A simple steady state kinetic model for alcohol dehydrogenase. Use of reaction progress curves for parameters estimation at pH 7.4

A simple rate equation for alcohol dehydrogenase was obtained by assuming independent binding sites for ethanol and NAD+ and fully competitive inhibition by the products of the reaction, acetaldehyde and NADH. A random binding order was also assumed. The rate equation is described by six parameters: four association constants (two for the substrates and two for the products of the reaction), Vf for the forward direction, and the equilibrium constant of the reaction. The six parameters were determined at pH 7.4 by numerical analysis of progress curves of reactions started with different concentrations of ethanol and NAD+. The parameters for alcohol dehydrogenase partially purified from rat liver were: Km for ethanol = 0.746 mM, Km for NAD+ = 0.0563 mM, Km for acetaldehyde = 7.07 microM, Km for NADH = 4.77 microM and Keq = 2.36 X 10(-4). The computed values allowed a very good simulation of the experimental progress curves and little variation was observed in the kinetic parameters when the reactions were started in the presence of either NADH or acetaldehyde.     

Reaction of the aminic form of aspartate transaminase with difluoro-oxaloacetate.

Addition of difluoro-oxaloacetate to the aminic form of aspartate transaminase causes a rapid shift of absorbance maximum of the enzyme from 332 nm to 328 nm, followed by a much slower shift to 360 nm corresponding to complete conversion of the aminic form of the enzyme into the aldimine form or a species with similar spectral parameters in rapid equilibrium with it. Kinetic analysis of both the initial fast reaction and the overall slow reaction by using repeated spectral scanning and stopped-flow techniques allows formulation of a basic reaction mechanism involving at least two intermediate enzyme complexes. Computer simulation of the progress curves of the initial fast reaction based on the suggested reaction mechanism gives kinetic parameters that are consistent with all the data obtained by other methods. A molecular reaction scheme involving a ketimine Schiff-base intermediate is proposed.     

Thermodynamic arguments for temperature-induced cryptic conformational change of human plasma cholinesterase

The temperature and pressure dependence of the kinetics of the hydrolysis of o-nitrophenylbutyrate by human plasma tetrameric form cholinesterase (EC 3.1.1.8) was studied. The study was carried out on the one hand at atmospheric pressure by spectrophotometry at various temperatures ranging from 0 to 40 degrees C and, on the other hand by high-pressure stopped-flow spectrophotometry at 3.5, 25 and 35 degrees C in the pressure range 10(-3) to 2 kbar. The Arrhenius plot showed a break at 21 +/- 1 degrees C. Kinetic parameters, activation parameters and volume changes are reported. Discontinuities in the thermodynamic quantities obtained from temperature and pressure (up to 0.8 kbar) dependence of hydrolysis rates are discussed; they have been interpreted as the result of a temperature-induced cryptic conformational change of the enzyme at around 20 degrees C. Beyond 1 kbar the kinetics exhibited several complexities: curvature of the progress curves and high positive or negative activation volume changes depending on temperature and substrate concentration. These complex interacting effects between temperature, pressure and substrate concentration are discussed.     

Stopped-flow solution scattering using synchrotron radiation: Apparatus,data collection and data analysis

We have constructed an experimental system, under remote control, for stopped-flow X-ray scattering using synchrotron radiation. It has been used, in conjunction with an annular detector and its associated electronics, to obtain good scattering curves, with time-slices as short as 200 ms, in a new study of the dissociation of the enzyme complex aspartate transcarbamylase. The data have been analysed by new statistical methods, and they agree well with the results from parallel chemical quench experiments. For studying dissociation reactions, stopped-flow X-ray scattering is a quite practical method, which need not use very much more material than conventional stopped-flow experiments.     

