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.     

A generalized theoretical treatment of the kinetics of an enzyme-catalysed reaction in the presence of an unstable irreversible modifier

A generalized theoretical treatment of the kinetics of an enzyme-catalysed reaction in the presence of an unstable irreversible inhibitor (or activator) is presented. Analytical expressions describing the time-dependence of product formation have been derived in coefficient form amenable to non-linear regression analysis for two operationally distinct types of reaction mechanism dependent on whether the reaction of the unstable modifier (X) with either or both the free enzyme (E) and enzyme-substrate complex (ES) occurs as a simple bimolecular process, or proceeds through the intermediacy of either or both adsorptive enzyme-modifier (EX) and enzyme-modifier-substrate (EXS) complexes in what may be considered as an extension of the Botts-Morales general modifier mechanism for (stable) reversible enzyme inhibitors and activators. Special cases of both models are classified in an analogous way to the traditional naming of reversible enzyme modifications, and guidelines concerning tests of mechanism and determination of kinetic parameters are given. In particular, it has been shown that kinetic constants describing enzyme inactivation by an unstable site-specific inhibitor forming a reversible EX complex prior to covalent modification step may be determined from a single progress curve. Kinetic analysis of the extended Botts-Morales mechanism describing irreversible enzyme inactivation has demonstrated that analytical expressions describing the time-course of product formation may be derived for a stable modifier by retaining the usual steady-state assumptions regarding the fluxes around ES and EXS provided quasi-equilibrium modifier binding to E and ES is assumed, but for unstable modifiers all of the binding steps must be assumed to be at quasi-equilibrium in the steady-state, except under restrictive circumstances.     

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.     

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.     

Experimental modelling of thermal inactivation of urease

Thermal inactivation of jack bean urease (EC 3.5.1.5) was investigated in a 0.1 M phosphate buffer with pH 7. An injection flow calorimetry method was adapted for the measurement of the enzyme activity. The inactivation curves were measured in the temperature range of 55 to 87.5 degrees C. The curves exhibited a biphasic pattern in the whole temperature range and they were well fitted with a biexponential model. A simultaneous fit of all inactivation data was based on kinetic models that were derived from different inactivation mechanisms and comprised the material balances of several enzyme forms and the enthalpy balance characterizing the initial heating period of enzyme solution. The multitemperature evaluation revealed that an adequate model had to incorporate at least three reaction steps. It was concluded that the key reaction steps at urease thermal inactivation were the reversible dissociation/denaturation of native form into an inactive denatured form, and irreversible association reactions of both the denatured and native forms.     

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.     

Kinetic analysis of a general model of activation of aspartic proteinase zymogens involving a reversible inhibitor. I. Kinetic analysis

Starting from a simple general reaction mechanism of activation of aspartic proteinases zymogens involving a uni- and a bimolecular simultaneous activation route and a reversible inhibition step, the time course equation of the zymogen, inhibitor and activated enzyme concentrations have been derived. Likewise, expressions for the time required for any reaction progress and the corresponding mean activation rates as well as the half-life of the global zymogen activation have been derived. An experimental design and kinetic data analysis is suggested to estimate the kinetic parameters involved in the reaction mechanism proposed.     

Suicide-peroxide inactivation of horseradish peroxidase in the presence of sodium n-dodecyl sulphate: a study of the enzyme deactivation kinetics

In the presence of the anionic surfactant sodium n-dodecyl sulphate (SDS), horseradish peroxidase (HRP) undergoes a deactivation process. Suicide inactivation of horseradish peroxidase by hydrogen peroxide(3 mM) was monitored by the absorbance change in product formation in the catalytic reaction cycle. The progress curve of the catalytic reaction cycle was obtained at 27degrees C and phosphate buffer 2.5 mM (pH = 7.0). The corresponding kinetic parameters i.e., intact enzyme activity (alpha i); the apparent rate constant of suicide inactivation by peroxide (ki); and the apparent rate constants of enzyme deactivation by surfactant (kd) were evaluated from the obtained kinetic equations. The experimental data are accounted for by the equations used in this investigation. Addition of SDS to the reaction mixture intensified the inactivation process. The deactivation ability of denaturant could be resolved from the observed inactivation effect of the suicide substrate by applying the proposed model. The results indicate that the deactivation and the inactivation processes are independent of each other.     

Kinetic study in the transient phase of the suicide inactivation of frog epidermis tyrosinase

This paper deals with the kinetic study of a multisubstrate mechanism with enzyme inactivation induced by a suicide substrate. A transient phase approach has been developed that enables the deduction of explicit equations of product concentration vs. time. From these equations kinetic constants which characterize the suicide substrate can be obtained. This study with tyrosinase enzyme, which acts on L-dopa and catechol allowed us to determine the corresponding kinetic parameters, indicating that catechol is about 8-times more powerful as a suicide substrate than is L-dopa.     

