Acetylcholinesterase inhibition by eserine: rate constants of reaction. Part II

The inhibition of eel acetylcholinesterase by physostigmine at 20 degrees and 25 degrees C have been investigated. In our evaluation the unimolecular reactivation rate constant, k3, the carbamylation rate constant, k2, and the binding constant, Ka, are the first simultaneously determined. The mechanism of this reaction is discussed.     

Mechanism of free radical-induced hemolysis of human erythrocytes: comparison of calculated rate constants for hemolysis with experimental rate constants.

We previously developed a simple competitive reaction model between lipid peroxidation and protein oxidation in erythrocyte membranes that accounts for radical-induced hemolysis of human erythrocytes. In this study, we compared the rate constants calculated from the hemolysis curves of erythrocytes in the presence of radical initiators with those obtained from experiments using erythrocyte ghosts treated with radicals. 2,2'-Azobis(amidinopropane) dihydrochloride and 2,2'-azobis(2,4-dimethylvaleronitrile) were used as radical initiators. Plots of the logarithm of concentration of the radical initiator against the logarithm of the rate constant gave straight lines. The slope of the lines for the calculated lipid peroxidation was nearly equal with the experimental value. Similar results were obtained for oxidation of membrane proteins, except for band 3 oxidation. The values for the rate constants calculated from hemolysis curves seem to be accurate. The slope of the lines for the calculated rate constants for proteins was larger than the experimental value for band 3 oxidation, because band 3 oxidation is accompanied by aggregation or redistribution of band 3 proteins to form hemolytic holes. These results indicate that the competitive reaction model may be useful for analyzing radical-induced hemolysis.     

Determination of rate constants for nucleotide dissociation from Na,K-ATPase.

A method for determining individual rate constants for nucleotide binding to and dissociation from membrane bound pig kidney Na,K-ATPase is presented. The method involves determination of the rate of relaxation when Na,K-ATPase in the presence of eosin is mixed with ADP or ATP in a stopped-flow fluorescence apparatus. It is shown that the nucleotide dependence of this rate of relaxation--taken together with measured equilibrium binding values for eosin and ADP--makes possible a reasonably reliable determination of the rate constant for dissociation of nucleotide, i.e., determination of the rate constant k-1 in the following model (where E denotes Na,K-ATPase): [formula: see text] All experiments are carried out at about 4 degrees C in a buffer containing 200 mM sucrose, 10 mM EDTA, 25 mM Tris and 73 mM NaCl (pH 7.4). Values obtained for the rate constants for dissociation are about 6 s-1 for ADP and 2-3 s-1 for ATP.     

Determination of association and dissociation rate constants for bilirubin--bovine serum albumin.

The association rate constant for the binding of bilirubin to bovine serum albumin has been determined in a continuous-flow experiment. The value obtained is 0.9 x 10⁶m^?1S^?1. Furthermore the dissociation rate constant is determined from the rate of the peroxidase-catalyzed oxidation of bilirubin in a bilirubin-albumin solution. This figure is 3.1 × 10^?2s ¹. Calculation of the apparent binding equilibrium constant from the two rate constants gives 2.9 x 10⁷m^?1. The above mentioned peroxidase oxidation has also been used for a direct estimation of the binding equilibrium constant giving 2.7 × 10⁷m^?1. All experiments are carried out at 36 °C and pH 7.4.     

A spectrophotometric assay for determining the rate constants of acetylcholinesterase inhibitions.

A spectrophotometric assay procedure has been developed for determining the rate constants for the inhibition of acetylcholinesterase by carbamates and phosphates. The method permits the investigation of inhibitors over a large range in the value of the phosphorylation or carbamylation rate constants without involving the kinetic parameters of the assay substrate in the calculations.     

Superoxide dismutase: a comparison of rate constants

O₂^?was introduced, at a constant rate, into buffered aqueous solutions, either by mechanical infusion of KO₂, dissolved in tetrahydrofuran, or by the in situ action of xanthine oxidase on xanthine plus oxygen. This O₂^? was allowed to react with ferricytochrome c or with tetranitromethane and the formation of the reaction products, ferrocytochrome c or nitroform, respectively, was monitored spectrophotometrically. That concentration of Superoxide dismutase, which competed equally with given levels of cytochrome c or tetranitromethane and which thus caused 50% inhibition of the rates of accumulation of ferrocytochrome c or of nitroform, was determined. The rate constant for the enzymatic dismutation of O₂^? by the copper and zinc containing enzyme from bovine erythrocytes was then calculated from the known rate constants for the reaction of O₂^? with ferricytochrome c and with tetranitromethane and was found to be 2 × 10⁹m^?1 sec^?1 at pH 7.8 and 8.5. This rate constant was obtained at steady-state concentrations of O₂^? in the 10^?8m → 10^?13m range and is in full agreement with the results of pulse radiolytic investigations which were performed at O₂^? concentrations in the 10^?5m range. The second order rate constant for the enzymatic dismutation of O₂^? is thus independent of the concentration of O₂^? in the range 10^?5 → 10^?13m.Several distinct types of Superoxide dismutase have been described. These include the mangano-enzymes from Escherichia coli and from chicken liver mitochondria and the iron-enzyme from E. coli. The rate constants for the dismutations catalyzed by these enzymes have also been investigated as a function of pH.     

Determining rate constants for irreversible polymerization where the initial step and propagation steps have different rate constants: Consideration of polyadenylate polymerase

A new relationship is derived between the amount of monomer incorporated and the amount of initiated primer in an irreversible polymerization where the first step, initiation, has a rate constant differing from the elongation rate constants. It is valid for template directed and template independent polymerization. This relationship can be used in kinetic simulation. It suggests a simpler curve fitting technique to attain rate constants from a relatively small data set. Our analysis reveals some limitations of the model of irreversible polymerization; these limitations have not been obvious previously. For example, the initiation rate constant is not attainable from simple monomer incorporation data. Reliable rate constants can be obtained with minimal time course studies.     