Kinetics of sickle hemoglobin polymerization. III. Nucleation rates determined from stochastic fluctuations in polymerization progress curves

The polymerization kinetics of sickle cell hemoglobin are found to exhibit stochastic variations when observed in very small volumes (approximately 10(-10) cm3). The distribution of progress curves has been measured at several temperatures for a 4.50 mM-hemoglobin S sample using a laser-photolysis, light-scattering technique. The progress curves at a given temperature are superimposable when translated along the time axis, showing that the variability of the kinetic progress curves results primarily from fluctuations in the time at which polymerization is initiated. The shapes of the initial part of the progress curves are well-fitted using the functional form I(t) = Io + As exp (Bt), derived from a dual nucleation model. When the distribution of the measured tenth times is broad, the rate of homogeneous nucleation can be obtained by fitting the exponential tail of the distribution. As the distribution sharpen, the rate of homogeneous nucleation can be estimated by modelling the width of the distribution function using a simple Monte-Carlo simulation of the polymerization kinetics. Using the rates of homogeneous nucleation obtained from the distributions, the rates of heterogeneous nucleation and polymer growth can be obtained from the experimental parameters As and B. The resulting nucleation rates are roughly 1000 times greater than those obtained from an analysis of bulk kinetic data. The results provide strong support for the dual-nucleation mechanism and show that the distribution of progress curves provides a powerful independent method for measuring the rate of homogeneous nucleation and thereby obtaining values for the other principal rates of the mechanism.     

Use of progress curves to investigate product inhibition in enzyme-catalysed reactions. Application to the soluble mitochondrial adenosine triphosphatase

1. Several methods of analysing progress curves of enzyme-catalysed reactions are discussed briefly in relation to their usefulness in a situation where a reaction product has a K(i) much lower than the K(m) for the substrate 2. A comparison is made of different methods of estimating initial rates in this situation. 3. The use of a computer curve-fitting routine capable of handling functions of more than one variable for the extraction of kinetic parameters from progress curves is described. 4. This method and that of fitting time as a polynomial in product concentration are applied to progress curves for the soluble mitochondrial adenosine triphosphatase and the results are compared with values obtained by more conventional methods.     

Transient kinetic approach to the study of acetylcholinesterase reversible inhibition by eseroline

The kinetic rate constants for interaction of (-)-eseroline-(3aS-cis)-1,2,3,3a,8,8a-hexahydro-1,3a,8-trimethylpyrrolo-[2,3-b]indol-5-ol with electric eel acetylcholinesterase (EC 3.1.1.7, acetylcholine acetylhydrolase) were measured at a low substrate concentration according to a transient kinetic approach by using a rapid experimental technique. The measurements were carried out on a stopped-flow apparatus where pre-incubated samples of enzyme with various inhibitor concentrations were diluted with a buffer solution containing the substrate. The experimental data in the form of sigmoid-shaped progress curves were analysed by applying an explicit progress curve equation that described the time dependence of product released during the reaction. The kinetic parameters were evaluated by non-linear regression treatment and the values of the corresponding constants showed approximately the equal affinities of eseroline and eserine (cf. Stojan, J. and Zorko, M. (1997) Biochim. Biophys. Acta, 1337, 75-84.) for binding into the active centre of the enzyme. On the other hand, the kinetic rates for association and dissociation of eseroline were two grades of magnitude higher than those of eserine. The explanation appears to be a substantionally impaired gliding of eserine into the active site gorge by the great mobility of the carbamoyl tail as well as by its numerous possible interactions with the residues lining the gorge. Additionally, a study of the dependence of the transition phase information on the inhibitor concentration was carried out using our experimental data.     

Quantification of chymosin action on nonlabeled kappa-casein-related peptide substrates by ultraviolet spectrophotometry: description of kinetics by the analysis of progress curves

A method is described for quantifying the proteolytic action of the milk-clotting enzyme chymosin on small and medium-sized peptide substrates by monitoring the decrease of absorbance at 230 nm during cleavage. The method is illustrated by the determination of the kinetic parameters of the specific splitting of a kappa-casein-related hexa- and pentadecapeptide by chymosin. The results are in good agreement with those found earlier with the same enzyme/substrate system by using an automated ninhydrin method. Erroneous results were obtained when the kinetic data were derived from one single progress curve. The significance of initial rate measurements for calculating correct kinetic parameters is briefly discussed. The usefulness of single progress curves measured at different initial substrate concentrations for obtaining information about the mechanism of the enzymic reaction is demonstrated.     

