Two types of rate-determining step in chemical and biochemical processes.

Close examination of the concept of the rate-determining step (RDS) shows that there are two types of RDS depending on the definition of 'rate'. One is represented by the highest peak of the free-energy diagram of consecutive reactions and holds true where the rate is defined in terms of the concentration of the first reactant. The other is represented by the peak showing the maximum free-energy difference, where the free-energy difference is the height of a peak measured from the bottom of any preceding troughs, where the definition of the rate is in terms of the total reactant concentration including intermediates. There are no criteria a priori for selecting one of them.     

Kinetics of inactivation of beta-lactamase I by 6 beta-bromopenicillanic acid.

The kinetics of the inactivation of beta-lactamase I from Bacillus cereus 569 by preparations of 6 alpha-bromopenicillanic acid showed unexpected features. These can be quantitatively accounted for on the basis of the inactivator being the epimer, 6 beta-bromopenicillanic acid. At pH 9.2, the rate-determining step in the inactivation is the formation of the inactivator. When pure 6 beta-bromopenicillanic acid is used to inactivate beta-lactamase I, simple second-order kinetics are observed. The inactivated enzyme has a new absorption peak at 326 nm. The rate constant for inactivation has the same value as the rate constant for appearance of absorption at 326 nm; the rate-determining step may thus be fission of the beta-lactam ring of 6 beta-bromopenicillanic acid. Inactivation is slower in the presence of substrate, and the observed kinetics can be quantitatively accounted for on a simple competitive model. The results strongly suggest that inactivation is a consequence of reaction at the active site.     

One-electron oxidation of Trolox C (a vitamin E analogue) by peroxidases

The oxidation mechanism of Trolox C (a vitamin E analogue) by peroxidases was examined by stopped flow and ESR techniques. The results revealed that during the oxidation of Trolox C, peroxidase Compound II was the catalytic intermediate. The rate constants for the reaction of Compound II with Trolox C, which should be the rate-determining step, were estimated to be 2.1 X 10(4) and 7.2 X 10(3) M-1.s-1 for horseradish peroxidase and lactoperoxidase, respectively, at pH 6.0. The formation of the Trolox C radical was followed by ESR. The time course of the signal was similar to that of the optical absorbance changes at 440 nm, assigned as the peak of the Trolox C radical. The signal exhibited a hyperfine structure characteristic of phenoxyl radicals. From an estimation of the radical concentration in the steady state and the velocity of the radical formation, the dismutation constant was calculated to be 5 X 10(5) M-1.s-1. The concentration of the signal in the steady state was reduced by the addition of GSH. The spectrum changed from that of the Trolox C radical to that of the ascorbate radical when the reaction was carried out in the presence of ascorbate.     

Transient kinetic and deuterium isotope effect studies on the catalytic mechanism of phosphoglycerate dehydrogenase.

The catalytic mechanism of the phosphoglycerate dehydrogenase reaction in both directions was investigated by studying: (a) pre-steady state transients in reduced coenzyme appearance or disappearance or disappearance and in protein fluorescence; (b) deuterium isotope effects on the transients and on the steady state reactions; and (c) the partial reaction between the enzyme-NADH complex and hydroxypyruvate-P. These studies led to the scheme below for the ternary complex interconversion. E1-NADH-hydroxypyruvate-P(1)equilibriumE2-NADH-hydroxypyruvate-P(2)equilibriumE3-NADH-hydroxypyruvate-P + H+(3)equilibriumE3-NAD+-3-phosphoglycerate(4)equilibriumE4-NAD+-3-phosphoglycerate Steps 1,2, and 4 are ternary complex isomerizations. Step 3 is the hydride transfer. Under steady state conditions isomerization 2 is the rate-determining step in the direction of hydroxypyruvate-P reduction at higher pH values. At lower pH values, the hydride transfer step is also partially rate-determining. The rate-determining step in the direction of 3-phosphoglycerate oxidation occurs subsequent to the hydride transfer step at higher pH values. At lower pH values the rate is determined by both isomerization 4 and the hydride transfer step. Isomerizations 1, 2, and 4 were inhibited by serine, an allosteric inhibitor, indicating that the inactive conformation of the enzyme is incapable of performing any of the steps of the ternary complex interconversion. Phosphoglycerate dehydrogenase corresponds to a V-type allosteric enzyme. When the enzyme-NADH complex was mixed with hydroxypyruvate-P at pH 8.5, a rapid quenching of enzymebound NADH fluorescence occurred. This process was studied under pseudo-first order conditions and shown to be the result of hydroxypyruvate-P binding.     

