Kinetic parameters for the elimination reaction catalyzed by triosephosphate isomerase and an estimation of the reaction's physiological significance

Kinetic parameters for triosephosphate isomerase catalysis of the elimination reaction of an equilibrium mixture of dihydroxyacetone phosphate (DHAP) and D-glyceraldehyde-3-phosphate (DGAP) to form methylglyoxal and phosphate ion are reported for the enzyme from rabbit muscle. Pseudo-first-order rate constants for the disappearance of substrate (kelim) were determined for reactions at [Enzyme] much greater than [Substrate]. The second-order rate constant kEnz = 10.1 M-1 s-1 was determined from a plot of kelim against enzyme concentration. The kinetic parameters, determined from a steady-state kinetic analysis at [Substrate] much greater than [Enzyme], are kcat = 0.011 s-1, Km = 0.76 mM, and kcat/Km = 14 M-1 s-1. The estimated rate-constant ratio for partitioning of the enzyme-bound intermediate between protonation at carbon 2 and elimination, 1,000,000, is much larger than the ratio of 6.5 determined for the reaction of the enediolate phosphate in a loose complex with quinuclidinonium cation, a small buffer catalyst. There is a 10(5)-10(8)-fold decrease in the rate constant for the elimination reaction of the enediolate phosphate when this species binds to triosephosphate isomerase. The kinetic parameters for the elimination reaction catalyzed by the native triosephosphate isomerase and for the reaction catalyzed by a mutant form of the enzyme, which is missing a segment that forms hydrogen bonds with the phosphate group of substrate [Pompliano, D. L., Peyman, A., & Knowles, J. R. (1990) Biochemistry 29, 3186-3194] are similar.(ABSTRACT TRUNCATED AT 250 WORDS)     

A kinetic study of cyclic adenosine 3':5'-monophosphate binding and mode of activation of protein kinase from Drosophila melanogaster embryos.

Cyclic AMP-dependent protein kinase and its regulatory subunit were isolated from Drosophila melanogaster embryos. The profiles of cyclic AMP binding by these proteins were significantly different. In order to explain such a difference and to find the mode of enzyme activation by cyclic AMP, a kinetic study of cyclic AMP binding was carried out. First, the association rate constant k1 and dissociation rate constant k-1 in the cyclic AMP-regulatory subunit interaction at 0 degrees C were estimated to be 2.3 X 10(6)M-1s-1 and 1.1 X 10(-3)s-1, respectively. Secondly, the three possible modes of enzyme activation by cyclic AMP were mathematically considered and could be described by a unique formula: r=APt + BQt (A + B=1) in which the parameters A, B, P, and Q are equivalent to rate constants in the sense that the rate constants are simply expressed by these parameters. Thirdly, the values of the parameters and subsequently the values of rate constants involved in the possible mechanisms were evaluated using a curve-fitting technique and compared with experimental observation. It was then found that the following mechanism was the only one which fitted the experimental observations. Namely, RC + L k3 equilibrium k-3 LRC k4 equilibrium k-4 RL + C where R, C, and L represent the regulatory and catalytic subunits and cyclic AMP as a ligand. Thus, our results indicate that in the presence of cyclic AMP the active enzyme (C) is released from a ternary intermediate which is the primary product of the cyclic AMP-holoenzyme interaction. The estimated values of the rate constants are: k3=3.5 X 10(6)M-1s-1;k-3=7.3 X 10(-1)s-1;and k4=3.8 X 10(-2)s. These estimates indicate that the reaction LRC leads to RL + C is relatively slow and limits the rate of the overall reaction. By comparing k-3 and k4, it is apparent that a large part of newly formed ternary intermediate reverts to the holoenzyme.     

