Kinetics of protein modification reactions

Explicit Treatment of Non-Michaelis-Menten and Atypical Kinetics in Early Drug Discovery*

Biological systems are highly regulated. They are also highly resistant to sudden perturbations enabling them to maintain the dynamic equilibrium essential to sustain life. This robustness is conferred by regulatory mechanisms that influence the activity of enzymes/proteins within their cellular context to adapt to changing environmental conditions. However, the initial rules governing the study of enzyme kinetics were mostly tested and implemented for cytosolic enzyme systems that were easy to isolate and/or recombinantly express. Moreover, these enzymes lacked complex regulatory modalities. Now, with academic labs and pharmaceutical companies turning their attention to more-complex systems (for instance, multiprotein complexes, oligomeric assemblies, membrane proteins and post-translationally modified proteins), the initial axioms defined by Michaelis-Menten (MM) kinetics are rendered inadequate, and the development of a new kind of kinetic analysis to study these systems is required. This review strives to present an overview of enzyme kinetic mechanisms that are atypical and, oftentimes, do not conform to the classical MM kinetics. Further, it presents initial ideas on the design and analysis of experiments in early drug-discovery for such systems, to enable effective screening and characterisation of small-molecule inhibitors with desirable physiological outcomes.

A THEORETICAL INVESTIGATION OF MECHANISM OF THE ADENOSINE DEAMINASE MODIFICATION: REACTION OF GLUTAMATE RESIDUE WITH WOODWARD REAGENT K

The kinetics and mechanism of the modification of adenosine deaminase with N-ethyl-5-phenyl isoxazoliom-3′-sulfonate (WR-K) are investigated using molecular dynamics simulations, QM and QM/MM minimization methods. Two methodological algorithms are employed. In the first algorithm, a glutamate residue is dissected from ADA and its reaction with WR-K is studied by employing minimization and frequency calculations under the B3LYP method. Results obtained show that ketoketenimine is produced from the interaction of WR-K with OH-in an exergonic two-step reaction. In this process, an intermediate is consumed in the rate-determining step. Next, the dissected residue is modified using ketoketenimine in a three-step reaction. This reaction is accompanied by the production of two intermediates, with the first intermediate produced in the rate-determining step.

For the second algorithm, modification of glutamate residue in the presence of water molecules and ions is investigated using conformational sampling, MM and QM/MM minimization. Stability of species in the reaction is evaluated using a combination of the B3LYP method and the WASA model. It is proved that the stability of an intermediate which is initially produced in the reaction of glutamate residue with ketoketenimine must be considered crucial when the reactivity of the different residues is compared. Results obtained indicate that these reactions have energetic features qualitatively similar to the glutamate-dissected case. It is also clear that protein structure plays a basic role in the formation of the product that arises from the reaction of ADA with ketoketenimine.

Diethylpyrocarbonate inhibition of vacuolar H+-pyrophosphatase possibly involves a histidine residue

Vacuolar proton pumping pyrophosphatase (H+-PPase; EC 3.6.1.1) plays a pivotal role in electrogenic translocation of protons from cytosol to the vacuolar lumen at the expense of PPi hydrolysis. A histidine-specific modifier, diethylpyrocarbonate (DEPC), could substantially inhibit enzymic activity and H+-translocation of vacuolar H+-PPase in a concentration-dependent manner. Absorbance of vacuolar H+-PPase at 240 nm was increased upon incubation with DEPC, demonstrating that an N-carbethoxyhistidine moiety was probably formed. On the other hand, hydroxylamine, a reagent that can deacylate N-carbethoxyhistidine, could reverse the absorption change at 240 nm and partially restore PPi hydrolysis activity as well. The pKa of modified residues of the enzyme was determined to be 6.4, a value close to that of histidine. Thus, we speculate that inhibition of vacuolar H+-PPase by DEPC possibly could be attributed to the modification of histidyl residues on the enzyme. Furthermore, inhibition of vacuolar H+-PPase by DEPC follows pseudo-first-order rate kinetics. A reaction order of 0.85 was calculated from a double logarithmic plot of the apparent reaction constant against DEPC concentration, suggesting that the modification of one single histidine residue on the enzyme suffices to inhibit vacuolar H+-PPase. Inhibition of vacuolar H+-PPase by DEPC changes Vmax but not Km values. Moreover, DEPC inhibition of vacuolar H+-PPase could be substantially protected against by its physiological substrate, Mg2+-PPi. These results indicated that DEPC specifically competes with the substrate at the active site and the DEPC-labeled histidine residue might locate in or near the catalytic domain of the enzyme. Besides, pretreatment of the enzyme with N-ethylmaleimide decreased the degree of subsequent labeling of H+-PPase by DEPC. Taken together, we suggest that vacuolar H+-PPase likely contains a substrate-protectable histidine residue contributing to the inhibition of its activity by DEPC, and this histidine residue may located in a domain sensitive to the modification of Cys-629 by NEM.