Kinetics of the hydrolysis of cellobiose and p-nitrophenyl-beta-D-glucoside by cellobiase of Trichoderma viride.

Cellobiase has been isolated from the crude cellulase mixture of enzymes of Trichoderma viride using column chromatographic and ion-exchange methods. The steady-state kinetics of the hydrolysis of cellobiose have been investigated as a function of cellobiose and glucose concentrations, pH of the solution, temperature, and dielectric constant, using isopropanol-buffer mixtures. The results show that (i) there is a marked activation of the reaction by initial glucose concentrations of 4 X 10(-3) M to 9 X 10(-2) M and strong inhibition of the reaction at higher initial concentrations, (ii) the log rate -pH curve has a maximum at pH 5.2 and enzyme pK values of 3.5 and 6.8, (iii) the energy of activation at pH 5.1 is 10.2 kcal mol-1 over the temperature range 5-56 degrees C, and (iv) the rate decreases from 0 to 20% (v/v) isopropanol. The hydrolysis by cellobiase (EC 3.2.1.21) of p-nitrophenyl-beta-D-glucoside was examined by pre-steady-state methods in which [enzyme]0 greater than [substrate]0, and by steady-state methods as a function of pH and temperature. The results show (i) a value for k2 of 21 S-1 at pH 7.0 (where k2 is the rate constant for the second step in the assumed two-intermediate mechanism (formula: see text), (ii) a log rate -pH curve, significantly different from that for hydrolysis of cellobiose, in which the rate increases with decreasing pH below pH 4.5, is constant in the region pH 4.5-6, and decreases above pH 6 (exhibiting an enzyme pK value of 7.3), and (iii) an activation energy of 12.5 kcal mol-1 at pH 5.7 over the temperature range 10-60 degrees C.     

The mechanism of binding of L-serine to tryptophan synthase from Escherichia coli

The mechanism of binding of L-serine to tryptophan synthase, which is the initial phase of the catalytic mechanism, has been studied by steady-state and stopped-flow kinetic techniques. The dependence of three separable rate processes on the concentration of L-serine is compatible with four different enzyme-substrate complexes, one of which lies on a branch in the pathway. By use of L-serine deuterated at the alpha carbon, it is possible to assign the deprotonation of the external aldimine of L-serine with pyridoxal 5'-phosphate to the most rapid observable binding step. Measurements at two pH values show that the rate-determining step in the synthesis of L-tryptophan changes from release of L-tryptophan at the optimal pH of 7.6 to the binding of L-serine at pH 6.5. Measurements at pH 7.6 in the presence of the substrate analogue indolepropanol phosphate show that the stronger binding of L-serine is probably due to stabilization of the catalytically competent enzyme--L-serine complex. At pH 7.6 L-serine is bound far more slowly to the beta 2 subunit than to the alpha 2 beta 2 complex of tryptophan synthase and retains its alpha carbon proton. For the beta 2 subunit, the rate-determining step of tryptophan synthesis is deprotonation of bound L-serine. The effect of bound alpha subunit is to increase both the rate of deprotonation and beta-elimination, shifting the rate-limiting step to the release of L-tryptophan.     