Acetylcholine receptor-controlled ion translocation caused by phenyltrimethylammonium and nereistoxin: simple estimation of equilibrium constants of the minimal model

The rate of slow Li+ influx and the fraction of active form of acetylcholine receptor (AChR) of Electrophorus electricus membrane vesicles at equilibrium between the active and desensitized forms of the receptor were measured in the presence of various concentrations of phenyltrimethylammonium (PTA) and nereistoxin (NTX), by a simple filtration assay and flame emission spectroscopy. The equilibrium constants of these ligands in the minimal model, which accounts for the AChR-mediated ion flux, were estimated simply from these two measurements, since the equilibrium constants for acetylcholine (ACh) and carbamylcholine (Carb) estimated from two kinetic measurements agreed well with those estimated from five sophisticated kinetic measurements of AChR-mediated ion fluxes. PTA showed high potency but not high efficacy, and showed inhibition when large doses were applied. NTX showed both low potency and low efficacy and acted as an inhibitor when it was added with Carb. The apparent dissociation constants of these three agonists evaluated from the minimal model and the equilibrium constants agreed with those obtained by assay of inhibition of radiolabeled ligand binding.     

Substrate specificity and stereoselectivity of horse liver alcohol dehydrogenase. Kinetic evaluation of binding and activation parameters controlling the catalytic cycles of unbranched, acyclic secondary alcohols and ketones as substrates of the native and active-site-specific Co(II)-substituted enzyme

1. The steady-state parameters kcat and Km and the rate constants of hydride transfer for the substrates isopropanol/acetone; (S)-2-butanol, (R)-2-butanol/2-butanone; (S)-2-pentanol, (R)-2-pentanol/2-pentanone; 3-pentanol/3-pentanone; (S)-2-octanol and (R)-2-octanol have been determined for the native Zn(II)-containing horse-liver alcohol dehydrogenase (LADH) and the specific active-site-substituted Co(II)LADH. 2. A combined evaluation of steady-state kinetic data and rate constants obtained from stopped-flow measurements, allowed the determination of all rate constants of the following ordered bi-bi mechanism: E in equilibrium E.NAD in equilibrium E.NAD.R1R2 CHOH in equilibrium E.NADH.R1R2CO in equilibrium E.NADH in equilibrium E. 3. On the basis of the different substrate specificities of LADH and yeast alcohol dehydrogenase (YADH), a procedure has been developed to evaluate the enantiomeric product composition of ketone reductions. 2-Butanone and 2-pentanone reductions revealed (S)-2-butanol (86%) and (S)-2-pentanol (95%) as the major products. 4. The observed enantioselectivity implies the existence of two productive ternary complexes; E.NADH.(pro-S) 2-butanone and E.NADH.(pro-R) 2-butanone. All rate constants describing the kinetic pathways of the system (S)-2-butanol, (R)-2-butanol/2-butanone have been determined. These data have been used to estimate the expected enantiomer product composition of 2-butanone reductions using apparent kcat/Km values for the two different ternary-complex configurations of 2-butanone. Additionally, these data have been used for computer simulations of the corresponding reaction cycles. Calculated, simulated and experimental data were found to be in good agreement. Thus, the system (S)-2-butanol, (R)-2-butanol/2-butanone is the first example of a LADH-catalyzed reaction for which the stereochemical course could be described in terms of rate constants of the underlying mechanism. 5. The effects of Co(II) substitution on the different steps of the kinetic pathway have been investigated. The free energy of activation is higher for alcohol oxidation and lower for ketone reduction when catalyzed by Co(II)LADH in comparison to Zn(II)LADH. However, the free energies of binding are affected by metal substitution in such a way that the enantioselectivity of ketone reduction is not significantly changed by the substitution of Co(II) for Zn(II). 6. Evaluation of the data shows that substrate specificity and stereoselectivity result from combination of the free energies of binding and activation, with differences in binding energies as the dominating factors. In this regard, the interactions of substrate molecules with the protein moiety are dominant over the interactions with the catalytic metal ion.     