Kinetic study on the suicide inactivation of tyrosinase induced by catechol

Tyrosinase has a suicide inactivation reaction when it acts on omicron-diphenols. In the present paper, this reaction has been studied using a transient phase approach. Explicit equations of product vs. time have been developed for the multisubstrate mechanism of tyrosinase, and the kinetic parameters which characterize the enzyme acting on the suicide substrate catechol have been determined. The effect of pH has also been considered.     

Mode of action of tetrahydrolipstatin: a derivative of the naturally occurring lipase inhibitor lipstatin

Tetrahydrolipstatin is a specific lipase inhibitor derived from lipstatin, a lipid produced by Streptomyces toxytricini. In addition to pancreatic lipase, it is shown in the present study that tetrahydrolipstatin also inhibits human gastric lipase, carboxyl ester lipase (cholesterol esterase) of pancreatic origin and the closely related bile-salt-stimulated lipase of human milk. It does not inhibit the exocellular lipase from Rhizopus arrhizus or a lipase recently isolated from Staphylococcus aureus. In the presence of a water-insoluble substrate, such as tributyrin, the inhibition has the characteristics of an irreversible inactivation of the uncompetitive type, thus indicating that an enzyme.substrate.inhibitor complex is formed, which cannot undergo further reaction to yield the normal product. This reaction probably takes place at the aqueous/oil interface of the substrate. In aqueous solution, in the absence of substrate, the inhibition of carboxyl ester lipase by tetrahydrolipstatin has the characteristics of being reversible, and finally becomes of a temporary nature analogues to the trypsin-trypsin inhibitor system. It is suggested that an enzyme-inhibitor complex of an acyl-enzyme type is formed that is slowly hydrolysed, with water as the final acceptor, leaving an intact enzyme and an inactive form of the inhibitor. The enzyme thus consumes the inhibitor, which undergoes a chemical conversion, as indicated by a change in mobility in an appropriate thin-layer chromatographic system, indicating an increase in hydrophilicity. Evidence is presented that the reaction product is an acid and that the functional group of tetrahydrolipstatin is the beta-lactone reacting with the active site of the enzyme.     

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.     

Enzyme-activated inhibition of bacterial D-amino acid transaminase by beta-cyano-D-alanine

beta-Cyano-D-alanine is an efficient suicide substrate (Ki = 10 microM) of D-amino acid transaminase. This apparent inactivation is temperature dependent: it is irreversible at 10 degrees C or below and becomes progressively reversible at higher temperatures. Since at higher temperatures the apparent reactivation process predominates over the inactivation reaction, the reactivation process is considered to be endothermic. The nature of this reversibility suggests the formation of a heat labile bond between the inhibitor molecule and a nucleophilic group on the enzyme.     

Hysteretic enzyme response induced by inhibitory antibodies against human leukocyte elastase

Polyclonal antibodies raised in rabbits against human leukocyte elastase contained two distinct populations of enzyme-inhibiting immunoglobulins. The enzyme-catalyzed reaction in the presence of antibodies (both IgG or monovalent Fab fragments) showed a transient state lasting up to several minutes depending on the inhibitor and substrate concentrations, which was followed by a linear steady-state. The transient was a concave upward or concave downward lag phase depending on whether the enzyme had been preincubated with the antibodies or not, respectively. The kinetic analysis of reaction progress curves showed that both antibody populations were slow inhibitors, which completely and reversibly excluded the substrate from binding to the enzyme. For both antibody populations, the formation of the enzyme-inhibitor complex was characterized by an initial rapid interaction followed by a slow isomerization to a catalytically inactive complex. The apparent pseudo first-order rate constant of the transient slow phase was a hyperbolic function of the inhibitor concentration for both antibodies, from which relevant kinetic constants and the half times for enzyme inactivation could be calculated. For instance, with a total antibody concentration of 1 mg/ml (as IgG), leukocyte elastase was inactivated with t1/2 = 0.31s and 24.8s by the faster and the slower of the two antibodies, respectively. It is suggested that the hysteretic response of the enzyme to the inhibitory action of its antibodies may be due to a kind of memory of the antibody molecule for a special inactive enzyme conformation resulting from inhibition by proteinase inhibitors during the immunization procedure. In turn, the purified antibodies would be able to reversibly induce a slow transition of the enzyme molecule from an active to a substrate-excluding conformation ("induced misfit").     

