Kinetics of binding of bovine trypsin-killikrein inhibitor (K unitz) in which the reactive-site peptide bond Lys-15--Ala-16 is cleaved, to alpha-chymotrypsin and beta-trypsin.

Equilibrium measurements of the binding of reactive-site-cleaved (modified) bovine trypsin-kallikrein inhibitor (Kunitz) to alpha-chymotrypsin and beta-trypsin show a stoichiometric 1:1 association with high binding constants. At least in the case of chymotrypsin much evidence is presented that the reaction with modified inhibitor leads to the same complex as the reaction with virgin inhibitor does. The association rate constant of modified inhibitor with chymotrypsin at pH 7, 22.5 degrees C is 15.8 M-1 S-1. This is about 2 x 10(4) times slower than the binding of virgin inhibitor to that enzyme. In the analogous reaction of modified inhibitor with beta-trypsin, however, the association rate constant (1.2 x 10(4) M-1 s-1 at pH 6.9, 22.5 degrees C) is of about the same order of magnitude as it is in the reaction of virgin inhibitor and trypsin. These and analogous phenomena observed in the reactions of virgin and modified soybean trypsin inhibitor (Kunitz) with alpha-chymotrypsin and beta-trypsin suggest that the specificity of both inhibitors to trypsin is strongly reflected in the association rate constants of the modified forms. The dissociation rate constants of the complexes of trypsin-kallikrein inhibitor with chymotrypsin or with trypsin towards the modified inhibitor are estimated to be unmeasurably slow (half-life times of 45 or 1.5 x 10(4) years, respectively).     

Wild-type enzyme as a reporter of inhibitor binding by catalytically impaired mutant enzymes.

A method for the determination of inhibition constants for catalytically-debilitated mutant enzymes is described. The inhibitor is partitioned between the mutant and wild-type enzymes. Catalytic rates of the wild-type enzyme are used as the signal of inhibitor binding to the mutant enzyme. The method is validated with scytalone dehydratase, the Y50F mutant, and a potent inhibitor. The K(i) value for Y50F determined by this method is 0.49 +/- 0.10 nM. The K(i) value determined using the Y50F catalytic report for inhibitor binding in the absence of wild-type enzyme is 0.20 +/- 0.030 nM. The wild-type enzyme binds the inhibitor ten-fold less tightly, thus indicating that the hydrogen-bonding interaction between the Y50 hydroxyl group and the inhibitor (suggested by X-ray crystallography) is weak. The method is most useful when the catalytic activity of the wild-type enzyme is the most sensitive report of inhibitor binding and the mutant enzyme is greatly crippled in catalytic activity.     

Methotrexate, a high-affinity pseudosubstrate of dihydrofolate reductase.

Investigations have been made of the slow, tight-binding inhibition by methotrexate of the reaction catalyzed by dihydrofolate reductase from Streptococcus faecium A. Quantitative analysis has shown that progress curve data are in accord with a mechanism that involves the rapid formation of an enzyme-NADPH-methotrexate complex that subsequently undergoes a relatively slow, reversible isomerization reaction. From the Ki value for the dissociation of methotrexate from the E-NADPH-methotrexate complex (23 nM) and values of 5.1 and 0.013 min-1 for the forward and reverse rate constants of the isomerization reaction, the overall inhibition constant for methotrexate was calculated to be 58 pM. The formation of an enzyme-methotrexate complex was demonstrated by means of fluorescence quenching, and a value of 0.36 muM was determined for its dissociation constant. The same technique was used to determine dissociation constants for the reaction of methotrexate with the E-NADP and E-NADPH complexes. The results indicate that in the presence of either NADPH or NADP there is enhancement of the binding of methotrexate to the enzyme. It is proposed that methotrexate behaves as a pseudosubstrate for dihydrofolate reductase.     

