The relationship between steady-state kinetic parameters and equilibrium parameters for one substrate-one product enzymic reactions

This paper discusses two mechanisms for one substrate/one product enzymic reactions:

Although these mechanisms can be distinguished by the use of product inhibition studies (Darvey, 1972), Haldane relationships cannot be used as a further criterion for discriminating between the two mechanisms.Equilibrium parameters are derived for mechanisms I and II in systems where the concentration of substrate and product bound to the enzyme is not negligible in comparison with the concentration of free substrate and product. Relationships between these parameters and the conventional steady-state kinetic parameters provide additional means for distinguishing the two mechanisms.     

Kinetic studies of the choline acetyltransferase reaction using isotope exchange at equilibrium

Isotope exchange at equilibrium has been used to study the kinetic mechanism of the choline acetyltransferase reaction. The choline-acetylcholine, acetyl-CoA-acetylcholine, and CoA-acetyl-CoA exchange patterns are qualitatively consistent with a Theorell-Chance mechanism. However, quantitative differences are observed when the experimental results are compared to theoretical fits of the data for a Theorell-Chance mechanism. It is concluded that the kinetic mechanism of the choline acetyltransferase reaction can best be described as a random Theorell-Chance mechanism in which a low but finite amount of ternary complex exists.     

Isotope exchange at equilibrium indicates a steady state ordered kinetic mechanism for human sulfotransferase

Cytosolic sulfotransferase (SULT)-catalyzed sulfation regulates biosignaling molecular biological activities and detoxifies hydroxyl-containing xenobiotics. The universal sulfuryl group donor for SULTcatalyzed sulfation is adenosine 3'-phosphate 5'-phosphosulfate (PAPS). The reaction products are a sulfated product and adenosine 3',5'-diphosphate (PAP). Although the kinetics has been reported since the 1980s,SULT-catalyzed reaction mechanisms remain unclear. Human SULT1A1 catalyzes the sulfation of xenobiotic phenols and has very broad substrate specificity. It has been recognized as one of the most important phase II drug-metabolizing enzymes. Understanding the kinetic mechanism of this isoform is important in understanding drug metabolism and xenobiotic detoxification. In this report, we investigated the SULT1A1-catalyzed phenol sulfation mechanism. The SULT1A1-catalyzed reaction was brought to equilibrium by varying substrate (1-naphthol) and PAPS initial concentrations. Equilibrium constants were determined. Two isotopic exchanges at equilibrium ([14C]1-naphthol <=>[14C]1-naphthyl sulfate and[35S]PAPS<=>[35S]1-naphthyl sulfate) were conducted. First-order kinetics, observed for all the is otopic exchange reactions studied over the entire time scale that was monitored, indicates that the system was truly at equilibrium prior to addition of an isotopic pulse. Complete suppression of the 35S isotopic exchange rate was observed with an increase in the levels of 1-naphthol and 1-naphthyl sulfate in a constant ratio,while no suppression of the 14C exchange rate was observed with an increase in the levels of PAPS and PAP in a constant ratio. Data are consistent with a steady state ordered kinetic mechanism with PAPS and PAP binding to the free enzyme.     

Analysis of Ter-Ter enzyme kinetic mechanisms by computer simulation of isotope exchange at chemical equilibrium: development and application of ISOTER, a personal-computer-based program

A convenient, personal-computer-based program has been developed that allows simulation of isotopic exchange kinetics at chemical equilibrium catalyzed by a three reactant-three product (TerTer) enzyme system: A + B + C integral of P + Q + R. This program, ISOTER, utilizes a rapid algebraic method to calculate the exchange rate between any reactant-product pair as a function of the substrate concentration and avoids altogether the necessity of deriving an explicit (but cumbersome and impractical) equation for exchange rate. ISOTER was used to generate model saturation patterns for 16 different TerTer kinetic mechanisms, varying different combinations of reactant-product pairs in constant ratio at equilibrium: [all substrates], [A, P], [B, Q], and [C, R], while holding the nonvaried components constant. These model studies indicate that virtually every one of these mechanisms can be distinguished from the others. In addition, ISOTER has been used to fit multiple sets of experimental data for Escherichia coli glutamine synthetase, which produced a set of rate constants consistent with the previously proposed "preferred order random" kinetic mechanism.     

NMR spin exchange kinetics at equilibrium in membrane transport and enzyme systems

A set of differential equations is formulated to describe the rapid exchange (time scale, approximately 0.01 to approximately 10 s) of a labelled solute across the membranes of cells in suspension. The labelling is achieved with nuclear magnetic resonance by exposure of the system to a high intensity radio-frequency pulse, and the excited nuclei relax to the equilibrium state with a short half life. An analytical expression for the decay of the magnetic resonance signal is presented; the solution involves the determination of eigenvalues, of an array of Laplace-Carson transformed differential equations, by use of the general solution of a quartic polynomial. Simulations of the behaviour of the exchange system using various conditions of cell number, rate constants and nuclear magnetic relaxation times are presented. The marked concentration dependence of the extent of reaction at a given time has not previously been reported for nuclear magnetic resonance exchange systems and is a feature anticipated from the known saturability of several membrane transport systems including glucose transport into human erythrocytes. The theory is readily generalized to other model systems by appropriate reinterpretation of the physical meaning of various parameters; the general form of the solution holds in many biological contexts other than membrane transport and includes equilibrium enzyme kinetics.     

