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.     

Kinetics of beta-lactamase inhibition by clavulanic acid]

The mechanisms of action of 3 R-factors on beta-lactamases (penicillin amido-beta-lactamhydrolase, EC 3.5.2.6) (TEM-1 pI = 5.4, TEM-2 pI = 5.6 and Pitton's type 2 pI = 7.7) have been kinetically analyzed for clavulanic acid inactivation. Clavulanic acid appears as a competitive and irreversible inhibitor (Kcat inhibitor) reacting in two steps: a, formation of a reversible enzyme . inhibitor complex (characterized by a Ki); b, evolution of the reversible complex into a new derivative (covalent, stable and inactive) by monomolecular kinetics characterized by a k6 (or Kcat) related to half-life. The kinetic constants are: TEM-1: Ki = 0.8 micrometer, k6 = 0.027 s-1; TEM-2: Ki = 0.7 micrometer, k6 = 0.03 s-1; type 2: Ki = 0.6 micrometer, k6 = 0.046 s-1. These results justify the 'progressive irreversible' character of the inhibition generally described.     

Inactivation of chymotrypsin and human skin chymase: kinetics of time-dependent inhibition in the presence of substrate

The reaction of chymase, a chymotryptic proteinase from human skin, and bovine pancreatic chymotrypsin with a number of time-dependent inhibitors has been studied. An integrated equation, relating product formation with time, has been derived for the reaction of enzymes with time-dependent inhibitors in the presence of substrate. This is based on a two-step model in which a rapidly reversible, non-covalent complex (EI) is formed prior to a tighter, less readily reversible complex (EI)*). The equation depends on the simplifying assumption [I] much greater than [E], but is applicable to reversible and irreversible slow-binding and tight-binding inhibitors whether or not they show saturation kinetics. The method has been applied to the reaction of chymase and chymotrypsin with the tetrapeptide aldehyde, chymostatin, basic pancreatic trypsin inhibitor and Ala-Ala-Phe-chloromethylketone (AAPCK). The irreversible inhibitor, AAPCK, showed the expected saturation kinetics for both enzymes and the apparent first-order rate constants (k2) and dissociation constants (Ki) for the non-covalent complexes were determined. Chymostatin was a much more potent inhibitor which failed to show a saturation effect. The second-order rate constant of inactivation (k2/Ki), the first-order reactivation rate constant (k-2), and the dissociation constant of the covalent complex (Ki*) were determined. Basic pancreatic trypsin inhibitor, a potent inhibitor of chymotrypsin, had similar kinetics to chymostatin but failed to inhibit chymase. The applicability of the two-step model and the integrated equation to slow- and tight-binding inhibitors is discussed in relation to a number of examples from the literature.     

Inhibition of Na,K-ATPase by a new ATP analog, adenosine-5-N'-(2,4-dinitro-5-fluorophenyl)phosphohydrazide.

A new ATP analog, adenosine-5-N'-(2,4-dinitro-5-fluorophenyl) phosphohydrazide (DNPH-AMP), has been synthesized, which is an irreversible inhibitor of Na,K-ATPase. Interaction of the analog with the enzyme in the presence of K+ is described by the scheme: [formula: see text] and corresponding kinetic constants k3 and Ki are found equal to 2.5 min-1 and 1.6 mM. In the presence of Na+ the time course of enzyme inactivation by DNPH-AMP is a biphasic curve in the semilogarithmic plot. The k3 and Ki values calculated for this case according to Fritzsch [Fritzsch (1985) J. Theor. Biol. 117, 397] are equal to 2.45 min-1 and 2.5 mM, respectively. ATP transforms the K(+)-type of Na,K-ATPase inactivation into the one that takes place in the presence of Na+.     

Species-specific irreversible inhibition of Neisseria gonorrhoeae dihydrofolate reductase by a substituted 2,4-diamino-5-benzylpyrimidine