Relations between biochemical thermodynamics and biochemical kinetics

The parameters in steady-state or rapid-equilibrium rate equations for enzyme-catalyzed reactions depend on the temperature, pH, and ionic strength, and may depend on the concentrations of specific species in the buffer. When the complete rate equation (i.e. the equation with parameters for the reverse reaction as well as the forward reaction) is determined, there are one or more Haldane relations between some of the kinetic parameters and the apparent equilibrium constant for the reaction that is catalyzed. When the apparent equilibrium constant can be calculated from the kinetic parameters, the equilibrium composition can be calculated. This is remarkable because the kinetic parameters all depend on the properties of the enzymatic site, but the apparent equilibrium constant and the equilibrium composition do not. The effects of ionic strength and pH on the unoccupied enzymatic site and the occupied enzymatic site have to cancel in the Haldane relation or in the calculation of the apparent equilibrium constant using the rate constants for the steps in the mechanism. Several simple enzymatic mechanisms and their complete rate equations are discussed.     

Understanding glucose transport by the bacterial phosphoenolpyruvate:glycose phosphotransferase system on the basis of kinetic measurements in vitro

The kinetic parameters in vitro of the components of the phosphoenolpyruvate:glycose phosphotransferase system (PTS) in enteric bacteria were collected. To address the issue of whether the behavior in vivo of the PTS can be understood in terms of these enzyme kinetics, a detailed kinetic model was constructed. Each overall phosphotransfer reaction was separated into two elementary reactions, the first entailing association of the phosphoryl donor and acceptor into a complex and the second entailing dissociation of the complex into dephosphorylated donor and phosphorylated acceptor. Literature data on the K(m) values and association constants of PTS proteins for their substrates, as well as equilibrium and rate constants for the overall phosphotransfer reactions, were related to the rate constants of the elementary steps in a set of equations; the rate constants could be calculated by solving these equations simultaneously. No kinetic parameters were fitted. As calculated by the model, the kinetic parameter values in vitro could describe experimental results in vivo when varying each of the PTS protein concentrations individually while keeping the other protein concentrations constant. Using the same kinetic constants, but adjusting the protein concentrations in the model to those present in cell-free extracts, the model could reproduce experiments in vitro analyzing the dependence of the flux on the total PTS protein concentration. For modeling conditions in vivo it was crucial that the PTS protein concentrations be implemented at their high in vivo values. The model suggests a new interpretation of results hitherto not understood; in vivo, the major fraction of the PTS proteins may exist as complexes with other PTS proteins or boundary metabolites, whereas in vitro, the fraction of complexed proteins is much smaller.     

Parameter estimation for ligand binding systems kinetics applied to 1,25-dihydroxycholecalciferol

A mathematical analysis of the kinetics of the hormone-receptor interaction was applied to the 1,25-dihydroxycholecalciferol-intestinal receptor system. The exact analytical solution and the numerical integration of the kinetic equation were installed in a Statistical Analysis System (SAS) computer program to estimate the rate constants of the reaction. Estimates of the parameters obtained by these two methods are similar, demonstrating that the numerical integration can be combined with the nonlinear regression procedure for least-squares parameter fitting using a simple SAS program. This enables estimation of kinetics rate constants when the kinetic equation cannot be solved analytically. The ratio of the rate constants (ka/kd) found by the nonlinear procedure is close to the independently determined equilibrium (Scatchard) constant in the nonlinear analysis.     

Kinetic Analysis of Ligand-Receptor Association Data that Display An Overshoot Phenomenon

Abstract

A binding overshoot was frequently observed in the time course of association of diazepam with rat brain membrane receptors shortly after the start of the interaction. Such time profiles most likely reflect the “receptor switch” mechanism, assuming an equilibrium between two forms of a receptor (R and R*) that possess different affinities to the ligand (L) in question. Similar effects could be caused by the presence of a slowly dissociating competitor. The kinetics of these mechanisms were verified by simulation of theoretical time courses. A computer program for simulation of the time course, and estimation of rate constants of the individual reaction steps, was developed and is described in this communication. It employs the Euler-Cauchy integration for simulation of theoretical time courses. Optimised estimates of the rate constants were computed by simultaneous random variation of parameters within a pre-set interval. Stable solutions can be obtained for this system, thus enabling evaluation of equilibrium constants defined by the model. The source code is available in Turbo-Pascal. It can be used, after re-writing the rate equations, for fitting of similar kinetic models to suitable experimental data.     