Algebraic methods for deriving steady-state rate equations. Practical difficulties with mechanisms that contain repeated rate constants.

Methods of deriving rate equations that rely on repetition of terms for identification of redundant or invalid terms give incorrect results if used with mechanisms in which some rate constants appear more than once.     

Integrated steady state rate equations and the determination of individual rate constants.

Integrated steady state rate equations have been used to determine the kinetic constants (Vs, Ks, Vp, and Kp) and rate constants (k1, k2, k3, and k4) of the reversible enzyme mechanism: (see article). The fumarase reaction has been used as a model to illustrate the procedures for determining these constants. In contrast to initial velocity studies, the values of the constants have been obtained by examining the enzyme reaction in only one direction rather than in both forward and reverse directions. To accomplish this, a new procedure is described for fitting data to integrated rate equations which eliminates problems encountered when data are analyzed graphically. The advantages of examining on enzyme reaction in one direction with these new procedures allow this method to be extended to the examination of enzymes with simple mechanisms where initial velocities are difficult to measure because either the substrate or product is not readily available, or because the reaction is not readily reversible.     

The role of electrostatic interactions in the process of diffusional encounter and docking of electron transport proteins

Electrostatic interaction of plastocyanin and cytochrome f in the process of protein–protein complex formation was investigated by computer simulation methods. It was shown that long-range electrostatic interaction promotes energetically favorable mutual orientation of protein molecules at distances between their cofactors shorter than 5 nm. At distances shorter than 3 nm, these electrostatic interactions lead to a significantly detectable increase in the rate of convergence of the cofactors.     

A thermal-variation method for analysing the rate constants of the Michaelis--Menten mechanism.

By analysing the variations of saturation velocity and Michaelis constant with temperature and invoking the mathematical constraint represented by the Arrhenius equation, it becomes possible to estimate k+2 and indistinguishably k+1 and k-1 for the Michaelis--Menten mechanism of one-substrate enzyme reactions. Distinction between k+1 and k-1 may be obtained through the determination of isotopic rate effects. This procedure thus provides a basis for evaluating all three rate constants of the one-substrate mechanism, and disproves the suggestion that k+1 and k-1 are intrinsically unobtainable from steady-state kinetic measurements.     

Determination of rate constants of antigen-antibody reaction. A theory

A new method of determination of rate constants for antigen-antibody interactions is proposed. This method is based on a solid phase immunoenzymatic analysis of the dynamics of elution of immobilized antigen-bound antibodies in the presence of a free antigen. The kinetics of this process is described by a system of differential equations, whose solution results in expression defining the dynamics of antibody interaction with immobilized and free antigens. Simple formulas were derived for the calculation of the rate and equilibrium constants for the antibody-antigen reaction on the basis of experimental kinetic curves. The use of theoretical kinetic curves for antibody elution showed that these formulas reflect with a high degree of accuracy the kinetic properties of the reaction under study.     

Identifiability and interval identifiability of mammillary and catenary compartmental models with some known rate constants

The identifiability problem is addressed for n-compartment linear mammillary and catenary models, for the common case of input and output in the first compartment and prior information about one or more model rate constants. We first define the concept of independent constraints and show that n-compartment linear mammillary or catenary models are uniquely identifiable under n-1 independent constraints. Closed-form algorithms for bounding the constrained parameter space are then developed algebraically, and their validity is confirmed using an independent approach, namely joint estimation of the parameters of all uniquely identifiable submodels of the original multicompartmental model. For the noise-free (deterministic) case, the major effects of additional parameter knowledge are to narrow the bounds of rate constants that remain unidentifiable, as well as to possibly render others identifiable. When noisy data are considered, the means of the bounds of rate constants that remain unidentifiable are also narrowed, but the variances of some of these bound estimates increase. This unexpected result was verified by Monte Carlo simulation of several different models, using both normally and lognormally distributed data assumptions. Extensions and some consequences of this analysis useful for model discrimination and experiment design applications are also noted.     

Stochastic models for chemical reactions: II. The unimolecular rate constant

Based on the author's stochastic treatment of the unimolecular reaction which contains a mathematical rationale for considering random fluctuations inherent in the reaction mechanism (Bartholomay, 1958,Bull. Math. Biophysics,20, 175-90), a new and simple formula is derived for calculating the rate constants of such reactions. This formula is then applied to data from the literature and the results compared with estimates obtained alternatively using current methods which attribute all irregularities about the usually expected smooth, decaying exponential curve to extraneous causes unrelated to reaction mechanism. Both estimates are seen to be almost identical despite the opposing assumptions about the origin of the random component of the kinetic data of such reactions.     

Forward rate constants for receptor clusters. Variational methods for upper and lower bounds

We are interested in the effect of receptor clustering on k+, the diffusion-limited forward rate constant for the binding of a ligand to a cell surface receptor. Here we estimate the reduction in k+ when receptors are clustered in various configurations. We obtain two alternative expressions for the flux of ligands into receptors distributed on a surface. Next we show through a variational principle that these provide both upper and lower bounds on the flux when evaluated for trial concentration functions which satisfy only the boundary conditions of the Laplace equation. We use an analogy with electrostatics to calculate rigorous bounds within approx. 10% of the exact result for a variety of planar clusters of hemispherical receptor sites. We also obtain an exact result for the flux into a spheroidal receptor and use this result to obtain bounds on the flux into certain receptor clusters.