The effects of systematic errors on the analysis of irreversible enzyme inhibition progress curves.
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ABSTRACT:
SUBMITTER: Gray P
PROVIDER: S-EPMC1149936 | biostudies-other | 1991 Feb
REPOSITORIES: biostudies-other
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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.
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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.
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Project description:Methods are given for analysing the time course of an enzyme-catalysed reaction when the concentration of the enzyme itself is high, a situation which is often found in vivo. (1) The integrated form of the kinetic equation for a concentrated Michaelian enzyme in absence of product inhibition is given. Parameters are shown to be calculated easily using non-linear fitting procedures. (2) A general algorithm to analyse progress-curve data in more complex cases (i.e. when the analytical form of the integrated rate equation is not known or is exceedingly complex) is proposed. This algorithm may be used for any enzyme mechanism for which the differential form of the kinetic equation may be written analytically. We show that the method allows differentiation between the main types of product inhibition which may occur in the case of a highly concentrated Michaelian enzyme.
| S-EPMC1152704 | biostudies-other
Project description:Many organophosphorus compounds are irreversible inhibitors of acetylcholinesterase. The methods used in the literature to determine the inhibition kinetic constants usually involve either manual determination of the slope at various points along the inhibition progress curve or fitting polynomials to the curve. The present study investigates the use of non-linear-regression analysis to determine the various parameters. A method is suggested that yields accurate values for the inhibition constants under a range of circumstances.
| S-EPMC1135596 | biostudies-other
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.
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Project description:The Michaelis-Menten model of enzyme kinetic assumes the free ligand approximation, the steady-state approximation and the rapid equilibrium approximation. Analytical methods to model slow-binding inhibitors by the analysis of initial velocities have been developed but, due to their inherent complexity, they are seldom employed. In order to circumvent the complications that arise from the violation of the rapid equilibrium assumption, inhibition is commonly evaluated by pre-incubating the enzyme and the inhibitors so that, even for slow inhibitors, the binding equilibrium is established before the reaction is started. Here, we show that for long drug-target residence time inhibitors, the conventional analysis of initial velocities by the linear regression of double-reciprocal plots fails to provide a correct description of the inhibition mechanism. As a case study, the inhibition of acetylcholinesterase by galantamine, a drug approved for the symptomatic treatment of Alzheimer's disease, is reported. For over 50 years, analysis based on the conventional steady-state model has overlooked the time-dependent nature of galantamine inhibition, leading to an erroneous assessment of the drug potency and, hence, to discrepancies between biochemical data and the pharmacological evidence. Re-examination of acetylcholinesterase inhibition by pre-steady state analysis of the reaction progress curves showed that the potency of galantamine has indeed been underestimated by a factor of ~100.
| S-EPMC9105972 | biostudies-literature
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: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: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: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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