Determining RuBisCO activation kinetics and other rate and equilibrium constants by simultaneous multiple non-linear regression of a kinetic model

The forward and reverse rate constants involved in carbamylation, activation, carboxylation, and inhibition of D-ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO) have been estimated by a new technique of simultaneous non-linear regression of a differential equation kinetic model to multiple experimental data. Parameters predicted by the model fitted to data from purified spinach enzyme in vitro included binding affinity constants for non-substrate CO2 and Mg2+ of 200+/-80 microM and 700+/-200 microM, respectively, as well as a turnover number (k(cat)) of 3.3+/-0.5 s(-1), a Michaelis half-saturation constant for carboxylation (K(M,C)) of 10+/-4 microM and a Michaelis constant for RuBP binding (K(M,RuBP)) of 1.5+/-0.5 microM. These and other constants agree well with previously measured values where they exist. The model is then used to show that slow inactivation of RuBisCO (fallover) in oxygen-free conditions at low concentrations of CO2 and Mg2+ is due to decarbamylation and binding of RuBP to uncarbamylated enzyme. In spite of RuBP binding more tightly to uncarbamylated enzyme than to the activated form, RuBisCO is activated at high concentrations of CO2 and Mg2+. This apparent paradox is resolved by considering activation kinetics and the fact that while RuBP binds tightly but slowly to uncarbamylated enzyme, it binds fast and loosely to activated enzyme. This modelling technique is presented as a new method for determining multiple kinetic data simultaneously from a limited experimental data set. The method can be used to compare the properties of RuBisCO from different species quickly and easily.     

Role of aspartate 27 in the binding of methotrexate to dihydrofolate reductase from Escherichia coli

Dihydrofolate reductase from wild-type Escherichia coli (WT-ECDHFR) and from a mutant enzyme in which aspartate 27 is replaced by asparagine have been compared with respect to the binding of the inhibitor methotrexate (MTX). Although the Asp27----Asn substitution causes only small changes in the association rate constants (kon) for the formation of binary and ternary (with NADPH) complexes, the dissociation rate constants for these complexes (koff) are increased for the mutant enzyme by factors of about 5- and 100-fold, respectively, at pH 7.65. In binding experiments, the initial MTX binary and ternary complexes of the mutant enzyme were found to undergo relatively rapid isomerization (kobs approximately 17 and 145 s-1, respectively). Although such rapid isomerization of complexes of WT-ECDHFR could not be detected in binding experiments, evidence of a slow isomerization (k = 4 x 10(-3) s-1) of the ternary WT-ECDHFR.MTX.NADPH complex was obtained from progress of inhibition experiments. This slow isomerization increases binding of MTX to WT-ECDHFR only 2.4-fold (much less than previously estimated). From presently available data, we could not determine the contribution of the rapid isomerization of complexes to the binding of MTX to the mutant enzyme. The Asp27----Asn substitution increases the overall dissociation constant (KD) 9-fold for the binary complex and 85-fold for the ternary complex. When it is also taken into account that a proton ultimately derived from the solvent must be added to MTX bound to the WT enzyme, but not to MTX bound to the mutant enzyme, these increases in KD for the mutant enzyme correspond to decreases in binding energy for MTX of 3.9 and 5.2 kcal/mol at pH 7.65 for the binary and ternary complexes, respectively.     

Role of isomerization of initial complexes in the binding of inhibitors to dihydrofolate reductase

Stopped-flow measurements of protein fluorescence quenching when methotrexate (MTX) binds to dihydrofolate reductase (isoenzyme II) of Streptococcus faecium (SFDHFR II) analyze as the sum of two differentials: a rapid binding phase and a second phase for which the observed rate constant is independent of methotrexate concentration. Analysis of variation of the ratio of the amplitude of the fast and slow phases with methotrexate concentration indicates that the second phase is an isomerization of the initial binary complex. At pH 7.3, the equilibrium constant for this isomerization is 21.9, and the forward and reverse rate constants are 0.57 and 0.026 s-1, respectively. Similar results were obtained for binding of 3-deazamethotrexate to SFDHFR II, but the forward rate constant is greater (2.9 s-1 at pH 7.3). The equilibrium constants for these isomerizations are pH independent, but the rate constants decrease as the pH is raised, probably due to deprotonation of one or more groups on the enzyme. Analysis of progress curves obtained by the development of inhibition when SFDHFR II is added last to reaction mixtures containing dihydrofolate, NADPH, and MTX gives an association constant for initial reactions of 4.3 X 10(7) M-1. Since a preliminary estimate of the association constant for the binding reaction is 7.6 X 10(5) M-1, this suggests an isomerization of the ternary complex(es) with an equilibrium constant of about 56. In addition, analysis of the progress of development of inhibition indicates a further very slow isomerization with equilibrium constant 419 and forward rate constant 2.6 min-1.(ABSTRACT TRUNCATED AT 250 WORDS)     

Kinetics of complexing activation by the magnesium ion on green crab (Scylla serrata) alkaline phosphatase.