Mechanism of bovine liver S-adenosylhomocysteine hydrolase. Steady-state and pre-steady-state kinetic analysis

The kinetic mechanism of S-adenosylhomocysteine hydrolase was investigated by stopped-flow spectrofluorometry at pH 7.0 and 25 degrees C. Pre-steady-state kinetic steps were identified with chemical steps proposed for the mechanism of this enzyme (Palmer, J.L., and Abeles, R.H. (1979) J. Biol. Chem. 254, 1217-1226). The steady-state kinetic constants for the hydrolysis or synthesis of S-adenosylhomocysteine were in good agreement with those values calculated from the pre-steady-state rate constants. The equilibrium constant for dehydration of 3'-ketoadenosine to 3'-keto-4',5'-dehydroadenosine on the enzyme was 3. The analogous equilibrium constant for addition of L-homocysteine to S-3'-keto-4',5'-dehydroadenosylhomocysteine on the enzyme was 0.3. The elimination of H2O from adenosine in solution had an equilibrium constant of 1.4 (aH2O = 1). Thus, the equilibrium constants for these elimination reactions on the enzyme were probably not perturbed significantly from those in solution. The equilibrium constant for the reduction of enzyme-bound NAD+ by adenosine was 8, and the analogous constant for the reduction of the enzyme by S-adenosylhomocysteine was 4. The equilibrium constant for the reduction of NAD+ by a secondary alcohol in solution was 5 x 10(-5) at pH 7.0. Consequently, the reduction of enzyme-bound NAD+ by adenosine was 10(5)-fold more favorable than the reduction of free NAD+. The magnitude of the first-order rate constants for the interconversion of enzyme-bound intermediates varied over a relatively small range (3-80 s-1). Similarly, the magnitude of the equilibrium constants among enzyme-bound intermediates varied over a narrow range (0.3-10). These results were consistent with the overall reversibility of the reaction.     

Requirements for reliable determination of binding affinity constants by kinetic approach

The nonspecific binding (equilibrium coefficient kn) of ligand (L) and/or the incomplete recovery (alpha < 1) of the receptor-ligand (RL) complex in binding measurements, could hamper accurate determination of the association and dissociation rate constants of the R/L system. For the simplest model of R/L interaction, characterized by a bimolecular association process (rate constant k1) and a monomolecular dissociation process (rate constant k2), the consequences of kn and/or alpha neglect on k1 and k2 determination were investigated. Various situations that are especially relevant for k1 determination, were examined in which nonspecific binding was: (i) negligible relative to specific binding, or (ii) developed progressively or very rapidly in association kinetics. When only the initial kinetic phase was used, according to the situation (i.e. the nonspecific binding characteristics, and the fact that kn and/or alpha were or were not taken into account to correct the binding measurements), k1 could be accurately determined or generally slightly overestimated or slightly underestimated (in the two latter cases by factors involving mainly kn and/or alpha but not the R concentration or the R/L equilibrium association constant, K), whereas k2 should always be fairly well estimated. Consequently, for the simplest R/L systems, the k1/k2 ratio derived from such kinetic experiments should be much less susceptible to substantial underestimation than K derived from R saturation experiments [Borgna, J. Steroid Biochem. Mol. Biol. (2004)]. Kinetic experiments could also be more appropriate than R saturation experiments to detect cooperative--positive or negative--binding of L to R.     

Kinetics and mechanism of hydrolysis of acetylthiocholine by butyrylcholine esterase

Kinetics and mechanism of hydrolysis of acetylthiocholine by the enzyme butyrylcholine esterase was studied. The spectrophotometric Ellman's method and potentiometric pH-stat method were used for continuous determination of the actual concentration of the products thiocholine and acetic acid in the reaction mixture. The validity of the Michaelis-Menten (Briggs-Haldane) equation in the whole course of the reaction under used conditions was proved. The corresponding kinetics parameters (Vm and KM) were calculated from the obtained dependences of concentration of thiocholine or acetic acid vs. time and compared. From this comparison the deciding kinetic role of the step producing thiocholine was derived. The values of initial molar concentration of the enzyme and of the rate constants of the kinetic model were estimated.     