Inhibition of plant vacuolar H(+)-ATPase by diethylpyrocarbonate

Treatment of the tonoplast H(+)-ATPase from mung bean seedlings (Vigna radiata L.) with histidine-specific modifier, diethyl pyrocarbonate (DEP), caused a marked loss of the ATP hydrolysis activity and the proton translocation in a concentration-dependent manner. The reaction order of inhibition was calculated to be 0.98, suggesting that at least one histidine residue of vacuolar H(+)-ATPase was modified by DEP. The absorbance of the vacuolar H(+)-ATPase at 240 nm was progressively increased after incubation with DEP, suggesting that N-carbethoxyhistidine had been formed. Hydroxylamine, which could break N-carbethoxyhistidine, reversed the absorbance change and partially restored the enzymic activity. The pK(a) of modified residues of vacuolar H(+)-ATPase was kinetically determined to be 6.73, a value close to that of histidine. Thus, it is assuredly concluded that histidine residues of the vacuolar H(+)-ATPase were modified by DEP. Kinetic analysis showed that V(max) but not K(m) of vacuolar H(+)-ATPase was decreased by DEP. This result is interpreted as that the residual activity after DEP inhibition was primarily due to the unmodified enzyme molecules. Moreover, simultaneous presence of DEP and DCCD (N,N'-dicyclohexyl-carbodiimide), an inhibitor modified at proteolipid subunit of vacuolar H(+)-ATPase, did not induce synergistic inhibition, indicating their independent effects. The stoichiometry studies further demonstrate that only one out of four histidine residues modified was involved in the inhibition of vacuolar H(+)-ATPase by DEP. Mg(2+)-ATP, the physiological substrate of vacuolar H(+)-ATPase, but not its analogs, exerted preferentially partial protection against DEP, indicating that the histidine residue involved in the inhibition of enzymatic activity may locate at/or near the active site and directly participate in the binding of the substrate.

Kinetic analysis of parallel reactions, the initial reactant of which presents with two interconvertible isomeric forms (hydrolysis and hydroxylaminolysis of 6-phosphogluconolactone)

A mathematical treatment is presented of two parallel reactions each one of which can be described by the sum of two exponential functions of time. The two simplest reaction models consistent with this requirement are presented, and are shown to be described by a second-order non-homogeneous differential equation with constant coefficients. Solutions of this equation in closed form are given, and it is shown that, as is the case with pairs of parallel first-order reactions, description of the time course of one of the two reactions yields a complete description of the time course of the other reaction. Hypothetical cases, consistent with the reaction models presented, are given and are compared with experimental results, obtained on the parallel reactions of 6-phosphogluconolactone hydrolysis and hydroxylaminolysis. Results are compatible with the existence of enzymically generated 6-phosphogluconolactone in two interconvertible isomeric forms. Copyright 1999 Academic Press.

Characterization of isoleucyl-tRNA synthetase from Staphylococcus aureus. II. Mechanism of inhibition by reaction intermediate and pseudomonic acid analogues studied using transient and steady-state kinetics

The interactions of isoleucyl-tRNA synthetase (IleRS, E) from Staphylococcus aureus with both intermediate analogues and pseudomonic acid (PS-A) have been investigated using transient and steady-state techniques. Non-hydrolyzable analogues of isoleucyl-AMP (I) were simple competitive inhibitors (Ile-ol-AMP, Ki = 50 nM and Ile-NHSO2-AMP, Ki = 1 nM;). PS-A (J) inhibits IleRS via a slow-tight binding competitive mechanism where E.J (Kj = approximately 2 nM), undergoes an isomerization to form a stabilized E*.J complex (K*j = 50 pM). To overcome tight-binding artifacts when K*j << [E], K*j values were estimated from PPi/ATP exchange where [S] >> Km, thus raising K*j,app well above [E]. Using [3H]PS-A, it was confirmed that binding occurs with 1:1 stoichiometry and is reversible. Formation of inhibitor complexes was monitored directly through changes in enzyme tryptophan fluorescence. For Ile-ol-AMP and Ile-NHSO2-AMP, the fluorescence intensity of E.I was identical to that when E.Ile-AMP forms catalytically. Binding of PS-A induced only a small change in IleRS fluorescence that was characterized using transient kinetic competition. SB-205952, a PS-A analogue, produced a 37% quenching of IleRS fluorescence upon binding as a result of radiationless energy transfer. Inhibitor reversal rates were obtained by measuring relaxation between spectroscopically different complexes. Together, these data represent a comprehensive solution to the kinetics of inhibition by these compounds.