As with mammalian enzymes, green crab (Scylla serrata) alkaline phosphatase can be activated by Mg2+ through a time-dependent course. The activation is mainly a Vmax effect. Tsou's method was used to study the kinetic course of activation. The results show that the enzyme was activated by a complexing scheme that had not been previously identified: the enzyme first reversibly and quickly binds Mg2+ and then undergoes a slow reversible course to activation, with a relatively high activation energy (78 +/- 4 kJ/mol) and a slow conformational change. The activation reaction is a single molecule reaction, and the apparent activation rate constant is independent of Mg2+ concentration if the concentration is sufficiently high. The microscopic rate constants of activation and the association constant were determined from the measurements. The proposed scheme may also be applied to the Mg2+ activation mechanism for mammalian enzyme, to explain why the activation rate is time-dependent and not diffusion controlled. Substrate binding was also shown to affect the activation rate constant.     

Elementary steps in the reaction mechanism of chicken liver fatty acid synthase. pH dependence of NADPH binding and isotope rate effect for beta-ketoacyl reductase

The stopped flow method has been used to determine the pH dependence of the kinetics of the binding of NADPH to chicken liver fatty acid synthase over the pH range 6.0-8.5. The kinetics is consistent with a one-step binding mechanism, and the pH dependence of the second order rate constant indicates that an ionizable group either on the enzyme or on NADPH with a pK alpha of 6.1 is of importance in the binding process. The isotope rate effects have been determined for the steady state reaction with (S)- and (R)-[4-2H] NADPH as substrates and are very small. The pH dependence of the rate constant characterizing the reduction of acetoacetyl by NADPH on the enzyme (beta-ketoacyl reductase) and the isotope rate effects on this constant with (S)-[4-2H]NADPH as substrate also have been measured with the stopped flow method. A small pH-dependent isotope rate effect is found; these results suggest hydride transfer is not rate limiting for the beta-ketoacyl reductase reaction on the enzyme surface. The pH dependence of this rate constant is bell shaped and is very similar to that of the turnover number for the overall reaction; this suggests that the beta-ketoacyl reductase reaction may be partially rate limiting for the overall reaction when the enzyme is saturated with substrates.     

Inhibition kinetics of green crab (Scylla serrata) alkaline phosphatase activity by dithiothreitol or 2-mercaptoethanol

Green crab (Scylla serrata) alkaline phosphatase (EC 3.1.3.1) is a metalloenzyme which catalyzes the nonspecific hydrolysis of phosphate monoesters. Some pollutants in seawater affect the enzyme activity causing loss of the biological function of the enzyme, which affects the exuviating crab-shell and threatens the survival of the animal. The present paper studies the effects of thiohydroxyal compounds on the activity of green crab alkaline phosphatase. The results show that thiohydroxyal compounds can lead to reversible inhibition. The equilibrium constants have been determined for dithiothreitol (DTT) and mercaptoethanol (ME) binding with the enzyme and/or the enzyme-substrate complexes. The results show that both DTT and ME are non-competitive inhibitors. The kinetics of enzyme inactivation by ME at low concentrations has been studied using the kinetic method of the substrate reaction. The results suggest that at pH 10.0, the action of ME on green crab ALP is first quick equilibrium binding and then slow inactivation. The microscopic rate constants were determined for inactivation and reactivation. The rate constant of the forward inactivation (k(+0)) is much larger than that of the reverse reactivation (k(-0)). Therefore, when the ME concentration is sufficiently large, the enzyme is completely inactivated.     

