Determination of rapid-equilibrium kinetic parameters of ordered and random enzyme-catalyzed reaction A+B=P+Q.
ABSTRACT: This article deals with the rapid-equilibrium kinetics of the forward and reverse reactions together for the ordered and random enzyme-catalyzed A+B=P+Q and emphasizes the importance of reporting the values of the full set of equilibrium constants. Equilibrium constants that are not in the rate equation can be calculated for random mechanisms using thermodynamic cycles. This treatment is based on the use of a computer to derive rate equations for three mechanisms and to estimate the kinetic parameters with the minimum number of velocity measurements. The most general of these three programs is the one to use first when the mechanism for A+B=P+Q is studied for the first time. This article shows the effects of experimental errors in velocity measurements on the values of the kinetic parameters and on the apparent equilibrium constant calculated using the Haldane relation.
Project description:The kinetic mechanism of glutamate dehydrogenase with the monocarboxylic substrate norvaline was examined by using initial-rate steady-state kinetics and inhibition kinetics. To a first approximation the reaction mechanism can be described as a rapid-equilibrium random-order one. Binding synergism between the monocarboxylic substrate and coenzyme is not observed. Dissociation constants for NAD+ and 2-oxoglutarate calculated from the kinetic data assuming a rapid-equilibrium random-order model are in good agreement with independently obtained estimates. Lineweaver-Burk plots with varied norvaline concentration are not strictly linear, and it is concluded that a steady-state random-order model more accurately reflects the observed kinetics with norvaline as substrate.
Project description:Determination of kinetic and thermodynamic protein binding constants using interferometry from a porous Si Fabry-Perot layer is presented. A protein A capture probe is adsorbed within the pores of an oxidized porous Si matrix, and binding of immunoglobulin G (IgG) antibodies derived from different species is investigated. The relative protein A/IgG binding affinity is human > rabbit > goat, in agreement with literature values. The equilibrium binding constant (Ka) for human IgG binding to surface-immobilized protein A is determined to be (3.0 +/- 0.5) x 107 M-1 using an equilibrium Langmuir model. Kinetic rate constants are calculated to be kd = (2.1 +/- 0.2) x 10-4 s-1 and ka = (1.2 +/- 0.4) x 104 M-1 s-1 using nonlinear least-squares analysis, yielding an equilibrium binding constant of Ka = (5.5 +/- 1.5) x 107 M-1. Both steady-state and time-dependent measurements yield equilibrium binding constants that are consistent with literature values. Kinetic rate constants determined through nonlinear least-squares analysis are also in agreement with protein A/IgG binding on a surface. Dosing with a high concentration of analyte leads to deviations from ideal binding behavior, interpreted in terms of restricted analyte diffusion within the porous SiO2 matrix. It is shown that the diffusion limitations can be minimized if the kinetic measurements are performed at low analyte concentrations or under conditions in which the protein A capture probe is not saturated with analyte. Potential limitations of the use of porous SiO2 interferometers for quantitative determination of protein binding constants are discussed.