Kinetic study of irreversible inhibition of an enzyme consumed in the reaction it catalyses. Application to the inhibition of the puromycin reaction by spiramycin and hydroxylamine

A systematic procedure for the kinetic study of irreversible inhibition when the enzyme is consumed in the reaction which it catalyses, has been developed and analysed. Whereas in most reactions the enzymes are regenerated after each catalytic event and serve as reusable transacting effectors, in the consumed enzymes each catalytic center participates only once and there is no enzyme turnover. A systematic kinetic analysis of irreversible inhibition of these enzyme reactions is presented. Based on the algebraic criteria proposed in this work, it should be possible to evaluate either the mechanism of inhibition (complexing or non-complexing), or the type of inhibition (competitive, non-competitive, uncompetitive, mixed non-competitive). In addition, all kinetic constants involved in each case could be calculated. An experimental application of this analysis is also presented, concerning peptide bond formation in vitro. Using the puromycin reaction, which is a model reaction for the study of peptide bond formation in vitro and which follows the same kinetic law as the enzymes under study, we have found that: (i) the antibiotic spiramycin inhibits the puromycin reaction as a competitive irreversible inhibitor in a one step mechanism with an association rate constant equal to 1.3 x 10(4) M-1 s-1 and, (ii) hydroxylamine inhibits the same reaction as an irreversible non-competitive inhibitor also in a one step mechanism with a rate constant equal to 1.6 x 10(-3) M-1 s-1.

Involvement of tyrosine residue in the inhibition of plant vacuolar H(+)-pyrophosphatase by tetranitromethane

Plant vacuolar vesicles contain a novel H(+)-translocating pyrophosphatase (H(+)-PPase, EC 3.6.1.1). Modification of tonoplast vesicles and purified vacuolar H(+)-PPase from etiolated mung bean seedlings with tetranitromethane (TNM) resulted in a progressive decline in H(+)-translocating pyrophosphatase activity. The half-maximal inhibition was brought about by 0.6, 1.0, and 0.8 mM TNM for purified and membrane-bound H(+)-PPases, and its associated proton translocation, respectively. The maximal inhibition of vacuolar H(+)-PPase by TNM occurred at a pH value above 8. Loss of activity of purified H(+)-pyrophosphatase followed pseudo-first order rate kinetics, yielding a first-order rate constant (k2) of 0.039 s(-1) and a steady-state dissociation constant of inactivation (Ki) of 0.02 mM. Covalent modification of vacuolar H(+)-PPase by TNM increased Km value of the enzyme for its substrate without a significant effect on Vmax. Double logarithmic plots of the pseudo-first order rate constant (kobs) versus TNM concentration exhibited a slope of 0.88, suggesting that at least one tyrosine residue was involved in the inactivation of H(+)-PPase enzymatic activity. Further spectrophotometric measurements of the nitrated H(+)-pyrophosphatase indicated that TNM could modify approximately two tyrosine residues/subunit of the enzyme. However, Tsou's analysis revealed that only one of those modified tyrosine residues directly participated in the inhibition of enzymatic activity of vacuolar H(+)-PPase. The physiological substrate, i.e., dimagnesium pyrophosphate, provided substantial protection against inactivation by TNM. Moreover, NEM pretreatment of the enzyme decreased the number of subsequent nitration of vacuolar H(+)-PPase. Taken together, we suggest that vacuolar H(+)-pyrophosphatase contains a substrate-protectable tyrosine residue conferring to the inhibition of its activity and this tyrosine residue may be located in a domain sensitive to the modification of Cys-634 by NEM.

Lophotoxin is a slow binding irreversible inhibitor of nicotinic acetylcholine receptors

Lophotoxin and the bipinnatins are members of the lophotoxin family of marine neurotoxins, which covalently react with Tyr190 in the alpha-subunits of the nicotinic acetylcholine receptor. Bipinnatin-A, -B, and -C are protoxins that have been shown to spontaneously convert from inactive to active toxins during preincubation in buffer. However, in this report, we show that preincubation of lophotoxin did not result in an increase in the subsequent rate of irreversible inhibition of nicotinic receptors. Thus, unlike the bipinnatins, lophotoxin does not appear to be an inactive protoxin. Lophotoxin preferentially inhibited one of the two acetylcholine-binding sites on the receptor, and this preference resulted from both a higher reversible affinity and a faster rate of irreversible inhibition at this site. Association of 125I-alpha-bungarotoxin in the presence of lophotoxin was analyzed to obtain the apparent reversible association and dissociation rate constants for lophotoxin. The apparent association rate constant of lophotoxin was approximately 10(6)-fold slower than expected for a diffusion-limited interaction, indicating that lophotoxin is a slow binding irreversible inhibitor. The kinetic constants that describe the interaction of lophotoxin with the receptor did not change in the presence of dibucaine, suggesting that, unlike agonists, the slow apparent association of lophotoxin does not result from a slow transition of the receptor to a desensitized conformation.

Kinetic study of an enzyme-catalysed reaction in the presence of novel irreversible-type inhibitors that react with the product of enzymatic catalysis

In the present paper a kinetic study is made of the behaviour of a Michaelis-Menten enzyme-catalysed reaction in the presence of irreversible inhibitors rendered unstable in the medium by their reaction with the product of enzymatic catalysis. A general mechanism involving competitive, non-competitive, uncompetitive and mixed irreversible inhibition with one or two steps has been analysed. The differential equation that describes the kinetics of the reaction is non-linear and computer simulations of its dynamic behaviour are presented. The results obtained show that the systems studied here present kinetic co-operativity for a target enzyme that follows the simple Michaelis-Menten mechanism in its action on the substrate, except in the case of an uncompetitive-type inhibitor.