Allosteric regulation of rat testis mitochondrial aldehyde dehydrogenase by capronaldehyde and magnesium ion.

1. The influence of Mg2+ on the kinetic behaviour of mitochondrial aldehyde dehydrogenase from rat testis has been investigated using capronaldehyde as substrate. 2. The kinetic data, obtained by numerical analysis of the progress curves of aldehyde oxidation, were fitted to a modified version of the Monod-Wyman-Changeux model and the fitting procedure resulted in a good correspondence between theoretical and experimental reaction rates over a wide range of capronaldehyde and Mg2+ concentrations. 3. According to the model, the tetrameric enzyme is in equilibrium between two conformational states R and T which display comparable affinities for capronaldehyde (the dissociation constants are 0.17 and 0.3 microM, respectively), but different catalytic power (VT = 2VR). The T state can bind with lower affinity a second molecule of aldehyde (K = 2.5 microM). 4. Mg2+ stabilizes the T state (the dissociation constants for the R and T states are 2.2 and 0.12 mM, respectively) and acts as a strong activator of the R state, but as a weak inhibitor of the T state. In the absence of substrates and Mg2+, the R<-->T equilibrium favors the R state ([T]/[R] = 0.16). 5. The model is able to predict the kinetic behaviour also when the NAD+ concentrations are not saturating and when inhibitory effects by NADH are taken into account.     

Rate and equilibrium constants for protein unfolding and refolding determined by hydrogen exchange-mass spectrometry

Studies of protein unfolding and refolding may help us understand the more general problem of protein folding. Recent studies from this laboratory demonstrated that the unfolding and refolding of a large protein, rabbit muscle aldolase (M(r) 157 kDa), can be studied by combining amide hydrogen exchange and mass spectrometry. Results of these studies indicated that aldolase has three unfolding domains which likely unfold sequentially. Urea was used to increase the populations of partially unfolded states which were labeled with deuterium following a brief exposure to D(2)O. Electrospray ionization mass spectra of both the intact protein and its peptic fragments had multiple envelopes of isotope peaks from which the populations of unfolded forms were determined. The present study extends the previous investigations to include different urea concentrations and kinetic modeling of data taken as the system approaches equilibrium. Analysis of these results gives rate and equilibrium constants describing the unfolding and refolding processes characteristic of aldolase destabilized in urea. The change in solvent-accessible surface, which has been used as a reaction coordinate for protein folding, is estimated from the dependence of the equilibrium and rate constants on the concentration of urea.     

Reaction rate constants of superoxide scavenging by plant antioxidants

Plant phenols may exert protective effects by scavenging superoxide, which is implicated in tissue damage and accelerated inactivation of vasorelaxing nitric oxide. Preventing the interaction of superoxide with tissue biomolecules depends not only on the extent of superoxide scavenging but also on scavenging velocity. However, information on superoxide scavenging kinetics of plant phenols is scarce. We describe an improved lucigenin-based chemiluminescence assay for kinetic analysis. The use of potassium superoxide (KO₂) as a nonenzymatic superoxide source allowed simple and reliable determination of the second-order reaction rate constants between superoxide and plant antioxidants at physiologically relevant conditions, avoiding unspecific effects of other reactive oxygen species or superoxide-generating enzymes. We calculated the rate constants for phenols of different structures, ranging from 2.9 × 10³ mol⁻¹ l s⁻¹ for morin to 2.9 × 10⁷ mol⁻¹ l s⁻¹ for proanthocyanidins. Compounds with pyrogallol or catechol moieties were revealed as the most rapid superoxide scavengers, and the gallate moiety was found to be the minimal essential structure for maximal reaction rate constants with superoxide.     