Neisseria gonorrhoeae dihydrofolate reductase undergoes a time-dependent, irreversible inactivation by 2,4-diamino-5-[3,5-dimethoxy-4-(p-bromoacetamidophenoxy)benzyl] pyrimidine. The kinetics of inactivation are consistent with the reversible formation of an enzyme-inhibitor complex followed by covalent binding to the enzyme. The reversible component is competitive with dihydrofolate and has an inhibitor binding constant of 10 nM. Irreversible inactivation proceeds as a pseudo first-order process with a minimum inactivation half-time of 20 min and a Ki of 28 nM. Using radiolabeled inhibitor, it was shown that approximately 1 mol of ligand was covalently bound to the enzyme/mol of methotrexate binding site when the enzyme was completely inhibited. Radiolabeled inhibitor remained associated with the enzyme following denaturation and sodium dodecyl sulfate-polyacrylamide gel electrophoresis. Cyanogen bromide cleavage of the 14C-labeled enzyme-inhibitor complex yielded only one radioactive polypeptide, and sequence determinations showed that His-25 was modified by covalent attachment of the inhibitor. When dihydrofolate reductases from Lactobacillus casei, Streptococcus faecium, Escherichia coli, SR-1 rodent lymphoma, and chicken liver were tested with the affinity label, only the L. casei enzyme showed a time-dependent increase in inhibition. These data, along with comparisons of known amino acid sequences and x-ray crystal structures, were used to make predictions concerning the three-dimensional conformation of the gonococcal enzyme.     

Production and purification of monoclonal T lymphocyte antigen binding molecules (TABM)

The thyroid hormone derivative N-bromoacetyl-3,3',5-triiodothyronine (BrAcT3) acts as an active site-directed inhibitor of rat liver iodothyronine deiodinase. Lineweaver Burk analysis of enzyme kinetic measurements showed that BrAcT3 is a competitive inhibitor of the 5'-deiodination of 3,3',5'-triiodothyronine (rT3) with an apparent Ki value of 0.1 nM. Preincubations of enzyme with BrAcT3 indicated that inhibition by this compound is irreversible. The inactivation rate obeyed saturation kinetics with a limiting inactivation rate constant of 0.35 min-1. Substrates and substrate analogs protected against inactivation by BrAcT3. Covalent incorporation of 125I-labeled BrAcT3 into "substrate-protectable" sites was proportional to the loss of deiodinase activity. The results suggest that BrAcT3 is a very useful affinity label for rat liver iodothyronine deiodinase.     

p-(Bromoacetamido)phenyl uridyl pyrophosphate: an active-site-directed irreversible inhibitor for uridine diphosphate galactose 4-epimerase.

The synthesis of p-(bromoacetamido)phenyl uridyl pyrophosphate (BUP) is described. This compound is an active-site-directed irreversible inhibitor of Escherichia coli UDP-galactose 4-epimerase. The inactivation follows pseudo-first-order kinetics at pH 8.5 in nonnucleophilic buffers, and a saturation effect is seen in the pseudo-first-order rate constant as the concentration of BUP is increased. The half-saturation parameter for BUP in the inactivation is 0.21 +/- 0.02 mM, which compares favorably with the inhibition constant of 0.3 +/- 0.05 mM for BUP acting as a competitive reversible inhibitor of the enzyme. The inactivation rate is slow, however, with a minimum half-time of 12 h at pH 8.5 and 27 degrees C. Both specific alkylation and nonspecific alkylation by BUP occur, but nonspecific alkylation is faster than the inactivation and the rate of inactivation correlates well with the rate of covalent incorporation of one molecule of [14C]BUP at the active site.     

Molecular recognition by acetylcholinesterase at the peripheral anionic site: structure-activity relationships for inhibitions by aryl carbamates

Substituted phenyl-N-butyl carbamates (1-9) are potent irreversible inhibitors of Electrophorus electricus acetylcholinesterase. Carbamates 1-9 act as the peripheral anionic site-directed irreversible inhibitors of acetylcholinesterase by the stop-time assay in the presence of a competitive inhibitor, edrophonium. Linear relationships between the logarithms of the dissociation constant of the enzyme inhibitor adduct (Ki), the inactivation constant of the enzyme-inhibitor adduct (k2), and the bimolecular inhibition constant (k(i)) for the inhibition of Electrophorus electricus acetylcholinesterase by carbamates 1-9 and the Hammett substituent constant (sigma), are observed, and the reaction constants (ps) are -1.36, 0.35 and -1.01, respectively. Therefore, the above reaction may form a positive charged enzyme-inhibitor intermediate at the peripheral anionic site of the enzyme and may follow the irreversible inactivation by a conformational change of the enzyme.     

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.     

Effects of temperature and ethanol on agonist and antagonist binding to rat heart muscarinic receptors in the absence and presence of GTP.