The reaction of cephalosporins with penicillin-binding protein 1b gamma from Escherichia coli

The kinetics of the reaction of purified penicillin-binding protein 1b gamma from Escherichia coli with cephalosporins suggest that the enzyme exists in two kinetically distinct conformations that are in slow equilibrium. One of these forms can effect rapid hydrolysis of some beta-lactams and it is only through its deactivation by conversion to the slower reacting form that complete inhibition can be achieved. With some cephalosporins and with penicillins having simple aromatic side-chains the reaction was slower and did not exhibit the same kinetic behaviour. This could be attributed to the rate of reaction being similar to the rate of conformation change and thus sets an upper limit on the isomerization rate.

Characterization of the type I dehydroquinase from Salmonella typhi

The type I dehydroquinase from the human pathogen Salmonella typhi was overexpressed in an Escherichia coli host and purified to homogeneity. The S. typhi enzyme was characterized in terms of its kinetic parameters, important active-site residues, thermal stability and c.d. and fluorescence properties. In all important respects, the enzyme from S. typhi behaves in a very similar fashion to the well-characterized enzyme from E. coli, including the remarkable conformational stabilization observed on reduction of the substrate/product mixture by NaBH4. This gives confidence that the information from X-ray studies on the S. typhi enzyme [Boys, Fawcett, Sawyer, Moore, Charles, Hawkins, Deka, Kleanthous and Coggins (1992) J. Mol. Biol. 227, 352-355] can be applied to other type I dehydroquinases. Studies of the quenching of fluorescence of the S. typhi enzyme by succinimide show that NaBH4 reduction of the substrate/product imine complex involves a dramatic decrease in the flexibility of the enzyme, with only very minor changes in the overall secondary and tertiary structure.

The kinetics of non-stoichiometric bursts of beta-lactam hydrolysis catalysed by class C beta-lactamases

Class C beta-lactamases from Pseudomonas aeruginosa and several species of the Enterobacteriaceae have been observed to undergo a rapid burst in hydrolysis of beta-lactam antibiotics before relaxation to a steady-state rate of hydrolysis. The amplitude of the burst corresponds to the hydrolysis of between 1 and 10,000 mol of the substrate per mol of enzyme. The decay of the rate of hydrolysis in the burst phase comprises two exponential reactions, which indicates that there are three different reactive states of the enzymes. Examination of the kinetics of acylation by slowly reacting beta-lactams suggests that there are three forms of the free enzyme in slow equilibrium. Thus it would appear that the burst kinetics exhibited by class C enzymes can be attributed to redistribution of the enzyme between different conformations induced by the reaction with substrate.

A kinetic study of simultaneous suicide inactivation and irreversible inhibition of an enzyme. Application to 1-aminocyclopropane-1-carboxylate (ACC) synthase inactivation by its substrate S-adenosylmethionine

This paper deals with the development of an experimental method for the kinetic study of the inactivation of an enzyme by a racemic mixture of an inhibitor, whose isomers operate as suicide substrate and irreversible inhibitor respectively. The ratio between the isomer concentration in the biological or commercial source must be determined, but no separation of them is required. The method involves a kinetic analysis and an experimental design that enables the affinity (1/Km), rate of catalysis (kcat), rate of inactivation (lambda max), efficiency of catalysis (kcat/Km) and efficiency of inactivation (lambda max/Km) to be determined. The method has been applied to the kinetic characterization of the inactivation of 1-aminocyclopropane-1-carboxylate (ACC) synthase from tomato fruits by its substrate, S-adenosylmethionine (AdoMet). The ratio between AdoMet isomers with respect to its sulfonium centre, namely (-)-AdoMet and (+)-AdoMet, present in the commercial sample used, has been determined by 1H nuclear magnetic resonance.

Kinetic evidence for the existence of an unstable intermediate in the trinitrophenylation-induced rhodanese inactivation reaction

1. Rhodanese inactivation by 2,4,6-trinitrobenzenesulphonate, in the presence of n-butylamine in the reaction medium, has been studied by a kinetic analysis of the data, based on the assumption that enzyme inactivation is brought about by direct reaction of this with the modifying agent. 2. Initial reaction rates for rhodanese activity loss were determined by a mathematical analysis of the first three recorded values of rhodanese residual activity. 3. It was found that fractional rhodanese activity values, at infinite reaction time with 2,4,6-trinitrobenzenesulphonate (end-point values), were significantly lower than the values calculated on the assumption of rhodanese inactivation being entirely due to direct trinitrophenylation of enzyme protein. 4. Also, initial enzyme inactivation values were higher in the presence, rather than in the absence, of n-butylamine. 5. These results indicate that 2,4,6-trinitrobenzenesulphonate-induced rhodanese inactivation, in the presence of n-butylamine in the reaction medium, is due to the generation of a highly reactive, unstable intermediate, probably a free radical species.