Determination of half-reaction equilibrium in a ping-pong enzyme mechanism

Substituted enzyme (or ping-pong) mechanisms usually involve enzymes that exist in two forms that alternate during the catalytic reaction. A method is described here for determining the position of the equilibrium of a half reaction in a ping-pong enzyme mechanism that is based on the kinetics of the burst reaction which occurs upon addition of reactants that recycle the enzyme from one form to another. The theoretical basis for the analysis is developed, and the method is applied to the half reaction of the aldimine form of aspartate transaminase with difluoro-oxaloacetate. Special issue dedicated to Herman Bachelard     

Kinetic mechanism of phosphoenolpyruvate carboxykinase (GTP) from rat liver cytosol. Product inhibition, isotope exchange at equilibrium, and partial reactions

Initial velocity studies of rat liver cytosolic P-enolpyruvate carboxykinase in the direction of P-enolpyruvate formation gave intersecting double reciprocal plots indicating that the reaction conforms to a sequential reaction pathway. A complete product inhibition study with MnGDP-, P-enolpyruvate, and HCO3- as product inhibitors indicated that all patterns were noncompetitive. Isotope exchange at equilibrium with exchange between the substrate/product pairs GTP/GDP oxalacetate/HCO3-, and oxalacetate/P-enolpyruvate while varying the concentration of substrate/product pairs in fixed constant ratio gave no complete inhibitory patterns as the concentration of the constant ratio pairs approached saturation. The exchange rates between the substrate/product pairs differed by a factor of 40 when compared under the same assay conditions. These results were interpreted in terms of a random reaction mechanism in which true dead-end complexes do not form and in which the rate-limiting step is not the interconversion of the ternary quarternary central complexes. In addition to the formation of P-enolpyruvate from oxalacetate and MnGTP2-, the enzyme catalyzes the decarboxylation of oxalacetate to pyruvate in the absence of MnGTP2-. This reaction occurs only slowly in the absence of GDP and most rapidly in the presence of MnGDP-. When only MnGTP2- and oxalacetate are present, no pyruvate is formed, and oxalacetate is converted stoichiometrically to P-enolpyruvate. The enzyme also catalyzes the exchange of [14C]GDP into GTP in the absence of P-enolpyruvate. This exchange is stimulated by the presence of HCO3-. When enzyme is incubated with MnGTP2- in the presence or absence of HCO3-, there is no hydrolysis to form GDP and P1. The two partial reactions, namely the exchange of [14C]GDP with the E.HCO3.MnGTP or E.MnGTP complex and the formation of pyruvate from the E.oxalacetate.MnGDP complex provide pathways by which the expected dead-end complexes can be converted to enzyme forms which can return to the catalytic or exchange sequence.     

Mechanisms of enzyme control as probed by equilibrium exchange rates: patterns of modifier effects with a two substrate, two product system

Measurements of reaction rates at equilibrium by isotopic exchange techniques can give considerable information about the mode of action of modifiers of enzymic reaction rates. To illustrate the various patterns that may be obtained, differing effects of modifiers on the exchange of A with P and of B with Q in the simple enzymic reaction of A + BP + Q are given. For this, reasonable values of rate constants are assumed, and calculations made for random and compulsory binding order systems. Cases where modifiers bind at the catalytic sites of substrate or at other binding sites, and where substrate association, substrate dissociation, covalent interconversion, or total catalytic capacity are modified are considered. Some quite distinctive patterns emerge, among the most interesting being those in which a modifier may block net catalysis yet allow one equilibrium exchange to occur essentially unhindered.     

Kinetics of tracer flows and isotope interaction in an ion exchange membrane

Summary The thermodynamic formulation of isotope interaction (coupling of abundant and tracer isotope flows) has been tested in a highly permselective anion exchange membrane in the absence of significant electroosmosis. A previous study of Cl^– permeation has now been extended to include permeation of I^–, Acetate, and SO ₄ ^2– in different bath concentrations, with the use of both electrical and chemical driving forces. The flux ratios were abnormal according to the usual criteria for simple passive flow, but were closely predicted by the theoretical expression incorporating the influence of isotope interaction. In the absence of coupled flows of other chemical species the extent of isotope interaction can be determined either from the flux ratio or from the measurement of a single unidirectional flux at two settings of the electrochemical potential difference. Direct evidence of negative isotope interaction was presented.     

Preferred order random kinetic mechanism for homoserine dehydrogenase of Escherichia coli (Thr-sensitive) aspartokinase/homoserine dehydrogenase-I: equilibrium isotope exchange kinetics.