Rate-determining step of Escherichia coli alkaline phosphatase altered by the removal of a positive charge at the active center

Escherichia coli alkaline phosphatase catalyzes both the nonspecific hydrolysis of phosphomonoesters and a transphosphorylation reaction in which phosphate is transferred to an alcohol via a phosphoseryl intermediate. The rate-determining step for the wild-type enzyme is pH dependent. At alkaline pH, release of the product phosphate from the noncovalent enzyme-phosphate complex determines the reaction rate, whereas at acidic pH hydrolysis of the covalent enzyme-phosphate complex controls the reaction rate. When the lysine at position 328 was substituted with a cysteine (K328C), the rate-determining step at pH 8.0 of the mutant enzyme was altered so that hydrolysis of the covalent intermediate became limiting rather than phosphate release. The transphosphorylation activity of the K328C enzyme was selectively enhanced, while the hydrolysis activity was reduced compared to that of the wild-type enzyme. The ratio of the transphosphorylation to the hydrolysis activities increased 28-fold for the K328C enzyme in comparison with the wild-type enzyme. Several other mutant enzymes for which a positive charge at the active center is removed by site-specific mutagenesis share this characteristic of the K328C enzyme. These results suggest that the positive charge at position 328 is at least partially responsible for maintaining the balance between the hydrolysis and transphosphorylation activities and plays an important role in determining the rate-limiting step of E. coli alkaline phosphatase.     

Identification and characterization of tyrosyl radical formation in Mycobacterium tuberculosis catalase-peroxidase (KatG)

The catalytic function of Mycobacterium tuberculosis catalase-peroxidase (KatG) and its role in activation of the anti-tuberculosis antibiotic isoniazid were investigated using rapid freeze-quench electron paramagnetic resonance (RFQ-EPR) experiments. The reaction of KatG with peroxyacetic acid was followed as a function of time using x-band EPR at 77 K. A doublet EPR signal appears within 6.4 ms after mixing and at time points through hundreds of milliseconds. Thereafter, a singlet signal develops and finally predominates after 1 s, with a total yield of radical approximately 0.5 spin/heme. Simulation of the spectra provided EPR parameters consistent with those for tyrosyl radicals. Changes in the hyperfine splitting and/or line width in spectra for l-3,3-[2H2]tyrosine-labeled, but not l-2,4,5,6,7-[2H5]tryptophan-labeled KatG confirmed this assignment. The initial rate of radical formation was unchanged using a 3-fold or 10-fold excess of peroxyacetic acid, consistent with a rate-determining step involving an intermediate. Although Compound I is likely to be the precursor of tyrosyl radical in KatG, neither its EPR signal nor its reduction to Compound II during formation of the radical(s) could be observed. The tyrosyl radical doublet signal was rapidly quenched by addition of isoniazid and benzoic hydrazide, but not by iproniazid, which binds poorly to KatG.     

The kinetics of the alkaline dissociation of myosin.

The rates of two processes in alkaline (pH 10.5–11.5) myosin solutions at 0 °C have been investigated: production of ionized tyrosine residues and production of light subunits. The progressive absorbance change is shown to result from a first-order irrevocable exposure to solvent and subsequent ionization of 40% of the tyrosine residues. Extrapolation to zero time gives the spectrophotometric ionization curve for native myosin; the pK of the abnormal tyrosines exceeds 12. Similarly, extrapolation to infinite time gives the curve for denatured myosin; the pK of the normal tyrosines (and of all tyrosines after denaturation) is 11.0–11.6. From the pH dependence of the rate, it is found that activation requires ionization of six residues and that their pK is much greater than 11.3. The rate of production of subunits was determined by fractionating the reaction mixture and determining the weight of light subunits produced. The process is also first order. Within experimental error, the rate constants for these two processes are equal. We conclude that they have the same rate-determining step. The data are consistent with either of two simple possible mechanisms. These are a rapid conformation change, followed by rate-determining subunit dissociation, followed by a rapid, irrevocable conformation change; or, a rapid conformation change, followed by a rate-determining, irrevocable conformation change, followed by rapid subunit dissociation.     