Inactivation of arginine esterase E-I of Bitis gabonica venom by irreversible inhibitors including a water-soluble carbodiimide, a chloromethyl ketone and isatoic anhydride

1. Esterase E-I from Bitis gabonica was inactivated with irreversible inhibitors which included studies with a water-soluble carbodiimide, an affinity labelling peptide and a mechanism-based inactivator. 2. The reaction with 1-ethyl-3(3-dimethylaminopropyl)-carbodiimide was biphasic and the dominant part followed saturation kinetics. At pH 5.5 a rate constant of 0.4 min-1 for inactive enzyme formation was calculated and a dissociation constant (Ki) of 0.2 M for the enzyme-inhibitor complex. 3. Inactivation with D-Phe-Pro-Arg-chloromethyl ketone indicated a two-step mechanism, for which the reaction parameters at pH 8.0 were determined. The Ki value was 0.2 microM and the inactivation rate was 2.5 min-1. 4. With isatoic anhydride pseudo-first-order kinetics was observed. At pH 8.0 a rate constant of 0.9 min-1 and a Ki of 2.0 mM were obtained. The inactivation of the enzyme was found to be governed by a group in the enzyme showing a pK value of 7.3.

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.

Kinetic analysis of regeneration by dilution of a covalently modified protein

An analysis of regeneration by dilution of a covalently modified protein is presented. It is shown that, when protein regeneration is realized through the intermediacy of a protein-modifying agent adsorptive complex, the reaction is described by a summation of two exponential functions of reaction time plus a constant-term equation. The conditions whereby this equation reduces to a single-exponential equation are delineated. It is shown that, when protein regeneration is described by a single-exponential function of reaction time, the first-order protein-regeneration rate constant is a function of modifying-agent concentration and also of the microscopic reaction rate constants. Accordingly, the protein-modifying agent dissociation constant (Ki), as well as the protein-covalent-modification and -regeneration, rate constants (k+2 and K-2), may be determined by an analysis of dilution-induced protein-regeneration (or enzyme-reactivation) data obtained at different dilutions of the covalently modified protein-modifying agent preparation.

Inactivation of skeletal-muscle UDP-glucose pyrophosphorylase by reaction with carboxylate-directed reagents

Skeletal-muscle UDP-glucose pyrophosphorylase is inactivated by reaction with 2-ethoxy-N-(ethoxy-carbonyl)-1,2-dihydroquinoline (EEDQ) and 1-(3-dimethylaminopropyl-3-ethylcarbodi-imide (EDAC), two reagents specific for carboxylate groups. The former reagent is a more effective inactivator than EDAC. Although no evidence of reversible enzyme-reagent complexes of the affinity-labelling type was obtained by kinetic analysis of the inactivation, the selective protection of UDP-glucose pyrophosphorylase activity against inactivation by EEDQ in the presence of uridine substrates is indicative of an active-site-directed effect. The results are consistent with the hypothesis that EEDQ modifies a single carboxylate group located in a hydrophobic domain close to the substrate-binding site, leading to enzyme inactivation. In contrast, the reaction between UDP-glucose pyrophosphorylase and EDAC appears to involve a different region of the enzyme.

Functional cysteinyl residues in human placental aldose reductase

Incubation of human placental aldose reductase (EC 1.1.1.21) with the sulfhydryl oxidizing reagents 5,5'-dithiobis(2-nitrobenzoic acid) (DTNB) and N-ethylmaleimide (NEM) results in a biexponential loss of catalytic activity. Inactivation by DTNB or NEM is prevented by saturating concentrations of NADPH. ATP-ribose offers partial protection against inactivation by DTNB, whereas NADP, nicotinamide mononucleotide (NMN), and the substrates glyceraldehyde and glucose offer little or no protection. The inactivation by DTNB was reversed by dithiothreitol and partially by 2-mercaptoethanol but not by KCN. When the release of 2-nitro-5-mercaptobenzoic acid was measured, 3 mol of sulfhydryl residues was found to be modified per mole of the enzyme by DTNB. Correlation of the fractional activity remaining with the extent of modification by the statistical method of C.-L. Tsou (1962, Sci. Sin. 11, 1535-1558) indicates that of the three reactive residues, one reacts at a faster rate than the other two, and that two residues are essential for the catalytic activity of the enzyme. Labeling of the total sulfhydryl by [14C]NEM and quantification of DTNB-reactive residues in the enzyme denatured by 6 M urea indicates that a total of seven sulfhydryl residues are present in the protein. The modification of the enzyme did not affect Km glyceraldehyde, but the modified enzyme had a lower Km NADPH. Kinetic analysis of the data suggests that a biexponential nature of inactivation could be due to the formation of a dissociable E:DTNB complex and the presence of a partially active enzyme species.