2 alpha-Cyanoprogesterone (I) and 2-hydroxymethyleneprogesterone (II) were synthesized and screened as irreversible active-site-directed inhibitors of the delta 5-3-oxosteroid isomerase (EC 5.3.3.1) from Pseudomonas testosteroni. Both compounds were found to inhibit the purified bacterial enzyme in a time-dependent manner. In either case the inactivated enzyme could be dialysed without return of activity, indicating that a stable covalent bond had formed between the inhibitor and the enzyme. Inactivation mediated by compounds (I) and (II) followed pseudo-first-order kinetics, and at higher inhibitor concentrations saturation was observed. The competitive inhibitor 17 beta-oestradiol offered protection against the inactivation mediated by both compounds, and initial-rate studies indicated that compounds (I) and (II) can also act as competitive inhibitors yielding Ki values identical with those generated during inactivation experiments. 2 alpha-Cyanoprogesterone (I) and 2-hydroxymethyleneprogesterone (II) thus appear to be active-site-directed. To compare the reactivity of these 2-substituted progesterones with other irreversible inhibitors of the isomerase, 3 beta-spiro-oxiranyl-5 alpha-pregnan-20 beta-ol (III) was synthesized as the C21 analogue of 3 beta-spiro-oxiranyl-5 alpha-androstan-17 beta-ol, which is a potent inactivator of the isomerase [Pollack, Kayser & Bevins (1979) Biochem. Biophys. Res. Commun. 91, 783-790]. Comparison of the bimolecular rate constants for inactivation (k+3/Ki) mediated by compounds (I)-(III) indicated the following order of reactivity: (III) greater than (II) greater than (I). 2-Mercaptoethanol offers complete protection against the inactivation of the isomerase mediated by 2 alpha-cyanoprogesterone (I). Under the conditions of inactivation compound (I) appears to be completely stable, and no evidence could be obtained for enolate ion formation in the presence or absence of enzyme. It is suggested that cyanoprogesterone inactivates the isomerase after direct nucleophilic attack at the electropositive 2-position, and that tautomerization plays no role in the inactivation event. By contrast, 2-mercaptoethanol offers no protection against the inactivation mediated by 2-hydroxymethyleneprogesterone, and under the conditions of inactivation this compound appears to exist in the semi-enolized form.     

Inactivation of delta 5-3-oxo steroid isomerase with active-site-directed acetylenic steroids.

Several steroid analogues containing conjugated acetylenic ketone groups as part of a seco-ring structure or as substituents on the intact steroid system are irreversible inhibitors of delta 5-3-oxo steroid isomerase (EC 5.3.3.1) from Pseudomonas testosteroni. Thus 10 beta-(1-oxoprop-2-ynyl)oestr-4-ene-3,17-dione (I), 5,10-seco-oestr-4-yne-3,10,17-trione (II), 17 beta-hydroxy-5,10-seco-oestr-4-yne-3,10-dione (III) and 17 beta-(1-oxoprop-2-ynyl)androst-4-en-3-one (IV) irreversibly inactivate isomerase in a time-dependent manner. In all cases saturation kinetics are observed. Protection against inactivation is afforded by the powerful competitive inhibitor 19-nortestosterone. The inhibition constants (Ki) for 19-nortestosterone obtained from such experiments are in good agreement with those determined from conventional competitive-inhibition studies of enzyme activity. These compounds thus appear to be active-site directed. In every case the inactivated enzyme could be dialysed without return of activity, indicating that a stable covalent bond probably had formed between the steroid and enzyme. Compound (I) is a very potent inhibitor of isomerase [Ki = 66.0 microM and k+2 = 12.5 x 10(-3) s-1 (where Ki is the dissociation constant of the reversible enzyme-inhibitor complex and k+2 is the rate constant for the inactivation reaction of the enzyme-inhibitor complex)] giving half-lives of inactivation of 30-45 s at saturation. It is argued that the basic-amino-acid residue that abstracts the intramolecularly transferred 4 beta-proton in the reaction mechanism could form a Michael-addition product with compound (I). In contrast, although compound (IV) has a lower inhibition constant (Ki = 14.5 microM), it is a relatively poor alkylating agent (k+2 = 0.13 x 10(-3) s-1). If the conjugated acetylenic ketone groups are replaced by alpha-hydroxyacetylene groups, the resultant analogues of steroids (I)-(IV) are reversible competitive inhibitors with Ki values in the range 27-350 microM. The enzyme binds steroids in the C19 series with functionalized acetylenic substituents at C-17 in preference to steroids in the C18 series bearing similar groups in the ring structure or as C-10 substituents. In the 5,10-seco-steroid series the presence of hydroxy groups at both C-3 and C-17 is deleterious to binding by the enzyme.     