On the oxidation of alkyl and aryl sulfides by [(Me3TACN)MnO(OH)2]: A density functional study

Density functional theory suggests that the formal 2-electron oxidation of sulfides, RR′S, to sulfoxides, by the model Mn^VO catalyst, [(TACN)Mn^V O(OH)₂]⁺, proceeds in two quite distinct 1-electron steps. Transfer of the first electron is barrierless and generates a sulfur radical cation, antiferromagnetically coupled to a Mn^IV centre via a covalent μ-oxo bridge. The second electron-transfer step is accompanied by migration of the oxygen atom to the sulfur centre, and is rate-determining. The absence of a barrier in the first step, where a sulfur radical is formed, means that the presence of electron-donating or withdrawing substituents on the sulfide has only a minor impact on the rate of reaction.     

Fundamental relationships for the effect of proton dissociation equilibria on enzymic reaction steps

Relationships have been derived which describe the pH dependence contributed to rate and equilibrium constants for an arbitrary enzymic reaction step by the ionization of an enzymic group or non-enzymic reactant when both protonation states of the ionizing species are assumed to participate in the catalytic reaction.     

Spontaneous electrical potential oscillation on a filter impregnated with soybean lecithin placed between identical solutions of alanine

Filters impregnated with soybean lecithin, placed between two identical aqueous alanine solutions, display spontaneous electric potential oscillations. Alanine solutions used in a large concentration range from 1 mM to 1 M produce damped oscillatory behaviour with an exponential decay in time. The dependence of decay time on concentration shows saturation behaviour which is well fitted with a sigmoidal curve. Power spectra obtained by Fourier transform show peaks specific for each concentration. When fitted with a Lorentzian curve in the peak domain, the centre of the peak height and width at half height could be extracted. All these parameters depend on alanine concentration in a saturating pattern.     

Carbon isotope effects on the decarboxylation of carboxylic acids. Comparison of the lactate oxidase reaction and the degradation of pyruvate by H2O2.

The isotope effect at C-1 on the H2O2-catalysed decarboxylation of pyruvate (used as a model reaction for the enzymic reaction) increases between pH 3 and 10 from 1.0007 +/- 0.0004 to 1.0283 +/- 0.0014 (25 degrees C). This result indicates a change in the rate-determining step from formation of the tetrahedral intermediate to decarboxylation of this intermediate. Practically no isotope fractionation at C-1 (1.0011 +/- 0.0002, pH 6.0, 25 degrees C) is found in the lactate oxidase-catalysed decarboxylation of lactate, which is indicative for the existence of an irreversible O2-dependent step prior to the enzyme-catalysed decarboxylation. In addition, the result provides further evidence that dissociation of pyruvate and H2O2 from the enzyme can be excluded. The isotope effect at C-2 of lactate in the enzymic reaction (1.0048 +/- 0.0004) is attributed to the hydrogen transfer step from lactate to the coenzyme.     

Mechanism of modulation of dopamine beta-monooxygenase by pH and fumarate as deduced from initial rate and primary deuterium isotope effect studies