Catalytic properties and active-site structural features of immobilized horse liver alcohol dehydrogenase

Alcohol dehydrogenase from horse liver was immobilized by covalent attachment to CNBr-Sepharose and by adsorption to octyl-Sepharose CL-4B, a hydrophobic analog of Sepharose. In each case, rate constants for the binding and release of coenzyme and for the oxidation of substrates were measured based on the concentration of accessible active-site zinc atoms determined by titration with a paramagnetic inhibitor. All rate constants were substantially reduced upon immobilization; however, the rate constant of immobilized enzyme for ethanol oxidation was independent of the immobilization method, whereas the rate constant for cyclohexanol oxidation was lower for enzyme immobilized to octyl-Sepharose. Consequently, the substrate specificity of the two immobilized enzyme samples differed by an order of magnitude. Moreover, EPR spectroscopy studies and computer graphic analyses of spin labels occupying three defined regions of the active-site domain indicated that the active-site conformation adjacent to the catalytic zinc atom was similar in the two samples while the conformation slightly further from the zinc atom was different. This result may explain why the two immobilized enzyme preparations exhibited the same rate constant toward a small substrate (ethanol) yet different rate constants toward a larger substrate (cyclohexanol), whose rate constant is expected to be sensitive to a larger portion of the active site.     

Ionization states of the complex formed between 2-benzyl-3-phosphonopropionic acid and carboxypeptidase A.

The binding to carboxypeptidase A of two phosphonic acid analogues of 2-benzylsuccinate, 2-DL-2-benzyl-3-phosphonopropionic acid (inhibitor I) and 2-DL-2-benzyl-3-(-O-ethylphosphono)propionic acid (inhibitor II) was studied by observing their 31P resonances when free and bound to the enzyme in the range of pH from 5 to 10. The binding of I by co-ordination to the active-site Zn(II) lowered the highest pKa of I from a value of 7.66(+/- 0.10) to a value of 6.71(+/- 0.17). No titration of any protons on II occurred over the pH range studied. The enzyme-bound inhibitor II also did not titrate over the pH range 6.17-7.60. The pH-dependencies of the apparent inhibition constants for I and II were also investigated by using N-(-2-(furanacryloyl)-L-phenylalanyl-L-phenylalanine as substrate. Two enzymic functional groups with pKa values of 5.90(+/- 0.06) and 9.79(+/- 0.14) must be protonated for binding of inhibitor I, and two groups with pKa values of 6.29(+/- 0.10) and 9.19(+/- 0.15) for binding of inhibitor II. Over the pH range from 6.71 to 7.66, inhibitor I binds to the enzyme in a complex of the enzyme in a more protonated form, and the inhibitor in a less protonated form than the predominant unligated forms at this pH. Mock & Tsay [(1986) Biochemistry 25, 2920-2927] made a similar finding for the binding of L-2-(1-carboxy-2-phenylethyl)-4-phenylazophenol over a pH range of nearly 4 units. The true inhibition constant for the dianionic form of inhibitor I (racemic) was calculated to be 54.0(+/- 5.9) nM and that of the trianionic form to be 5.92(+/- 0.65) nM. The true inhibition constant of the fully ionized II (racemic) was calculated to be 79.8(+/- 6.4) nM.     

Possible role for water dissociation in the slow binding of phosphorus-containing transition-state-analogue inhibitors of thermolysin

A number of phosphonamidate and phosphonate tripeptide analogues have been studied as transition-state-analogue inhibitors of the zinc endopeptidase thermolysin. Those with the form Cbz-GlyP(Y)Leu-X [ZGP(Y)LX, X = NH2 or amino acid, Y = NH or O linkage] are potent (Ki = 9-760 nM for X = NH, 9-660 microM for X = O) but otherwise ordinary in their binding behavior, with second-order rate constants for association (kon) greater than 10(5) M-1 s-1. Those with the form Cbz-XP(Y)-Leu-Ala [ZXP(Y)LA,XP = alpha-substituted phosphorus amino acid analogue] are similarly potent (Ki for ZFPLA = 68 pM) but slow binding (kon less than or equal to 1300 M-1 s-1). Several kinetic mechanisms for slow binding behavior are considered, including two-step processes and those that require prior isomerization of inhibitor or enzyme to a rare form. The association rates of ZFPLA and ZFP(O)LA are first order in inhibitor concentration up to 1-2 mM, indicating that any loose complex along the binding pathway must have a dissociation constant above this value. The crystallographic investigation described in the preceding paper [Holden, H. M., Tronrud, D. E., Monzingo, A. F., Weaver, L. H., & Matthews, B. W. (1987) Biochemistry (preceding paper in this issue)] identifies a specific water molecule in the active site that may hinder binding of the alpha-substituted inhibitors. The implication of this observation for a mechanism for slow binding is discussed.     