Project description:The process of receptor-mediated endocytosis for receptors that recycle to the cell surface in an active form can be considered as being kinetically analogous to that of a uni-substrate, uni-product enzyme-catalysed reaction. In this study we have derived steady-state initial-velocity rate equations for this process, based on classical Briggs-Haldane and King-Altman kinetic approaches to multi-step reactions, and have evaluated this kinetic paradigm, using as a model system the low-density lipoprotein (LDL)-receptor-mediated endocytosis of the trapped label [14C]sucrose-LDL in uninduced, steady-state Hep-G2 cells. Using the derived rate equations, together with experimentally determined values for Bmax (123 fmol/mg of cell protein), Kd (14.3 nM), the endocytotic rate constant ke (analogous to kcat; 0.163 min-1), Km (80 nM) and maximal internalization velocity (26.4 fmol/min per mg), we have calculated the ratio ke/Km (0.00204 nM-1.min-1), the bimolecular rate constant for LDL and LDL-receptor association (0. 00248 nM-1.min-1), the first-order rate constant for LDL-LDL-receptor complex dissociation (0.0354 min-1), the total cellular content of LDL receptors (154 fmol/mg of cell protein), the intracellular LDL receptor concentration (30.7 fmol/mg of cell protein) and the pseudo-first-order rate constant for LDL receptor recycling (0.0653 min-1). Based on this mathematical model, the kinetic mechanism for the receptor-mediated endocytosis of [14C]sucrose-LDL by steady-state Hep-G2 cells is one of constitutive endocytosis via independent internalization sites that follows steady-state Briggs-Haldane kinetics, such that LDL-LDL-receptor interactions are characterized by a rapid-high-affinity ligand-receptor association, followed by ligand-receptor complex internalization that is rapid relative to complex dissociation, and by receptor recycling that is more rapid than complex internalization and that serves to maintain 80% of cellular LDL receptors on the cell surface in the steady-state. The consistency with which these quantitative observations parallel previous qualitative observations regarding LDL-receptor-mediated endocytosis, together with the high correlation between theoretical internalization velocities (calculated from determined rate constants) and experimental internalization velocities, underscore the validity of considering receptor-mediated endocytotic processes for recycling receptors in catalytic terms.
Project description:The preceding paper (Südi, 1974) reports partial success in describing the conversion of E(NADH) plus pyruvate into E(NAD+) plus lactate in terms of a simple Haldane-type scheme which involves two intermediates (E(NADH) (Pyr) and E(NAD+) (Lac)), where E represents lactate dehydrogenase. This information is completed here by reporting kinetic results obtained by carrying out the same reaction in the opposite direction. The combined results of these two papers confirm the findings of Holbrook & Gutfreund (1973) that the observed spectral changes do take place at the level of resolution of this simple two-intermediate scheme. The following numerical values for the rate (and equilibrium) constants involved in their formation and decomposition are reported: [Formula: see text] It is shown that although the precision of estimation of some of these numerical values is subject to some experimental uncertainty, their derivation from direct experimental observations only involves the principle of microscopic reversibility. This paper describes stopped-flow kinetic observations made with E(NAD+) and lactate as the two reactants. It is shown that fluorescence and u.v.-absorption measurements yield the same experimental rate constant for the last reaction step in which E(NADH) is generated. On the other hand, the generation of E(NADH) (Pyr) can only be indirectly observed, as a less than stoicheiometric ;burst', and by u.v.-absorption measurements only. It is shown that the stoicheiometry of this partial ;burst reaction', and a pre-equilibrium factor in the directly observed rate of E(NADH)-production, yield equivalent information about the reversible oxidation-reduction step. It is further shown that the pre-equilibrium factor that is involved in the generation of E(NADH) can be determined because k(+4)=222s(-1) is already known (Südi, 1974). Since the fluorescence measurements yield much more precise estimations, and their interpretation is considered by the author to be free of ambiguity, the presented quantitative analysis is based on the fluorescence observations.
Project description:The mechanism of the enzymic reaction responsible for chloramphenicol resistance in bacteria was examined by steady-state kinetic methods. The forward reaction catalysed by chloramphenicol acetyltransferase leads to inactivation of the antibiotic. Use of alternative acyl donors and acceptors, as well as the natural substrates, has yielded data that favour the view that the reaction proceeds to the formation of a ternary complex by a rapid-equilibrium mechanism wherein the addition of substrates may be random but a preference for acetyl-CoA as the leading substrate can be detected. Chloramphenicol and acetyl-CoA bind independently, but the correlation between directly determined and kinetically derived dissociation constants is imperfect because of an unreliable slope term in the rate equation. The reverse reaction, yielding acetyl-CoA and chloramphenicol, was studied in a coupled assay involving citrate synthase and malate dehydrogenase, and is best described by a rapid-equilibrium mechanism with random addition of substrates. The directly determined dissociation constant for CoA is in agreement with that derived from kinetic measurements under the assumption of an independent-sites model.