Inhibition and inactivation of horseradish peroxidase by thiourea

The kinetics of horseradish peroxidase (EC 1.11.1.7)-catalyzed oxidation of o-dianisidine by hydrogen peroxide in the presence of thiourea were studied. At the first, fast step of this process thiourea acts as a competitive reversible inhibitor with respect to o-dianisidine (Ki = 0.22 mM). The formation of a thiourea-peroxidase complex was determined by the increase in the absorbance at A495 and A638 of the enzyme. The dissociation constant for the peroxidase-thiourea complex is equal to 2.0-2.7 mM. Thiourea is not a specific substrate of peroxidase during the oxidation reaction by H2O2, but is an oxidase substrate (although not a very active one) of peroxidase. The irreversible inactivation of the enzyme during its incubation with thiourea was studied. The first-order inactivation rate constant (kin) was shown to increase with a fall in the enzyme concentration. The curve of the dependence of kin on the initial concentration of thiourea shows a maximum at 5-7 mM. The enzyme inactivation is due to its modification by intermediate free radical products of thiourea oxidation. The inhibitors of the free radical reactions (o-dianisidine) protect the enzyme against inactivation. The degree of inactivation depends on concentrations and ratio of thiourea and peroxidase. A possible mechanism of peroxidase interaction with thiourea is discussed.     

Studies on the Alkylation of Choline Acetyltransferase by Choline Mustard Aziridinium Ion

Although a potent irreversible inhibitor of high-affinity choline transport in rat brain synaptosomes, choline mustard aziridinium ion (ChM Az) appeared to be a relatively weak inhibitor of choline acetyltransferase (ChAT) in rat brain homogenates, and evidence for irreversible binding of this compound to the enzyme had not been established. Accordingly, the irreversible inactivation of partially purified rat brain ChAT by ChM Az was studied. This compound is a rather weak inhibitor of the enzyme, with 50% inhibition of ChAT activity achieved following 30 min incubation at 37 degrees C with 0.6 mM ChM Az. This result indicates that although ChM Az has affinity for many nucleophiles there was little diluting effect of the inhibitor in the crude brain homogenate which could be attributed to such reactions (50% inhibition caused by 1.8 mM ChM Az following 10 min incubation). Although the initial binding of ChM Az to ChAT may be of a competitive nature, irreversible bond formation resulted. The time-dependent alkylation reaction conformed to pseudo-first-order kinetics with an observed forward rate constant (kobs) of 0.173 min-1; the half-time (t 1/2) for irreversible binding was about 4 min. The irreversible inactivation of ChAT by ChM Az would appear to be slower than the alkylation of high-affinity choline carriers in synaptosomes by this compound, and the relatively weak inhibitory action of ChM Az against either partially purified ChAT or ChAT activity in crude rat brain homogenates is in striking contrast to previous evidence that ChAT in intact synaptosomes was inhibited irreversibly by lower concentrations of the inhibitor.     

Hydrodynamic properties of porin isolated from outer membranes of rat liver mitochondria

The reaction of gamma-glutamyltranspeptidase with phenobarbital or with thiobarbituric acid resulted in a irreversible loss of its enzymatic activity. The inactivation followed pseudo-first-order kinetics. Half-maximal velocity of inactivation (Ki) at 37 degrees C in the presence of phenobarbital or thiobarbituric acid was calculated to be 43 mM and 20 mM, respectively. The inactivation of the enzyme activity by both these inhibitors was prevented by serine borate, a known competitive inhibitor, and by the substrate, reduced glutathione, suggesting an active-site-directed nature of the these inhibitors. Maleate provided slight protection against inactivation by thiobarbituric acid. Complete inactivation of the enzyme with tritium-labeled phenobarbital resulted in a stoichiometric incorporation of radioactivity into the enzyme protein. Upon sodium dodecyl sulfate polyacrylamide gel electrophoresis of tritium-labeled phenobarbital-enzyme complex, nearly all the radioactivity was found to be associated with the small subunit (Mr = 22 000) of the enzyme, indicating that the catalytic component of the enzyme is on the small subunits.     

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.     