Dopamine beta-monooxygenase catalyzes a reaction in which 2 mol of protons are consumed for each turnover of substrate. Studies of the pH dependence of initial rate parameters (Vmax and Vmax/Km) and their primary hydrogen isotope effects show that at least two ionizable residues are involved in catalysis. One residue (B1, pK = 5.6-5.8) must be protonated prior to the carbon-hydrogen bond cleavage step, implying a role for general-acid catalysis in substrate activation. A second protonated residue (B2, pK = 5.2-5.4) facilitates, but is not required for, product release. Recent measurement of the intrinsic isotope effect for dopamine beta-monoxygenase [Miller, S. M., & Klinman, J. P. (1983) Biochemistry (preceding paper in this issue)] allows an analysis of the pH dependence of rate constant ratios and in selected instances individual rate constants. We demonstrate large changes in the rate-determining step as well as an unprecedented inversion in the kinetic order of substrate release from ternary complex over an interval of 2 pH units. Previously, fumarate has been used in dopamine beta-monooxygenase assays because of its property of enzyme activation. Studies of the pH behavior in the presence of saturating concentrations of fumarate have shown two causes of the activation: (i) fumarate perturbs the pK of B1 to pK = 6.6-6.8 such that the residue remains protonated and the enzyme optimally active over a wider pH range; (ii) fumarate decreases the rate of dopamine release from the ternary enzyme-substrate complex, increasing the equilibrium association constant for dopamine binding. Both effects are consistent with a simple electrostatic stabilization of bound cationic charges by the dianionic form of fumarate.     

Correlation of kinetic parameters of nitroreductase enzymes with redox properties of nitroaromatic compounds

The well-established mechanism of regeneration of the parent nitro compound by the reaction of the nitro anion radical with oxygen in aerobic systems is the basis of the correlation of kinetic parameters of purified flavoenzymes with electron affinities of some selected nitroaryl and nitroheterocyclic compounds. We have found that there is a linear relationship between log Vmax/Km and the one-electron reduction potentials of these compounds and that the measured values of redox dependence for these compounds is similar to that determined by other methods. Our results support the proposal of a rate-determining single electron-transfer as the initial step in the reduction of nitro compounds by purified flavoenzymes and are discussed in terms of the Marcus electron transfer theory.     

Oxidation of p-cresol by horseradish peroxidase compound I.

Rate constants for the reaction between horseradish peroxidase compound I and p-cresol have been determined at several values of pH between 2.98 and 10.81. These rate constants were used to construct a log (rate) versus pH profile from which it is readily seen that the most reactive form of the enzyme is its most basic form within this pH range so that base catalysis is occurring. At the maximum rate a second order rate constant of (5.1 +/- 0.3) x 10(-7) M-1 s-1 at 25 degrees is obtained. The activation energy of the reaction at the maximum rate was determined from an Arrhenius plot to be 5.0 +/- 0.5 kcal/mol. Evidence for an exception to the generally accepted enzymatic cycle of horseradish peroxidase is presented. One-half molar equivalent of p-cresol can convert compound I quantitatively to compound II at high pH, whereas usually this step requires 1 molar equivalent of reductant. The stoichiometry of this reaction is pH-dependent.     

The resolution of some steps of the reactions of lactate dehydrogenase with its substrates

1. The reaction of pig heart lactate dehydrogenase (EC 1.1.1.27) with NAD(+) and lactate to form pyruvate and NADH was followed by rapid spectrophotometric methods. The distinct spectrum of enzyme-bound NADH permits the measurement of the rate of dissociation of this compound. 2. The reduction of the first mole equivalent of NAD(+) per mole of enzyme sites can also be observed, and is much more rapid than the steady-state rate of NADH production. 3. At pH8 the dissociation of the enzyme-NADH complex is rate-determining for the steady-state oxidation of lactate. At lower pH some other step after the interconversion of the ternary complex and before the dissociation of NADH is rate-determining. Other evidence for a compulsory-order mechanism is provided.     

Rapid-equilibrium rate equations for the enzymatic catalysis of A+B=P+Q over a range of pH