Kinetic analysis of protein modification reactions at equilibrium

A kinetic analysis is presented of reactions of protein modification, and/or of modification-induced enzyme inactivation, which can formally be described by a single exponential function, or by a summation of two exponential functions, of reaction time plus a constant term. The reaction schemes compatible with the kinetic formalism of these cases are given, and a simple kinetic criterion is described whereby the identification of one of these cases, strong negative protein modification co-operativity, may be carried out. The treatment outlined in this paper is applied to a case from the literature, the inactivation of glyceraldehyde-3-phosphate dehydrogenase by butane-2,3-dione [Asriyants, Benkevich & Nagradova (1983) Biokhimiya (Engl. Transl.) 48, 164-171].

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.

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.

Modification and inactivation of rhodanese by 2,4,6-trinitrobenzenesulphonic acid

Bovine liver rhodanese (thiosulphate sulphurtransferase, EC 2.8.1.1) is modified by 2,4,6-trinitrobenzenesulphonic acid, by the use of modifying agent concentrations in large excess over enzyme protein concentration. The end-point of the reaction, viz., the number, n, per enzyme protein molecule, of modifiable amino groups was determined graphically by the Kézdy-Swinbourne procedure. It was found that the value for n depends on the pH of the reaction medium, and ranges from 2, at pH 7.00, to 10.66, at pH 9.00. Again, the value for n increases with an increase in the concentration of 2,4,6-trinitrobenzenesulphonic acid used, with values ranging from 3.52, at 0.10 mM modifying agent, to 8.96, at 2 mM modifying agent. Rhodanese primary amino groups modification by 2,4,6-trinitrobenzenesulphonic acid is described by a summation of exponential functions of reaction time at pH values of 8.00 or higher, while at lower pH values it is described by a single exponential function of reaction time. However, the log of the first derivative, at initial reaction conditions, of the equation describing protein modification, is found to be linearly dependent on the pH of the reaction. An identical linear dependence is also found when the log of the first derivative, at the start of the reaction, of the equation describing modification-induced enzyme inactivation is plotted against the pH values of the medium used. In consequence, the fractional concentration of rhodanese modifiable amino groups essential for enzyme catalytic function is equal to unity at all reaction pH values tested. It is accordingly concluded that, when concentrations of 2,4,6-trinitrobenzenesulphonic acid in excess of protein concentration are used, all rhodanese modifiable amino groups are essential for enzyme activity. A number of approaches were used in order to establish a mechanism for the modification-induced enzyme inactivation observed. These approaches, all of which proved to be negative, include the possible modification of enzyme sulfhydryl groups, disulphide bond formation, enzyme inactivation due to sulphite released during modification, modification-induced enzyme protein polymerization, syncatalytic enzyme modification and hydrogen peroxide-mediated enzyme inactivation.

Inactivation of carbonyl reductase from human brain by phenylglyoxal and 2,3-butanedione: a comparison with aldehyde reductase and aldose reductase

Aldehyde reductase (alcohol:NADP+ oxidoreductase, EC 1.1.1.2), aldose reductase (alditol:NAD(P)+ 1-oxidoreductase, EC 1.1.1.21) and carbonyl reductase (secondary-alcohol:NADP+ oxidoreductase, EC 1.1.1.184) constitute the enzyme family of the aldo-keto reductases, a classification based on similar physicochemical properties and substrate specificities. The present study was undertaken in order to obtain information about the structural relationships between the three enzymes. Treatment of human aldehyde and carbonyl reductase with phenylglyoxal and 2,3-butanedione caused a complete and irreversible loss of enzyme activity, the rate of loss being proportional to the concentration of the dicarbonyl reagents. The inactivation of aldehyde reductase followed pseudo-first-order kinetics, whereas carbonyl reductase showed a more complex behavior, consistent with protein modification cooperativity. NADP+ partially prevented the loss of activity of both enzymes, and an even better protection of aldehyde reductase was afforded by the combination of coenzyme and substrate. Aldose reductase was partially inactivated by phenylglyoxal, but insensitive to 2,3-butanedione. The degree of inactivation with respect to the phenylglyoxal concentration showed saturation behavior. NADP+ partially protected the enzyme at low phenylglyoxal concentrations (0.5 mM), but showed no effect at high concentrations (5 mM). These findings suggest the presence of an essential arginine residue in the substrate-binding domain of aldehyde reductase and the coenzyme-binding site of carbonyl reductase. The effect of phenylglyoxal on aldose reductase may be explained by the modification of a reactive thiol or lysine rather than an arginine residue.

Diethyl pyrocarbonate inactivation of human placental aldehyde reductase II

Diethyl pyrocarbonate inactivated aldehyde reductase II (L-gulonate:NADP+ 6-oxidoreductase, EC 1.1.1.19) from human placenta. A concentration of 0.5-1.0 mM diethyl pyrocarbonate caused 40-65% loss of activity. The inactivation of the enzyme by diethyl pyrocarbonate was reversed by hydroxylamine and was accompanied by a large change in the absorbance of the protein at 242 nm, but not at 278 nm, indicating that only the histidine residues were modified. NADPH, but not glucuronate afforded significant protection to the enzyme from inactivation by diethyl pyrocarbonate. With 0.2-1.0 mM diethyl pyrocarbonate, 4-5 histidine residues were modified with a pseudo-first-order rate process. A double log plot of the fraction of the unmodified residues indicates that only one functional histidine residue is essential for the catalytic activity of aldehyde reductase II.

