analysis as an Alternative for Exploration of Activation-inhibition Phenomena in Cholinesterases

The kinetic behaviour of insect acetylcholinesterases deviates from the Michaelis-Menten pattern. These deviations are known as activation or inhibition at various substrate concentrations and can be more or less observable depending on mutations around the active site of the enzyme. Most kinetic studies on these enzymes still rely on initial rate measurements. It is demonstrated here that according to this method one of the deviations can be overlooked. We attempt to point out that in such cases a detailed step-by-step progress curves analysis is successful. The study is focused on two different methods of analysing progress curves: (i) the first one is based on an integrated initial rate equation which can sufficiently fit truncated progress curves under corresponding conditions; and (ii) the other one precludes the algebraic formulae, but uses numerical integration for searching a non analytical solution of ordinary differential equations describing a kinetic model. All methods are tested on three different acetylcholinesterase mutants from Drosophila melanogaster. The results indicate that kinetic parameters for the E107K mutant with highly expressive activation and inhibition can be well evaluated applying any analysis method. It is quite different for E107W and E107Y mutants where latent activation is present, but discovered only using one or the other progress curves analysis methods.     

Kinetic analysis of enzymatic chiral resolution by progress curve evaluation

The present study deals with kinetic modeling of enzyme-catalyzed reactions by integral progress curve analysis, and shows how to apply this technique to kinetic resolution of enantiomers. It is shown that kinetic parameters for both enantiomers and the enantioselectivity of the enzyme may be obtained from the progress curve measurement of a racemate only.A parameter estimation procedure has been established and it is shown that the covariance matrix of the obtained parameters is a useful statistical tool in the selection and verification of the model structure. Standard deviations calculated from this matrix have shown that progress curve analysis yields parameter values with high accuracies.Potential sources of systematic errors in (multiple) progress curve analysis are addressed in this article. Amongst these, the following needed to be dealt with: (1) the true initial substrate concentrations were obtained from the final amount of product experimentally measured (mass balancing); (2) systematic errors in the initial enzyme concentration were corrected by incorporating this variable in the fitting procedure as an extra parameter per curve; and (3) enzyme inactivation is included in the model and a first-order inactivation constant is determined.Experimental verification was carried out by continuous monitoring of the hydrolysis of ethyl 2-chloropropionate by carboxylesterase NP and the alpha-chymotrypsin-catalyzed hydrolysis of benzoylalanine mathyl ester in a pH-stat system. Kinetic parameter values were obtained with high accuracies and model predictions were in good agreement with independent measurements of enantiomeric excess values or literature data. (c) 1994 John Wiley & Sons, Inc.     

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 analysis of enzyme reactions with slow-binding inhibition.

In this paper we present a general kinetic study of slow-binding inhibition processes, i.e. enzyme reactions that do not respond instantly to the presence of a competitive inhibitor. The analysis that we present is based on the equation that describes the formation of products with time in each case on the experimental progress curve. It is carried out under the condition of limiting enzyme concentration and allows the discrimination between the different cases of slow-binding inhibition. The mechanism in which the formation of complex enzyme-inhibitor is a single or two slow steps or follow a rapid equilibrium, has been considered. The corresponding explicit equations of each case have been obtained and checked by numerical integration. A kinetic data analysis to evaluate the corresponding kinetic parameters is suggested. We illustrate the method, numerically by computer simulation, of the reaction and present some numerical examples that demonstrate the applicability of our procedure.     

Chorismate lyase: kinetics and engineering for stability

By removing the enolpyruvyl group from chorismate, chorismate lyase (CL) produces p-hydroxybenzoate (p-HB) for the ubiquinone biosynthetic pathway. We have analyzed CL by several spectroscopic and chemical techniques and measured its kinetic (kcat=1.7 s(-1), K(m)=29 microM) and product inhibition parameters (K(p)=2.1 microM for p-HB). Protein aggregation, a serious problem with wild type CL, proved to be primarily due to the presence of two surface-active cysteines, whose chemical modification or mutation (to serines) gave greatly improved solution behavior and minor effects on enzyme activity. CL is strongly inhibited by its product p-HB; for this reason activity and inhibition measurements were analyzed by both initial rate and progress curve methods. The results are consistent, but in this case where the stable enzyme-product complex rapidly becomes the predominant form of the enzyme, progress curve methods are more efficient. We also report inhibition measurements with several substrate and product analogs that give information on ligand binding interactions of the active site. The biological function of the unusual product retention remains uncertain, but may involve a mechanism of directed delivery to the membrane-bound enzyme that follows CL in the ubiquinone pathway.     

Determination of enzyme kinetic parameters by continuous addition of substrate to a single reaction mixture and analysis by a tangent-slope procedure: I. Analysis of the method using computed progress curves

A new method has been developed which provides reliable estimates of enzyme kinetic constants from single reaction progress curves recorded under conditions of continuously increasing substrate concentration. Equally spaced data points simulating such progress curves and containing known amounts of superimposed random noise were fit to the Hill equation by (i) direct nonlinear curve-fitting of raw data, and (ii) a tangent-slope technique in which the raw data are numerically differentiated, transformed into substrate versus velocity data, and then analyzed as linear plots. Both integral and differential procedures provided accurate and precise estimates of the Hill parameters (S_0.5, V, and n) from single reaction mixtures. However, the tangent-slope method was at least 10-fold faster to compute and was not dependent on accurate initial guesses of the Hill parameters or integration of the rate equation. With the tangent-slope method, the optimal number of data points used in calculating tangent slopes was found to be 9 or 11. The reliability of the Hill parameters determined with the tangent-slope method was relatively insensitive to the maximum substrate concentration over a range of $\text{S}{}_{\mathrm{<mtext>max</mtext>}}\text{S}{}_{0.5}$ of 1.5 to 10; the optimal value was 3. Through further analysis of simulated data, it was found that slow enzyme inactivation (<4% loss during the assay), or product competitive inhibition (maximum product concentration < 30% of the inhibitor dissociation constant) does not produce serious errors in the Hill parameters. Methods are presented to detect and distinguish enzyme inactivation and product competitive inhibition. It is suggested that continuous addition methodology combined with tangent-slope analysis provides the basis for a flexible system for kinetic characterization of enzymes which has wider applicability and other advantages over multicuvette or conventional progress curve methodology. A major advantage in contrast to the progress curve approach is that product accumulation and associated product effects are lowest at lower substrate concentrations.     

Competitive and uncompetitive inhibitors simultaneously acting on an autocatalytic zymogen activation reaction

The time course of the residual enzyme activity of a general model consisting of an autocatalytic zymogen activation process inhibited by an irreversible competitive inhibitor and an irreversible uncompetitive inhibitor has been studied. Approached analytical expressions which furnish the time course of the residual enzyme activity from the onset of the reaction depending on the rate constants and initial concentration have been obtained. The goodness and limitations of the analytical equations were checked by comparing with the results obtained from the numerical integration, i.e. with the simulated progress curves. A dimensionless parameter giving the relative contributions of both the activation and the inhibitions routes is suggested, so that the value of this parameter determines whether the activation or the inhibitions routes prevail or if both processes are balanced during the time for which the analytical expressions are valid. The effects of the initial zymogen, free enzyme and inhibitors concentrations are analysed. Finally an experimental design and kinetic data analysis is proposed to evaluate simultaneously the kinetic parameters involved and to discriminate between different zymogen activation processes which can be considered particular cases of the general model.