Kinetics of Chemical Modification of Arginine Residues in Mitochondrial Creatine Kinase from Bovine Heart: Evidence for Negative Cooperativity

The kinetics of chemical modification of arginine residues in mitochondrial creatine kinase (mit-CK) from beef heart by 4-hydroxy-3-nitrophenylglyoxal (HNPG) have been studied with simultaneous registration of enzyme inactivation. Experiments showed that complete inactivation of mit-CK corresponded to modification of two arginine residues per mit-CK monomer. The data on the modification kinetics can be described by the sum of two exponential terms and suggest strong negative cooperativity in the binding of HNPG to arginine residues. The rate constants for the fast and slow phases of modification differ by a factor of about 50. The corresponding rate constants for inactivation differ by a factor of about 30. The rate constant for the slow stage of inactivation is twice as large as that for the rate constant for the slow stage of modification, i.e., the inactivation process is ahead of the modification process.     

Inhibition kinetics of green crab (Scylla serrata) alkaline phosphatase by zinc ions: a new type of complexing inhibition

The Tsou method was used to study the kinetic course of inactivation of green crab alkaline phosphatase by zinc ions. The results show that the enzyme was inactivated by a complexing scheme which has not been previously identified. The enzyme first reversibly and quickly binds Zn(2+) and then undergoes a slow reversible course to inactivation and slow conformational change. The inactivation reaction is a single molecule reaction and the apparent inactivation rate constant is for a saturated reaction being independent of Zn(2+) concentration if the concentration is sufficiently high. The microscopic rate constants of inactivation and the association constant were determined from the measurements.     

Interaction of Asp. melleus Semi-alkaline protease with benzeneboronic acid.

Benzeneboronic acid (BBA), a possible transition-state analog for serine proteases, was found to inhibit Asp. melleus semi-alkaline protease [EC 3.4.21.15]. The pH dependence of inhibitor constants was studied by the pH-stat method using N-acetyl-L-tyrosine ethyl ester as a substrate at 25 degrees C. From the pH dependence of the association constant (reciprocal inhibitor constant), a pK value of 6.6, which may be attributable to the catalytic histidine residue of the enzyme, was estimated. The BBA-enzyme interaction was studied kinetically by the temperature-jump method. Apparent association and dissociation rate constants were determined at pH 6.5.     

Horse liver alcohol dehydrogenase. A study of the essential lysine residue.

1. The inactivation of horse liver alcohol dehydrogenase by pyridoxal 5'-phosphate in phosphate buffer, pH8, at 10 degrees C was investigated. Activity declines to a minimum value determined by the pyridoxal 5'-phosphate concentration. The maximum inactivation in a single treatment is 75%. This limit appears to be set by the ratio of the first-order rate constants for interconversion of inactive covalently modified enzyme and a readily dissociable non-covalent enzyme-modifier complex. 2. Reactivation was virtually complete on 150-fold dilution: first-order analysis yielded an estimate of the rate constant (0.164min-1), which was then used in the kinetic analysis of the forward inactivation reaction. This provided estimates for the rate constant for conversion of non-covalent complex into inactive enzyme (0.465 min-1) and the dissociation constant of the non-covalent complex (2.8 mM). From the two first-order constants, the minimum attainable activity in a single cycle of treatment may be calculated as 24.5%, very close to the observed value. 3. Successive cycles of modification followed by reduction with NaBH4 each decreased activity by the same fraction, so that three cycles with 3.6 mM-pyridoxal 5'-phosphate decreased specific activity to about 1% of the original value. The absorption spectrum of the enzyme thus treated indicated incorporation of 2-3 mol of pyridoxal 5'-phosphate per mol of subunit, covalently bonded to lysine residues. 4. NAD+ and NADH protected the enzyme completely against inactivation by pyridoxal 5'-phosphate, but ethanol and acetaldehyde were without effect. 5. Pyridoxal 5'-phosphate used as an inhibitor in steady-state experiments, rather than as an inactivator, was non-competitive with respect to both NADH and acetaldehyde. 6. The partially modified enzyme (74% inactive) showed unaltered apparent Km values for NAD+ and ethanol, indicating that modified enzyme is completely inactive, and that the residual activity is due to enzyme that has not been covalently modified. 7. Activation by methylation with formaldehyde was confirmed, but this treatment does not prevent subsequent inactivation with pyridoxal 5'-phosphate. Presumably different lysine residues are involved. 8. It is likely that the essential lysine residue modified by pyridoxal 5'-phosphate is involved either in binding the coenzymes or in the catalytic step. 9. Less detailed studies of yeast alcohol dehydrogenase suggest that this enzyme also possesses an essential lysine residue.     