Project description:1. The equilibrium and kinetics of cyanide binding to ferroperoxidase were investigated. At pH9.1 the equilibrium and kinetic measurements agree closely and disclose a single process with an affinity constant of 1.1x10(3)m(-1) and combination and dissociation velocity constants of 29m(-1).s(-1) and 2.5x10(-2)s(-1) respectively. 2. At pH values below 8 the affinity constant falls until at pH6.0 the ferroperoxidase.cyanide complex is no longer formed. This is shown to be associated with the formation of ferriperoxidase.cyanide complex in the mixture even in the presence of excess of sodium dithionite. 3. Rapid-pH-jump experiments show a fast pseudo-first-order interconversion between ferroperoxidase.cyanide complex at pH9.1 and ferriperoxidase.cyanide complex at pH6.0. 4. The kinetics of binding of cyanide to dithionite-reduced peroxidase at pH6.0 are complicated and radically different from those observed at pH9.1. 5. Above pH8 the change of affinity constant with pH is consistent with the undissociated species, HCN, being bound by the ferroperoxidase. The enthalpy for this process measured both by equilibrium and kinetic methods is about -8kcal/mol. 6. The binding of cyanide to reconstituted peroxidases, proto, meso and deutero, was investigated. 7. The results are discussed in relation to known data on cyanide binding to other haemoproteins.
Project description:The stopped-flow kinetic studies described in this and the following paper (Südi, 1974) demonstrate that a Haldane-type description of the reversible lactate dehydrogenase reaction presents an experimentally feasible task. Combined results of these two papers yield numerical values for the six rate constants defined by the following equilibrium scheme, where E represents lactate dehydrogenase: [Formula: see text] The experiments were carried out at pH8.4 at a relatively low temperature (6.3 degrees C) with the pig heart enzyme. Identification of the above two intermediates and determination of the corresponding rate constants actually involve four series of independent observations in these studies, since (a) the reaction can be followed in both directions, and (b) both the u.v. absorption and the fluorescence of the coenzymes are altered in the reaction, and it is shown that these two spectral changes do not occur simultaneously. Kinetic observations made in the reverse direction are reported in this paper. It is demonstrated that the fluorescence of NADH can no longer be observed in the ternary complex E(NADH) (Pyr). Even though the oxidation-reduction reaction rapidly follows the formation of this complex, the numerical values of k(-4) (8.33x10(5)m(-1).s(-1)) and k(+4) (222s(-1)) are easily obtained from a directly observed second-order reaction step in which fluorescent but not u.v.-absorbing material is disappearing. U.v.-absorption measurements do not clearly resolve the subsequent oxidation-reduction step from the dissociation of lactate. It is shown that this must be due partly to the instrumental dead time, and partly to a low transient concentration of E(NAD+) (Lac) in the two-step sequential reaction in which the detectable disappearance of u.v.-absorbing material takes place. It is estimated that about one-tenth of the total change in u.v. absorption is due to a ;burst reaction' in which E(NAD+) (Lac) is produced, and this estimation yields, from k(obs.)=120s(-1), k(-2)=1200s(-1).
Project description:The binding of the transport inhibitor, forskolin, to the galactose-H+ symporter, GalP, of Escherichia coli was evaluated by equilibrium and time-resolved fluorescence measurements. A quench in protein fluorescence of 8-12% was observed upon the binding of forskolin. The overall dissociation constant (Kd) for forskolin determined by fluorescence titration ranged between 1.2 and 2.2 microM, which is similar to that reported from equilibrium dialysis measurements of the binding of [3H]forskolin (Kd = 0.9-1.4 microM). The kinetics of forskolin binding were measured by stopped-flow fluorescence methods. The protein fluorescence was quenched in a biphasic manner; the faster of these two rates was dependent on the concentration of forskolin and was interpreted as the initial binding step from which both the association (kon) and dissociation (koff) rate constants were determined. The association and dissociation rate constants were 5.4-6.2 microM-1.s-1 and 5.1-11.5 s-1 respectively, and the Kd was calculated to be 1.5 microM. The binding of forskolin was inhibited by D-galactose, but not by L-galactose, and displacement by sugar provided an additional method to calculate the dissociation rate constant for forskolin (koff = 12.4-13.0 s-1). The rate of the slow change in protein fluorescence (3-5 s-1) was independent of the forskolin concentration, indicating an isomerization of the transporter between different conformations, possibly outward- and inward-facing forms. These kinetic parameters were determined at a series of temperatures, so that the thermodynamics of forskolin binding and transporter re-orientation could be analysed. The binding process was entropically driven (delta S = 83.7 J.K-1.mol-1; delta H = 8.25 kJ.mol-1), similar to that for cytochalasin B, which is also an inhibitor of GalP. Measurements of the binding of [3H]forskolin by equilibrium dialysis revealed competitive displacement of bound forskolin by cytochalasin B, possibly suggesting that the sugar, forskolin and cytochalasin B binding sites are overlapping; the Kds for forskolin and cytochalasin B were calculated to be 0.85 microM and 4.77 microM respectively, and the concentration of binding sites was 10.2 nmol.mg-1.