In vivo significance of kinetic constants of protein proteinase inhibitors

We describe the in vivo significance of the kinetic parameters which characterize the interaction between proteinases and protein proteinase inhibitors. Knowledge of the second-order association rate constant kass and in vivo inhibitor concentration allows the calculation of the delay time of inhibition, i.e., the time required for complete inhibition of a proteinase in vivo. The influence of biological substrates on the delay time is also analyzed. The extent of substrate breakdown during the delay time of inhibition may be computed from the various constants describing the proteinase/substrate/inhibitor interactions and the biological concentrations of proteinase and inhibitor. The in vivo partition of a proteinase between two inhibitors may be calculated if the kinetic parameters are known. We define a stability time for enzyme-inhibitor complexes as a minimal time during which the complexes may be considered as stable. This time is related to kdiss the dissociation rate constant of the reversible enzyme-inhibitor complex or to k, the breakdown rate constant of the complex formed with temporary inhibitors. The overall stability of the complex depends upon the ratio between the inhibitor concentration and Ki, the equilibrium dissociation constant of the complex. If this ratio is higher than 1000, a reversible inhibitor behaves like an irreversible one in vivo whatever the enzyme concentration.     

An affinity label for the regulatory dithiol of ribulose-5-phosphate kinase from maize (Zea mays).

Ribulose-5-phosphate kinase from maize (Zea mays) can exist in either a reduced, active form or an oxidized, inactive form. Reduced ribulose-5-phosphate kinase is rapidly and irreversibly inactivated by the dichlorotriazine dye Reactive Red 1 (Procion Red MX-2B), but the irreversible inactivation of the oxidized form of ribulose-5-phosphate kinase occurs at only 0.05% of this rate. The rate of inactivation of the reduced enzyme by Reactive Red 1 (apparent bimolecular rate constant 10(4)M-1 X s-1 at pH 7.4 and 25 degrees C) is several orders of magnitude greater than previous estimates of the rates of dye-mediated inactivation of other enzymes. The dye-dependent inactivation of the reduced enzyme is inhibited by Hg2+ or p-mercuribenzoate (thiol reagents that reversibly inhibit ribulose-5-phosphate kinase activity), or by ATP and ADP, the nucleotide substrates of the enzyme. Hydrolysed Reactive Red 1, which does not inactivate the enzyme, is a reversible inhibitor of ribulose-5-phosphate kinase. This inhibition is competitive with respect to ATP (Ki approximately 0.5 mM). The dye appears to act as an affinity label for the ATP/ADP-binding site by preferentially arylating a thiol residue generated during the reductive activation of the enzyme that is achieved by dithiothreitol or thioredoxin in vitro or during illumination of leaves.     

Affinity labeling of bovine adrenal 3 beta-hydroxysteroid dehydrogenase/steroid isomerase by 5'-[p-(fluorosulfonyl)benzoyl]adenosine

Incubation of bovine adrenal 3 beta-hydroxysteroid dehydrogenase/steroid isomerase with 5'-[p-(fluorosulfonyl)benzoyl]adenosine (5'-FSBA) results in the inactivation of the 3 beta-hydroxysteroid dehydrogenase enzyme activity following pseudo-first-order kinetics. A double-reciprocal plot of 1/kobs versus 1/[5'-FSBA] yields a straight line with a positive y intercept, indicative of reversible binding of the inhibitor prior to an irreversible inactivation reaction. The dissociation constant (Kd) for the initial reversible enzyme-inhibitor complex is estimated at 0.533 mM, with k2 = 0.22 min-1. The irreversible inactivation could be prevented by the presence of NAD+ during the incubation, indicating that 5'-FSBA inactivates the 3 beta-hydroxysteroid dehydrogenase activity by reacting at the NAD+ binding site. Although the enzyme was inactivated by incubation with 5'-FSBA, no incorporation of the inhibitor was found in labeling studies using 5'-[p-(fluorosulfonyl)benzoyl] [14C]adenosine. However, the inactivation of 3 beta-hydroxysteroid dehydrogenase activity caused by incubation with 5'-FSBA could be completely reversed by the addition of dithiothreitol. This indicates the presence of at least two cysteine residues at or in the vicinity of the NAD+ binding site, which may form a disulfide bond catalyzed by the presence of 5'-FSBA. The intramolecular cysteine disulfide bridge was found between the cysteine residues in the peptides 274EWGFCLDSR282 and 18IICLLVEEK26, by comparing the [14C]iodoacetic acid labeling before and after recovering the enzyme activity upon the addition of dithiothreitol.