Progress curves analysis as an alternative for exploration of activation-inhibition phenomena in cholinesterases

The kinetic behaviour of insect acetylcholinesterases deviates from the Michaelis-Menten pattern. These deviations are known as activation or inhibition at various substrate concentrations and can be more or less observable depending on mutations around the active site of the enzyme. Most kinetic studies on these enzymes still rely on initial rate measurements. It is demonstrated here that according to this method one of the deviations can be overlooked. We attempt to point out that in such cases a detailed step-by-step progress curves analysis is successful. The study is focused on two different methods of analysing progress curves: (i) the first one is based on an integrated initial rate equation which can sufficiently fit truncated progress curves under corresponding conditions; and (ii) the other one precludes the algebraic formulae, but uses numerical integration for searching a non analytical solution of ordinary differential equations describing a kinetic model. All methods are tested on three different acetylcholinesterase mutants from Drosophila melanogaster. The results indicate that kinetic parameters for the E107K mutant with highly expressive activation and inhibition can be well evaluated applying any analysis method. It is quite different for E107W and E107Y mutants where latent activation is present, but discovered only using one or the other progress curves analysis methods.     

Progress Curves Analysis as an Alternative for Exploration of Activation-inhibition Phenomena in Cholinesterases

The kinetic behaviour of insect acetylcholinesterases deviates from the Michaelis-Menten pattern. These deviations are known as activation or inhibition at various substrate concentrations and can be more or less observable depending on mutations around the active site of the enzyme. Most kinetic studies on these enzymes still rely on initial rate measurements. It is demonstrated here that according to this method one of the deviations can be overlooked. We attempt to point out that in such cases a detailed step-by-step progress curves analysis is successful. The study is focused on two different methods of analysing progress curves: (i) the first one is based on an integrated initial rate equation which can sufficiently fit truncated progress curves under corresponding conditions; and (ii) the other one precludes the algebraic formulae, but uses numerical integration for searching a non analytical solution of ordinary differential equations describing a kinetic model. All methods are tested on three different acetylcholinesterase mutants from Drosophila melanogaster. The results indicate that kinetic parameters for the E107K mutant with highly expressive activation and inhibition can be well evaluated applying any analysis method. It is quite different for E107W and E107Y mutants where latent activation is present, but discovered only using one or the other progress curves analysis methods.     

Transient Kinetic Approach to the Study of Acetylcholinesterase Reversible Inhibition by Eseroline

The kinetic rate constants for interaction of (?)-eseroline-(3aS-cis)-1,2,3,3a,8,8a-hexahydro-1,3a,8-trimethylpyrrolo-[2,3-b]indol-5-ol with electric eel acetylcholinesterase (EC 3.1.1.7, acetylcholine acetylhydrolase) were measured at a low substrate concentration according to a transient kinetic approach by using a rapid experimental technique. The measurements were carried out on a stopped-flow apparatus where pre-incubated samples of enzyme with various inhibitor concentrations were diluted with a buffer solution containing the substrate. The experimental data in the form of sigmoid-shaped progress curves were analysed by applying an explicit progress curve equation that described the time dependence of product released during the reaction. The kinetic parameters were evaluated by non-linear regression treatment and the values of the corresponding constants showed approximately the equal affinities of eseroline and eserine (cf. Stojan, J. and Zorko, M. (1997) Biochim. Biophys. Acta, 1337, 75-84.) for binding into the active centre of the enzyme. On the other hand, the kinetic rates for association and dissociation of eseroline were two grades of magnitude higher than those of eserine. The explanation appears to be a substantionally impaired gliding of eserine into the active site gorge by the great mobility of the carbamoyl tail as well as by its numerous possible interactions with the residues lining the gorge. Additionally, a study of the dependence of the transition phase information on the inhibitor concentration was carried out using our experimental data.     

