Determination of initial velocities of enzymic reactions from progress curves.
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ABSTRACT:
SUBMITTER: Dagys R
PROVIDER: S-EPMC1147062 | biostudies-other | 1986 Aug
REPOSITORIES: biostudies-other
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Project description:Most methods for studying the kinetic properties of an enzyme involve the determination of initial velocities. When the reaction progress curve shows significant curvature due to depletion of the substrate, accumulation of inhibitory products or instability of the enzyme, estimation of the initial velocity is a subjective and inexact process. Two methods have been suggested [Cornish-Bowden (1975) Biochem. J. 144, 305-312; Boeker (1982) Biochem J. 203, 117-123] that attempt to eliminate this subjective element. The present study offers a third alternative, which is based on fitting a reparameterized form of the integrated Michaelis-Menten equation to the progress curves by non-linear regression. This method yields estimates and standard errors of the initial velocity and of the time to reach 50% reaction. No prior knowledge of the apparent product concentration at zero time or infinite time is required, since both of these quantities are also estimated from the data. It is shown that this method yields reliable estimates of the initial velocity under a wide range of circumstances, including those where the two previously published methods perform poorly.
| S-EPMC1144952 | biostudies-other
Project description: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.
| S-EPMC1152440 | biostudies-other
Project description:A method is described for fitting the velocities obtained from progress curves to a steady-state rate equation. It is based on the method of Markus & Plesser [(1981) in Kinetic Data Analysis: Design and Analysis of Enzyme and Kinetic Data (Edrenyi, ed.), pp. 317-339, Plenum Press, New York]. The obstacle of needing good initial estimates of kinetic parameters is removed by using the parameters provided graphically by a minor modification of the method of Yun & Suelter [(1977) Biochim, Biophys. Acta 480, 1-13]. This progress-curved-based method allows the same discrimination among rival models as do the initial-velocity-based methods, with a great saving of experimental time. The BASIC and FORTRAN 77 programs are deposited as Supplementary Publication SUP 50132 (17 pages) at the British Library (Lending Division), Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1986) 233, 5-6.
| S-EPMC1153069 | biostudies-other
Project description:The computer analysis of progress curves for enzyme-catalysed reactions involves a series of mathematical and computational tasks. The three most daunting of these are the derivation of an integrated rate equation, solving this equation so that the amount of product formed by the reaction at any time can be calculated, and incorporating this solution into a non-linear-regression computer program. This paper describes the basis of a computer program that greatly simplifies the problem. The proposed mechanism is specified in the familiar kinetic constant form, which is automatically translated into a program capable of fitting this mechanism to a series of experimental progress curves. The approach is illustrated for a reversible reaction with one substrate and one product, and tested with some data obtained for the fumarase reaction. A copy of the program has been deposited as Supplementary Publication SUP 50148 (13 pages) at the British Library Document Supply Centre, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1989) 257, 5.
| S-EPMC1138375 | biostudies-other
Project description: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.
| S-EPMC1165854 | biostudies-other
Project description:A new method is described for estimating initial velocities of enzyme-catalysed reactions. It is simple to apply either graphically or numerically, and is particularly appropriate for experiments in which the initial straight part of the progress curve is very short or non-existent. It requires no more knowledge than is readily available about the details of the system, such as the extent of reaction at equilibrium, the rate of enzyme inactivation, the nature of product inhibition etc., unlike some other methods of analysing progress curves, which are often invalidated by small errors in the defining assumptions.
| S-EPMC1165624 | biostudies-other
Project description:Chaotic flows drive mixing and efficient transport in fluids, as well as the associated beautiful complex patterns familiar to us from our every day life experience. Generating such flows at small scales where viscosity takes over is highly challenging from both the theoretical and engineering perspectives. This can be overcome by introducing a minuscule amount of long flexible polymers, resulting in a chaotic flow dubbed 'elastic turbulence'. At the basis of the theoretical frameworks for its study lie the assumptions of a spatially smooth and random-in-time velocity field. Previous measurements of elastic turbulence have been limited to two-dimensions. Using a novel three-dimensional particle tracking method, we conduct a microfluidic experiment, allowing us to explore elastic turbulence from the perspective of particles moving with the flow. Our findings show that the smoothness assumption breaks already at scales smaller than a tenth of the system size. Moreover, we provide conclusive experimental evidence that 'ballistic' separation prevails in the dynamics of pairs of tracers over long times and distances, exhibiting a memory of the initial separation velocities. The ballistic dispersion is universal, yet it has been overlooked so far in the context of small scales chaotic flows.Elastic turbulence, a random-in-time flow, can drive efficient mixing in microfluidics. Using a 3D particle tracking method, the authors show that the smoothness assumption breaks at scales far smaller than believed and the ballistic pair dispersion holds over much longer distances than expected.
| S-EPMC5589773 | biostudies-literature
Project description:A method is described whereby net rate constants can be directly inferred from the progress curves of enzyme intermediates without the need for model specification, numerical analysis, curve fitting, or the steady-state approximation. Specifically, if an enzyme intermediate in an ultimately irreversible serial subsequence is perturbed from and returns back to its equilibrium state as the substrate is consumed, then its net rate constant is given by the ratio of the total substrate consumed and the area under the progress curve for the enzyme intermediate. A rigorous analysis demonstrates this result to hold independent of the complete enzymatic reaction in which the subsequence is embedded, making it broadly applicable to a very wide range of kinetic mechanisms, including those complicated by inhibition. As a theoretical consequence, it is shown that traditionally steady-state parameters such as kcat, kcat/KM, and net rate constants can be expressed as limiting ratios of averages without requiring the steady-state hypothesis. Finally, a mock data set is generated for a system of contemporary interest that can serve as both an example of how the methodology would be used in practice and a proof of concept.
| S-EPMC6910778 | biostudies-literature
Project description:A difficulty associated with high throughput screening for enzyme inhibitors is to establish reaction conditions that maximize the sensitivity and resolution of the assay. Deduction of information from end-point assays at single concentrations requires a detailed understanding of the time progress of the enzymatic reaction, an essential but often difficult process to model. A tool to simulate the time progress of enzyme catalyzed reactions and allows adjustment of reactant concentrations and parameters (initial concentrations, K(m), k(cat), K(i) values, enzyme half-life, product•enzyme dissociation constant, and the rate constant for the reversed reaction) has been developed. This tool provides comparison of the progress of uninhibited versus inhibited reactions for common inhibitory mechanisms, and guides the tuning of reaction conditions. Possible applications include: analysis of substrate turnover, identification of the point of maximum difference in product concentration (?(max)[P]) between inhibited and uninhibited reactions, determination of an optimal observation window unbiased for inhibitor mechanisms or potency, and interpretation of observed inhibition in terms of true inhibition. An important observation that can be utilized to improve assay signal strength and resolution is that ?(max)[P] occurs at a high degree of substrate consumption (commonly >75%) and that observation close to this point does not adversely affect observed inhibition or IC(50) values.
| S-EPMC3468632 | biostudies-literature
Project description:A highly flexible computer program written in FORTRAN is presented which fits computer-generated simulations to experimental progress-curve data by an iterative non-linear weighted least-squares procedure. This fitting procedure allows kinetic rate constants to be determined from the experimental progress curves. Although the numerical integration of the rate equations by a previously described method [Barshop, Wrenn & Frieden (1983) Anal. Biochem. 130, 134-145] is used here to generate predicted curves, any routine capable of the integration of a set of differential equations can be used. The fitting program described is designed to be widely applicable, easy to learn and convenient to use. The use, behaviour and power of the program is explored by using simulated test data.
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