Project description:<h4>Background</h4>Translating a known metabolic network into a dynamic model requires rate laws for all chemical reactions. The mathematical expressions depend on the underlying enzymatic mechanism; they can become quite involved and may contain a large number of parameters. Rate laws and enzyme parameters are still unknown for most enzymes.<h4>Results</h4>We introduce a simple and general rate law called "convenience kinetics". It can be derived from a simple random-order enzyme mechanism. Thermodynamic laws can impose dependencies on the kinetic parameters. Hence, to facilitate model fitting and parameter optimisation for large networks, we introduce thermodynamically independent system parameters: their values can be varied independently, without violating thermodynamical constraints. We achieve this by expressing the equilibrium constants either by Gibbs free energies of formation or by a set of independent equilibrium constants. The remaining system parameters are mean turnover rates, generalised Michaelis-Menten constants, and constants for inhibition and activation. All parameters correspond to molecular energies, for instance, binding energies between reactants and enzyme.<h4>Conclusion</h4>Convenience kinetics can be used to translate a biochemical network--manually or automatically--into a dynamical model with plausible biological properties. It implements enzyme saturation and regulation by activators and inhibitors, covers all possible reaction stoichiometries, and can be specified by a small number of parameters. Its mathematical form makes it especially suitable for parameter estimation and optimisation. Parameter estimates can be easily computed from a least-squares fit to Michaelis-Menten values, turnover rates, equilibrium constants, and other quantities that are routinely measured in enzyme assays and stored in kinetic databases.
Project description:The acetylcholine receptor (AChR) from vertebrate skeletal muscle initiates voluntary movement, and its kinetics of activation are crucial for maintaining the safety margin for neuromuscular transmission. Furthermore, the kinetic mechanism of the muscle AChR serves as an archetype for understanding activation mechanisms of related receptors from the Cys-loop superfamily. Here we record currents through single muscle AChR channels with improved temporal resolution approaching half an order of magnitude over our previous best. A range of concentrations of full and partial agonists are used to elicit currents from human wild-type and gain-of-function mutant AChRs. For each agonist-receptor combination, rate constants are estimated from maximum likelihood analysis using a kinetic scheme comprised of agonist binding, priming, and channel gating steps. The kinetic scheme and rate constants are tested by stochastic simulation, followed by incorporation of the experimental step response, sampling rate, background noise, and filter bandwidth. Analyses of the simulated data confirm all rate constants except those for channel gating, which are overestimated because of the established effect of noise on the briefest dwell times. Estimates of the gating rate constants were obtained through iterative simulation followed by kinetic fitting. The results reveal that the agonist association rate constants are independent of agonist occupancy but depend on receptor state, whereas those for agonist dissociation depend on occupancy but not on state. The priming rate and equilibrium constants increase with successive agonist occupancy, and for a full agonist, the forward rate constant increases more than the equilibrium constant; for a partial agonist, the forward rate and equilibrium constants increase equally. The gating rate and equilibrium constants also increase with successive agonist occupancy, but unlike priming, the equilibrium constants increase more than the forward rate constants. As observed for a full and a partial agonist, the gain-of-function mutation affects the relationship between rate and equilibrium constants for priming but not for channel gating. Thus, resolving brief single channel currents distinguishes priming from gating steps and reveals how the corresponding rate and equilibrium constants depend on agonist occupancy.