Circular dichroism and fluorescence studies on the binding of ligands to the alpha subunit of tryptophan synthase.

Binding to the alpha subunit of tryptophan synthase induces extrinsic Cotton effects in the substrates indole (IND), indoleglycerol phosphate (IGP), and D-glyceraldehyde-3-P (D-GAP) and in the inhibitor indolepropanol phosphate (IPP). These effects disappear when the enzyme is denatured in guanidinium chloride. The induced circular dichroism (CD) was used to determine the dissociation constant and the number of binding sites for IPP. The dissociation constant so determined is equal to 48 muM and is in good agreement with the value of 48 muM obtained by equilibrium dialysis. From the temperature dependence of the dissociation constant, a value of -2.8 kcal/mol for the binding enthalpy was obtained. The determination of dissociation constants by means of extrinsic Cotton effects is shown to be quite feasible. CD competition experiments with glycerol phosphate (GP) suggest that IPP binds bifunctionally to the enzyme: via its indole part and its phosphate group. Indolepropanol, which lacks the phosphate group, does not show an extrinsic Cotton effect. Since the induced CD is strongly dependent on the binding geometry, the close similarity between the induced spectra in IPP and IGP is additional evidence that IPP is a good substrate analog. Binding to the enzyme results in a blue shift of the IPP fluorescence emission maximum. The dissociation constant determined by fluorescence titration equals 46 muM and agrees well with the values determined by the other two methods. Previous biochemical and fast kinetic studies suggested the existence of multiple conformational states for the enzyme and of ligand-induced conformational changes. No evidence was found in the far-uv CD spectra for conformational changes upon binding of IND and D-GAP. For IPP a very small effect was observed.     

General method for exact evaluation of parameters of the elementary steps of coupled reactions. Invariant analysis.

A general method has been devised for the exact evaluation of the rate constants of the elementary steps of a system consisting of any number of coupled reactions. The method is independent of the structure of the network of coupled steps. The precision of the data evaluation is solely dependent on the quality of the detection unit. The application of the method is illustrated with data collected for the binding of the competitive inhibitor proflavine to chymotrypsin under such conditions that five states of the enzyme are required to interpret the results. In the absence of a substance possessing the binding specificity, the enzyme is present as an equilibrium between an active and an inactive conformer. The latter prevails. The binding of the specific inhibitor releases a slow proton transfer from the medium to the alpha-amino group of Ile-16. Subsequently, the enzyme-inhibitor (or enzyme-substrate) complex re-arranges to the catalytically active form, which is retained until the supply of specific substrate is exhausted. The control features described are general, but are particularly conspicuous under the special environmental conditions used here. A comparison between data for alpha- and delta-forms of chymotrypsin showed that the chain ends of the former impeded the substrate binding and that the activity controlling conformational change occurred in the interior of the enzyme molecule.     

Methods of determining rate constants in single-substrate–single-product enzyme reactions. Use of induced transport: limitations of product inhibition

1. The calculation of the rate constants from steady-state kinetics of a single-substrate-single-product enzyme reaction in which there is an isomerization of the enzyme is described. 2. It is shown that even with the use of isotopically labelled substrates a set of solutions for the constants is obtained rather than a unique solution. However, limits are derived within which they must lie. 3. The most appropriate observations to determine the rate constants are measurements of V(max.) and K(m) for both substrate and product, and measurement of the degree of countertransport in an induced-transport test. 4. Experimental procedures for induced-transport tests and the quantitative interpretation of the results obtained are discussed. 5. Product inhibition is shown to be an ambiguous and imprecise means of determining the rate constants. Further, the absence of a [substrate]x[product] term in the denominator of the steady-state rate equation does not necessarily mean that the isomerization of the enzyme is rapid, since the term also disappears when the isomerization is very slow. 6. Similar considerations apply to carrier mechanisms.