This article shows how pKs for the enzymatic site and enzyme-substrate complexes can be obtained from kinetic experiments on the reaction A+B=P+Q, with and without the consumption of hydrogen ions. The rapid-equilibrium rate equation makes it possible to obtain the pKs and chemical equilibrium constants involved in the mechanism, the apparent equilibrium constant K' for the catalyzed reaction, and the number of hydrogen ions consumed in the rate-determining reaction. Experimentally-determined Michaelis constants can be adjusted for the pKs of the substrates A, B, P, and Q so that it is easier to obtain the pKs of E, EA, EB, EAB, EQ, and EPQ, and the chemical equilibrium constants. Reaction rates are discussed for the forward reaction ordered A+B=ordered P+Q with zero, one, or two hydrogen ions consumed in the rate-determining reaction and for random A+B=ordered P+Q with zero, one, or two hydrogen ions consumed in the rate-determining reaction. When hydrogen ions are consumed in the rate-determining reaction, there is a new factor 10(n)(pH) in the rate equation, where n is the number of hydrogen ions consumed in the rate-determining reaction for the forward reaction. The integer n can be obtained from rate measurements over a range of pH, but it cannot be determined from thermodynamic measurements.     

Reaction of Desulfovibrio vulgaris two-iron superoxide reductase with superoxide: insights from stopped-flow spectrophotometry

Stopped-flow mixing of the Desulfovibrio vulgaris two-iron superoxide reductase (2Fe-SOR) containing the ferrous active site with superoxide generates a dead time intermediate whose absorption spectrum is identical to that of a putative ferric-hydroperoxo intermediate previously observed by pulse radiolysis. The dead time intermediate is shown to be a product of reaction with superoxide and to be generated at a much higher proportion of active sites than by pulse radiolysis. This intermediate decays smoothly to the resting ferric active site ( approximately 30 s-1 at 2 degrees C and pH 7) with no other detectable intermediates. Deuterium isotope effects demonstrate that solvent proton donation occurs in the rate-determining step of dead time intermediate decay and that neither of the conserved pocket residues, Glu47 or Lys48, functions as a rate-determining proton donor between pH 6 and pH 8. Fluoride, formate, azide, and phosphate accelerate decay of the dead time intermediate and for azide or fluoride lead directly to ferric-azido or -fluoro complexes of the active site, which inhibit Glu47 ligation. A solvent deuterium isotope effect is observed for the azide-accelerated decay, and the decay rate constants are proportional to the concentrations and pKa values of HX (X- = F-, HCO2-, N3-). These data indicate that the protonated forms of the anions function analogously to solvent as general acids in the rate-determining step. The results support the notion that the ferrous SOR site reacts with superoxide by an inner sphere process, leading directly to the ferric-hydroperoxo intermediate, and demonstrate that the decay of this intermediate is subject to both specific- and general-acid catalysis.     

Rearrangement of L-2-hydroxyglutarate to L-threo-3-methylmalate catalyzed by adenosylcobalamin-dependent glutamate mutase

Adenosylcobalamin-dependent enzymes catalyze a variety of chemically difficult isomerizations in which a nonacidic hydrogen on one carbon is interchanged with an electron-withdrawing group on an adjacent carbon. We describe a new isomerization, that of L-2-hydroxyglutarate to L-threo-3-methylmalate, involving the migration of the carbinol carbon. This reaction is catalyzed by glutamate mutase, but k(cat) = 0.05 s(-)(1) is much lower than that for the natural substrate, L-glutamate (k(cat) = 5.6 s(-)(1)). EPR spectroscopy confirms that the major organic radical that accumulates on the enzyme is the C-4 radical of L-2-hydroxyglutarate. Pre-steady-state kinetic measurements revealed that L-2-hydroxyglutarate-induced homolysis of AdoCbl occurs very rapidly, with a rate constant approaching those measured previously with glutamate and methylaspartate as substrates. These observations are consistent with the rearrangement of the 2-hydroxyglutaryl radical being the rate-determining step in the reaction. The slow rearrangement of the 2-hydroxyglutaryl radical can be attributed to the poor stabilization by the hydroxyl group of the migrating glycolyl moiety of the radical transiently formed on the migrating carbon. In contrast, with the normal substrate the migrating carbon atom bears a nitrogen substituent that better stabilizes the analogous glycyl moiety. These studies point to the importance of the functional groups attached to the migrating carbon in facilitating the carbon skeleton rearrangement.