The use of steady-state rate equations to analyse progress curve data.

Analysis of progress curves for enzyme-catalyzed reactions has been made by using a procedure that does not require the derivation of complex integrated rate equations. The method involves conversion of progress curve data to reaction velocities that are then fitted to the appropriate differential rate equation. Application of the procedure to data obtained for the reaction catalyzed by aspartate aminotransferase (L-aspartate:2-oxoglutarate aminotransferase, EC 2.6.1.1), showed that the resulting values for the kinetic parameters agreed well with those obtained by conventional progress curve analysis (Duggleby, R.G. and Morrison, J.F. (1978) Biochim. Biophys. Acta 526, 398--409).     

Determination of Michaelis parameters from differentials of progress curves.

First differentials of progress curves are easily obtainable in many enzyme assay systems. Such curves may be more readily applicable to kinetic analysis than are the usual progress curves. The theory for this approach is developed, and simple graphical procedures for the determination of Michaelis parameters are indicated. By using an electronic differentiator device the application of the method is demonstrated on the kinetics of three different serine proteinases with various synthetic substrates. Whenever the steady-state concentration of an intermediate of the reaction is proportional to the rate, the transition of this intermediate in substrate-depletion experiments may be analysed in similar terms. This is demonstrated with cytochrome c oxidase kinetics. A number of other possible applications are discussed.     

Determination of the dead time of a stopped-flow fluorometer

This investigation was carried out to develop a convenient alternative method for examining the performance and determining the dead time of a stopped-flow fluorometer. We examined the kinetics for the formation of the fluorescent Mg2+-8-hydroxyquinoline chelate in aqueous solutions. The reversible association of the Mg2+ ion with 8-hydroxyquinoline is a second-order process whose on and off rate constants are dependent on pH. We estimated that the Mg2+ ion chelate has a fluorescence quantum yield of 0.02 in aqueous solutions. Using this reaction we measured the dead time of a stopped-flow fluorometer at different pH values. Measurements of the dead time were found to be reproducible and accurate. The Mg2+-8-hydroxyquinoline reaction fulfills the requirements for a convenient test reaction for dead time measurement of stopped-flow fluorometers. Although the usefulness of the reaction is primarily to determine the dead times of stopped-flow instruments operating in the fluorescence mode, the reaction can also be used for testing an instrument operating in the absorbance mode.     

The use of light-scattering and turbidity measurements to study the kinetics of extensively aggregating proteins: αs-Casein

The Ca²⁺-induced association of α_s-casein has been studied using the methods of stopped-flow light-scattering and stopped-flow turbidity. The methods used are described, and the analysis of the results to give plots of M _w against time in the time-scale 0–15 sec is demonstrated. The validity of the method is discussed, and it is shown to be applicable to the association kinetics of aggregating proteins whose molecular-weight averages lie between 10⁷ and 10⁹. The method was used to study the association of bovine α_s-casein in the presence of Ca²⁺, and results obtained are briefly discussed in terms of possible association mechanisms, and a mechanism for the overall reaction of α_s-casein with Ca²⁺, and the subsequent precipitation of the caseinate is proposed.     