Kinetic studies on the enzyme (S)-hydroxynitrile lyase from hevea brasiliensis using initial rate methods and progress curve analysis

(S)-Hydroxynitrile lyase (EC 4.1.2.39) from Hevea brasiliensis(rubber tree) catalyzes the reversible cleavage of cyanohydrins to aldehydes or ketones and prussic acid (HCN). Enzyme kinetics in both directions was studied on a model system with mandelonitrile, benzaldehyde, and HCN using two different methods-initial rate measurements and progress curve analysis. To discriminate between possible mechanisms with the initial rate method, product inhibition was studied. Benzaldehyde acts as a linear competitive inhibitor against mandelonitrile whereas HCN shows S-linear I-parabolic mixed-type inhibition. These results indicate an Ordered Uni Bi mechanism with the formation of a dead-end complex of enzyme, (S)-mandelonitrile and HCN. Prussic acid is the first product released from the enzyme followed by benzaldehyde. For progress curve analysis, a kinetic model of an Ordered Uni Bi mechanism including a dead-end complex, enzyme inactivation, and the chemical parallel reaction was set up, which described the experimental values very well. From the reaction rates obtained the kinetic constants were calculated and compared with the ones obtained from the initial rate method. Good agreement could be achieved between the two methods supporting the suggested mechanism. Copyright 1999 John Wiley & Sons, Inc.     

Mechanism of lectin-cell interactions: thermodynamic and kinetic analysis of the binding of winged bean acidic lectin (WBA II) to human erythrocytes.

In order to identify the forces involved in the binding and to understand the mechanism involved, equilibrium and kinetic studies were performed on the binding of the winged bean acidic lectin to human erythrocytes. The magnitudes of delta S and delta H were positive and negative respectively, an observation differing markedly from the lectin-simple sugar interactions where delta S and delta H are generally negative. Analysis of the sign and magnitudes of these values indicate that ionic and hydrogen bonded interactions prevail over hydrophobic interactions resulting in net -ve delta H (-37.12 kJ.mol-1) and +ve delta S (14.4 J.mole-1 K-1 at 20 degrees C), thereby suggesting that this entropy driven reaction also reflects conformational changes in the lectin and/or the receptor. Presence of two kinds of receptors for WBA II on erythrocytes, as observed by equilibrium studies, is consistent with the biexponential dissociation rate constants (at 20 degrees C K1 = 1.67 x 10(-3) M-1 sec-1 and K2 = 11.1 x 10(-3) M-1 sec-1). These two rate constants differed by an order of magnitude accounting for the difference in the association constants of the two receptors of WBA II. However, the association process remains monoexponential suggesting no observable difference in the association rates of the lectin molecule with both the receptors, under the experimental conditions studied. The thermodynamic parameters calculated from kinetic data correlate well with those observed by equilibrium. A two-step binding mechanism is proposed based on the kinetic parameters for WBA II-receptor interaction.(ABSTRACT TRUNCATED AT 250 WORDS)     

Lipase reaction in AOT-isooctane reversed micelles: effect of water on equilibria

The effect of water on equilibria for hydrolytic reaction in reversed micelles has been investigated using lipase as a model enzyme. The effect of water on equilibria has been ignored for hydrolase reactions in an aqueous phase. In a reversed micellar system, however, the equilibrium of the lipase reaction was changed when water was added during the hydrolytic reaction. Furthermore, equilibrium fractional conversion is affected by the initial water concentration, being shifted to higher values with higher water concentrations, with other reaction conditions being held constant, indicating that the reaction should be regarded as a two-substrate process. Equations corresponding to a two-substrate, second-order reversible model are derived and used for further analysis. The progress curves predicted from the rate equations agree very well with the experimental results under various reaction conditions. The values of the molar ratio of water to surfactant (R) which maximize the initial reaction rate and maximum fractional conversion is predictable from the derived rate equations and the resulting relationship between R and the kinetic constants.