The presence of functional arginine residues in phosphoenolpyruvate carboxykinase from Saccharomyces cerevisiae

Saccharomyces cerevisiae phosphoenolpyruvate carboxykinase (ATP:oxaloacetate carboxy-lyase (transphosphorylating), EC 4.1.1.49) is completely inactivated by phenylglyoxal and 2,3-butanedione in borate buffer at pH 8.4, with pseudo-first-order kinetics and a second-order rate constant of 144 min-1 X M-1 and 21.6 min-1 X M-1, respectively. Phosphoenolpyruvate, ADP and Mn2+ (alone or in combination) protect the enzyme against inactivation, suggesting that the modification occurs at or near to the substrate-binding site. Almost complete restoration of activity was obtained when a sample of 2,3-butanedione-inactivated enzyme was freed of excess modifier and borate ions, suggesting that only arginyl groups are modified. The changes in the rate of inactivation in the presence of substrates and Mn2+ were used to determine the dissociation constants for enzyme-ligand complexes, and values of 23 +/- 3 microM, 168 +/- 44 microM and 244 +/- 54 microM were found for the dissociation constants for the enzyme-Mn2+, enzyme-ADP and enzyme-phosphoenolpyruvate complexes, respectively. Based on kinetic data, it is shown that 1 mol of reagent must combine per enzyme active unit in order to inactivate the enzyme. Complete inactivation of the carboxykinase can be correlated with the incorporation of 3-4 mol [7-14C]phenylglyoxal per mol of enzyme subunit. Assuming a stoichiometry of 1:1 between phenylglyoxal incorporation and arginine modification, our results suggest that the modification of only two of the three to four reactive arginine residues per phosphoenolpyruvate carboxykinase subunit is responsible for inactivation.

Phenylglyoxal modification of arginines in mammalian D-amino-acid oxidase

The presence of arginine in the active center of D-amino-acid oxidase is well documented although its role has been differently interpreted as being part of the substrate-binding site or the positively charged residue near the N1-C2 = O locus of the flavin coenzyme. To have a better insight into the role of the guanidinium group in D-amino-acid oxidase we have carried out inactivation studies using phenylglyoxal as an arginine-directed reagent. Loss of catalytic activity followed pseudo-first-order kinetics for the apoprotein whereas the holoenzyme showed a biphasic inactivation pattern. Benzoate had no effect on holoenzyme inactivation by phenylglyoxal and the coenzyme analog 8-mercapto-FAD did not provide any additional protection in comparison to the native coenzyme. Spectroscopic experiments indicated that the modified protein is unable to undergo catalysis owing to the loss of coenzyme-binding ability. Analyses of time-dependent activity loss versus arginine modification or [14C]phenylglyoxal incorporation showed the presence of one arginine essential for catalysis. The protection exerted by the coenzyme is consistent with the involvement of an active-site arginine in the correct binding of FAD to the protein moiety. Comparative analyses of CNBr fragments obtained from apoenzyme, holoenzyme and the 8-mercapto derivative of D-amino-acid oxidase after reaction with phenylglyoxal did not provide unequivocal identification of the essential arginine residue within the primary structure of the enzyme. However, they suggest that it might be localized in the N-terminal portion of the polypeptide chain and point to a role of phenylglyoxal-modifiable arginine in binding to the adenylate/pyrophosphate moiety of the flavin coenzyme.

Kinetics of suicide substrate:enzyme inactivation. Methylenecyclopropaneacetyl-CoA and general acyl-CoA dehydrogenase

Kinetics of inactivation of general acyl-CoA dehydrogenase from pig kidney by methylenecyclopropaneacetyl-CoA have been analyzed using the theoretical treatment and exact steady-state kinetic solutions reported by Tatsunami (Tatsunami, S., Yago, N., and Hosoe, M. (1981) Biochim. Biophys. Acta 662, 226-235). Thus practical application of these analytical solutions for an important class of enzyme:substrate reactions has been demonstrated for the first time.

Kinetics of protein modification reactions: analysis of modification-induced protein unfolding

A mathematical treatment of a two-sited, modification-induced protein unfolding model is presented, and it is shown that the dependence of the concentration of modified protein groups on reaction time is described by a linear, second-order, differential equation with nonzero right hand side. The analytic solution of this equation consists of a summation of exponential functions of reaction time. By assigning arbitrary values to the modification and isomerization rate constants of these equations, simulated cases of protein modification are presented, and the apparent end-point of the reaction is determined graphically. It is found that the apparent end-point of the reaction is, in most cases studied, different from the true value of two groups modified per protein molecule, and is a function of both the modification, and isomerization rate constants of the model. The first derivative of the protein modification reaction, at the start of the reaction, [E]'mod (0), is determined, for the same simulated cases of protein modification, by two different analytical methods. It is found that the [E]'mod(0) value, obtained from graphical and numerical analysis data, is in most cases in good agreement with the value expected from first principles. Finally, the different irreversible enzyme inhibition forms, contingent upon the different kinds of the enzyme inactivation-protein modification relationships of the protein modification model under consideration, are presented and discussed.