Influence of substrate and product diffusion on the heterogeneous kinetics of enzymic reversible reactions

When a reversible reaction is catalyzed by a surface bound enzyme, the diffusion of both substrate and product can considerably modify the kinetic properties of the reaction. According to this theoretical analysis, the enzyme activity is decreased due to the presence of substrate and product concentration gradients in the enzyme microenvironment, and the relative kinetic importance of the two diffusion steps mainly depend on the value of a dimensionless criterion inversely proportional to the equilibrium constant. Moreover diffusional effects increase with increasing bound enzyme activity, but decrease with increasing substrate and product concentration. Analytical expressions are established for the limiting values of substrate and product concentrations in the enzyme microenvironment, as well as for the increase in half-maximal-activity substrate concentration in the presence of substrate and product diffusional limitations.     

Acceleration of Drosophila melanogaster acetylcholinesterase methanesulfonylation: peripheral ligand D-tubocurarine enhances the affinity for small methanesulfonylfluoride

D-Tubocurarine, a reversible peripheral inhibitor of cholinesterases accelerates methanesulfonylation of Drosophila melanogaster wild type and W359L mutant. The kinetic evaluation of the process was performed in a step-by-step analysis. The second order overall sulfonylation rate constants, determined from classical residual activity measurements, were used in the subsequent analysis of progress curves. The latter were obtained by measuring the hydrolysis of acetylthiocholine in a complex reaction system of enzyme, substrate, irreversible and reversible inhibitor. The underlying kinetic mechanisms, from such a complex data, could only be untangled by targeted inspection and successive incorporation of reaction steps for which experimental evidence existed. The study showed that the peripheral ligand D-tubocurarine, by binding at the entrance into the active site of the two investigated enzymes (Golicnik et al., Biochemistry 40 (2001) 1214), enhances the affinity for small methanesulfonylfluoride, rather to speeding up the formation of a stable covalent enzyme-inhibitor complex. The specific arrangements at the rim of the active site of each individual enzyme dictate the actual events which can be detected by kinetic means.     

Suicide inactivation of fructose-1,6-bisphosphate aldolase

2-Keto-4,4,4-trifluorobutyl phosphate (HTFP) was prepared from 3,3,3-trifluoropropionic acid. HTFP acts as an irreversible inhibitor of rabbit muscle aldolase: the loss of activity was time dependent and the inactivation followed a pseudo-first-order process. Values of 1.4 mM for the dissociation constant and 2.3 X 10(-2) s-1 for the reaction rate constant were determined. The kinetic constants do not depend on the enzyme concentration. No effect of thiols on the inactivation rate was detected. Only 1-2 mol of fluoride ions was liberated per inactivated subunit, indicative of a low partition ratio. Dihydroxyacetone phosphate protected the enzyme against the inactivation in a competitive manner, and glyceraldehyde 3-phosphate protected as if it formed a condensation product with HTPF. 5,5'-Dithiobis(2-nitrobenzoic acid) thiol titration showed the loss of one very reactive thiol group per enzyme subunit after inactivation. All those observations seem to agree with a suicide substrate inactivation of aldolase by HTPF.     

Kinetics of suicide substrates.

When suicide substrates inactivate enzymes during catalysis, formation of product and inactivation of enzyme proceed concurrently. The steady-state hypothesis is applicable when catalytic quantities of enzyme are used. Equations for the rate of inactivation have been derived and integrated to obtain equations describing progress curves.     

The inactivation of lipoxygenase-1 from soybeans by amidrazones

Several compounds containing an amidrazone moiety are known to be potent inhibitors of lipoxygenase-1 activity from soybeans (L-1) with IC(50)-values in the range of 10 microM to 38 nM. Recently it was proposed that phenylhydrazones act as irreversible mechanism-based inhibitors of lipoxygenases. Because of the structural similarities between both compounds it was assumed for the amidrazones to affect the lipoxygenase reaction in the same suicide manner. Cyclisation of the amidrazone moiety to the corresponding triazoline should yield compounds without substrate properties. However, they are still able to inactivate the enzyme. The inhibition of L-1 from soybeans by two representative compounds of a series of amidrazones and triazolines has been characterised as a slow, tight-binding interaction via a two-step mechanism. Dialysis experiments indicate the reversible nature of interaction of the amidrazone with the ferrous enzyme while the ferric enzyme was irreversibly inactivated. In contrast, the interaction of the triazoline with both the ferric and ferrous species of the enzyme was completely reversible which demonstrates the noncovalent and reversible mode of binding and inactivation. The triazoline was found not to be a substrate of the dioxygenase reaction of lipoxygenase whereas the amidrazone is only a very poor substrate of the enzymatic oxidation reaction. The presented results point out the inhibition of L-1 by amidrazones and triazolines to fall into the same kinetic classification. Therefore it is obvious that the inhibition of L-1 by these compounds cannot be attributed to a truly mechanism-based inactivation.