Binding of a fluorescent lipid amphiphile to albumin and its transfer to lipid bilayer membranes

Kinetics and thermodynamics of the binding of a fluorescent lipid amphiphile, Rhodamine Green(TM)-tetradecylamide (RG-C(14:0)), to bovine serum albumin were characterized in an equilibrium titration and by stopped-flow fluorimetry. The binding equilibrium of RG-C(14:0) to albumin was then used to reduce its concentration in the aqueous phase to a value below its critical micelle concentration. Under these conditions, the only two species of RG-C(14:0) in the system were the monomer in aqueous solution in equilibrium with the protein-bound species. After previous determination of the kinetic and thermodynamic parameters for association of RG-C(14:0) with albumin, the kinetics of insertion of the amphiphile into and desorption off lipid bilayer membranes in different phases (solid, liquid-ordered, and liquid-disordered phases, presented as large unilamellar vesicles) were studied by stopped-flow fluorimetry at 30 degrees C. Insertion and desorption rate constants for association of the RG-C(14:0) monomer with the lipid bilayers were used to obtain lipid/water equilibrium partition coefficients for this fluorescent amphiphile. The direct measurement of these partition coefficients is shown to provide a new method for the indirect determination of the equilibrium partition coefficient of similar molecules between two defined lipid phases if they coexist in the same membrane.     

Double mixing stopped-flow method for the study of equilibria and kinetics of dimer-tetramer association of hemoglobins: studies on Hb Carp, Hb A, and Hb Rothschild.

A double mixing stopped-flow method is described for studying the dimer-tetramer equilibria of oxyhemoglobins and the kinetics of association of unliganded dimers. The three hemoglobins studied were: Hb Carp, Hb A, and Hb Rothschild (Trp beta 37 (C3)----Arg). The new method reproduces the data obtained for oxyHb A by other established methods. In agreement with previous studies, the new method indicates little, if any, dissociation of oxyHb carp into dimers even in 2 M urea solutions (0.1 M Bis-Tris pH 7.0). OxyHb Rothschild, on the other hand, is extensively dissociated into dimers (K(Hb4L4 in equilibrium with 2Hb2) = 37.3 x 10(-6) M) and the rate constant for the association of deoxy dimers of Hb Rothschild is about one-tenth of the value for Hb A indicating that the deoxy tetramer of Hb Rothschild is at least 10 times more dissociated into dimers than deoxyHb A.     

Enzyme kinetics above denaturation temperature: a temperature-jump/stopped-flow apparatus

We constructed a "temperature-jump/stopped-flow" apparatus that allows us to study fast enzyme reactions at extremely high temperatures. This apparatus is a redesigned stopped-flow which is capable of mixing the reactants on a submillisecond timescale concomitant with a temperature-jump even as large as 60 degrees C. We show that enzyme reactions that are faster than the denaturation process can be investigated above denaturation temperatures. In addition, the temperature-jump/stopped-flow enables us to investigate at physiological temperature the mechanisms of many human enzymes, which was impossible until now because of their heat instability. Furthermore, this technique is extremely useful in studying the progress of heat-induced protein unfolding. The temperature-jump/stopped-flow method combined with the application of structure-specific fluorescence signals provides novel opportunities to study the stability of certain regions of enzymes and identify the unfolding-initiating regions of proteins. The temperature-jump/stopped-flow technique may become a breakthrough in exploring new features of enzymes and the mechanism of unfolding processes.     

Kinetics of dissociation of parvalbumin complexes with calcium and magnesium ions

Dissociation kinetics of parvalbumin complexes with calcium and magnesium ions were studied by means of stopped-flow method employing intrinsic protein fluorescence registration. In the temperature range from 10 to 30 degrees C the kinetic curves of Ca2+ and Mg2+ dissociation are best fitted with a sum of two exponential terms, each term is ascribed to a dissociation process in one of two bindings sites of parvalbumin. Dissociation rate constants in this temperature range increase from 0.03 to 0.8 s-1 and from 0.18 to 5 s-1 for Ca2+, and from 0.9 to 4.5 s-1 and from 4 to 33 s-1 for Mg2+. Parvalbumin equilibrium binding constants of Ca2+ and Mg2+ were also measured in the same temperature range. It makes possible to estimate the rate constants of association of Ca2+ and Mg2+. In the case of Ca2+ the rate of association approaches the diffusion controlled limit.