Isotope exchange kinetics at chemical equilibrium have been used to investigate the kinetic mechanism of homoserine dehydrogenase (EC 1.1.1.3) of the (Thr-sensitive) aspartokinase/homoserine dehydrogenase-I multifunctional enzyme from E. coli. For the reaction (L-ASA + NADPH + H+ = L-Hse + NADP+), at pH 9.0, 37 degrees C, Keq = 100 (+/- 20). Under these conditions, the rate for exchange of [14C]-L-homoserine (Hse) in equilibrium L-aspartate-beta-semialdehyde (ASA) is nearly twice that for the [3H]-NADP+ in equilibrium NADPH exchange. This indicates that covalent interconversion between reactants and products bound in the active site cannot be rate-limiting. Upon variation of the concentrations of all four substrates in constant ratio at equilibrium (to minimize dead-end complex formation), the Hse in equilibrium ASA exchange increased smoothly toward a maximum. In contrast, the NADP+ in equilibrium NADPH exchange rate increased to a maximum value at partial saturation, then decreased to approximately half the maximum rate. These data are consistent with a preferred-order random kinetic mechanism in which the dominant pathway involves association of NADPH prior to L-ASA and dissociation of L-Hse prior to NADP+.     

Examination of the mechanism of sucrose synthetase by positional isotope exchange

The mechanism of the sucrose synthetase reaction has been probed by the technique of positional isotope exchange. [beta-18O2, alpha beta-18O]UDP-Glc has been synthesized starting from oxygen-18-labeled phosphate and the combined activities of carbamate kinase, hexokinase, phosphoglucomutase, and uridine diphosphoglucose pyrophosphorylase. The oxygen-18 at the alpha beta-bridge position of the labeled UDP-Glc has been shown to cause a 0.014 ppm upfield chemical shift in the 31P NMR spectrum of both the alpha- and beta-phosphorus atoms in UDP-Glc relative to the unlabeled compound. The chemical shift induced by each of the beta-nonbridge oxygen-18 atoms was 0.030 ppm. Incubation of [beta-18O2, alpha beta-18O]UDP-Glc with sucrose synthetase in the presence and absence of 2,5-anhydromannitol did not result in any significant exchange of an oxygen-18 from the beta-nonbridge position to the anomeric oxygen of the glucose moiety. It can thus be concluded that either sucrose synthetase does not catalyze the cleavage of the scissile carbon-oxygen bond of UDP-Glc in the absence of fructose or, alternatively, the beta-phosphoryl group of the newly formed UDP is rotationally immobilized.     

The accuracy of the rapid equilibrium assumption in steady-state enzyme kinetics in the case of a multipath arbitrary enzyme mechanism with a number of equilibrium segments

A quantitative evaluation of the accuracy of the rapid-equilibrium assumption in steady-state enzyme kinetics was obtained for a multipath arbitrary enzyme mechanism with a number of equilibrium segments. Explicit expressions for estimating the contribution of any equilibrium segment to the accuracy of the rapid-equilibrium assumption were obtained. This allowed us to determine the accuracy of the rapid-equilibrium assumption (Δ) in general: 1 + Δ = (1 + Δ₁)(1 + Δ₂)... (1 + Δ_k), where Δ₁, Δ₂,..., Δ_k is the contribution of each individual equilibrium segment. The accuracy depends only on the structure and properties of equilibrium segments, which have been accounted for in the rapid-equilibrium assumption, but it is independent of the number of paths in the mechanism of the enzymatic reaction and on the structure and properties of the remaining part (steady-state) of the kinetic scheme.     

The mechanism of glycogen synthetase as determined by deuterium isotope effects and positional isotope exchange experiments

The reaction mechanism for glycogen synthetase from rabbit muscle was examined by alpha-secondary deuterium isotope effects and positional exchange experiments. Incubation of glycogen synthetase with [beta-18O2,alpha beta-18O]UDP-Glc did not result in any detectable positional isotope exchange from the beta-nonbridge position to the anomeric oxygen of the glucose moiety. Glucono-1,5-lactone was found to be a noncompetitive inhibitor versus UDP-Glc. The kinetic constants, K(is) and K(ii), were found to be 91 +/- 4 microM and 0.70 +/- 0.09 mM, respectively. Deoxynojirimycin was a nonlinear inhibitor at pH 7.5. The alpha-secondary deuterium isotope effects were measured with [1-2H]UDP-Glc by the direct comparison method. The isotope effects on Vmax and Vmax/K were found to be 1.23 +/- 0.04 and 1.09 +/- 0.06, respectively. The inhibitory effects by glucono-lactone and deoxynojirimycon plus the large alpha-secondary isotope effect on Vmax have been interpreted to show that an oxocarbonium ion is an intermediate in this reaction mechanism. The lack of a detectable positional isotope exchange reaction in the absence of glycogen suggests the formation of a rigid tight ion pair between UDP and the oxocarbonium ion intermediate.