Computer simulations of the kinetics of irreversible enzyme inhibition by an unstable inhibitor

Computer simulations of the irreversible inhibition of an enzyme by an unstable inhibitor are presented. Data obtained at the end point of reaction are shown to conform poorly in many situations with relationships derived from integrated rate equations by setting t = infinity, and the implications concerning the experimental use of this method to determine kinetic constants describing inactivation are considered. The alternative approach of conducting experiments under conditions of inhibitor excess over enzyme is further discussed, and a graphical procedure is suggested for the description of time courses of reaction of enzyme with unstable inhibitor when an enzyme-inhibitor adsorptive complex is involved.

Kinetics of protein-modification reactions. Determination of the fractional concentration of enzyme protein groups, or group reactivities, essential for catalytic function

A mathematical treatment of modification-induced enzyme protein inactivation is presented, and it is shown that, at initial reaction conditions, the ratio of the first derivative of the equation describing enzyme activity loss to the first derivative of the equation describing protein groups modification is equal to the fractional concentration of enzyme protein reactive groups, or group reactivities, essential for catalytic function.

Inactivation of macromolecules by ionizing radiation. Deterministic single-hit or stochastic multievent process?

A stochastic theory concerning the radiation inactivation of macromolecules such as enzymes or receptors is elaborated. In contrast with the single-hit theory, which assumes a complete inactivation of the target as the result of one hit, the stochastic theory postulates that the degree of inactivation by one hit is a random variable. This distinguishing feature has been considered in order to give a possible interpretation to the observed effect of temperature on the radiation-sensitivity of enzymes. As a consequence of the progressive inactivation during irradiation, the binding affinity of a ligand for the macromolecule is impaired by irradiation. Although this property might discriminate the stochastic theory from the classical single-hit theory on the basis of a statistical analysis of experimentally obtained data, it is shown that the commonly obtained degree of inaccuracy may render the statistical test non-conclusive.

A kinetic analysis of enzyme inactivation as applied to the covalent modification of Na+ + K+ -ATPase and Ca2+ -ATPase

A kinetic analysis of enzyme inactivation due to the covalent binding of chemically modified ligands is presented. Reaction schemes similar to the Michaelis-Menten scheme have been studied as well as schemes with two states of the enzyme or two binding sites. The resulting kinetic equations lead to time courses of inactivation which can be represented by two exponential functions at least in a quasi-steady state approximation. These curves are frequently encountered in inactivation experiments. Since rapid methods for model selection and parameter estimation are desirable, but not available, a technique for a preliminary analysis of the experimental data is presented. A mere glance at the time courses shows what reaction schemes are inapplicable. For each family of inactivation curves, the construction of a line of intersections is proposed. This line contains essential kinetic information and can further be utilized for a rough parameter estimation. The technique is illustrated for three sets of experimental data where Na+ + K+ -ATPase and Ca2+ -ATPase have been inactivated by ATP-analogs.

Kinetics of protein-modification reactions. Stoichiometry of modification-produced enzyme inactivation: modification of rhodanese by 2,4,6-trinitrobenzenesulphonic acid

A mathematical treatment is presented for the dependence of enzyme activity loss on the numbers and reactivities of the groups essential for catalytic function, when enzyme protein modification is carried out by the use of concentrations of protein reactive groups well in excess of that of modifying agent. Experimentally obtained data on the modification of rhodanese (thiosulphate sulphurtransferase, EC 2.8.1.1) by 2,4,6-trinitrobenzenesulphonic acid are presented, and it is shown that, at pH9.00, the fractional concentration of rhodanese groups, or of rhodanese group reactivities, essential for enzyme catalytic function is 0.88; this value is found to decrease with decreasing pH of the reaction medium. The possibility that rhodanese inactivation by 2,4,6-trinitrobenzenesulphonic acid is brought about by modification of groups other than amino groups is ruled out by a comparison of the enzyme-inactivation and protein-modification stoichiometries, for putative reaction models for enzyme and modifying agent.

Kinetics of protein modification reactions. Plot of fractional enzyme activity versus extent of protein modification in cases where all modifiable groups are essential for enzyme activity

The plot of fractional enzyme activity versus extent of protein modification, for cases where all enzyme modifiable groups of a certain kind are essential for activity, is found to be nearly independent of the number, per enzyme active site, of modifiable groups involved. Such plots usually, by a fallacious extension of the initial portion of the plot on the extent-of-modification axis, are interpreted to mean the modification of one single group per enzyme active site (or per enzyme molecule). The possible relevance of these findings to cases in the literature is discussed.