The use of the direct linear plot for determining initial velocities.
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ABSTRACT:
SUBMITTER: Cornish-Bowden A
PROVIDER: S-EPMC1165624 | biostudies-other | 1975 Aug
REPOSITORIES: biostudies-other
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Project description:A new plot is described for analysing the results of kinetic experiments in which the Michaelis-Menten equation is obeyed. Observations are plotted as lines in parameter space, instead of points in observation space. With appropriate modifications the plot is applicable to most problems of interest to the enzyme kineticist. It has the following advantages over traditional methods of plotting kinetic results: it is very simple to construct, because it is composed entirely of straight lines and requires no calculation or mathematical tables; the kinetic constants are read off the plot directly, again without calculation; it may be used during the course of an experiment to judge the success of the experiment, and to modify the experimental design; it provides clear and accurate information about the quality of the observations, and identifies aberrant observations; it provides a clear indication of the precision of the kinetic constants; constructed with care, it provides unbiased estimates of the kinetic constants, the same as those provided by a computer program; it may be used to simulate results for illustrative purposes very rapidly and simply.
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Project description:Excellent estimations of initial rates can be obtained from plots of delta P/t versus product formed (where P is the instantaneous concentration of the product). delta P/t is the chord from P0,t0 to P,t on an ordinary P-versus-t plot. When the chord is plotted as a function of product, the intercept at P0 of the resulting curve is necessarily dP/dt0. This curve approximates to a straight line extremely closely in all cases tested thus far. If delta P/t versus product is calculated from the integrated rate equation for a first-order reaction, and if a straight line is fitted through points representing the first 50% of the reaction, the discrepancy between the true initial rate and dP/dt0 estimated from the plot is 0.68%. For the most common form of the integrated rate equation for catalysed reactions the discrepancy varies between 0 and 0.90%. Because of the complexities of the integrated rate equations, catalysed second-order reactions have not been evaluated directly; uncatalysed reactions have been done instead. For a reaction with one reactant and two products, the discrepancy varies from 0.68 to 2.02%. For two reactants and one product, it varies from 0 to 0.68%; for two and two, 0 to 2.02%. The larger discrepancies occur only when unfavourable equilibrium constants are being overcome by the initial conditions.
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Project description:The statistical implications of the direct linear plot for enzyme kinetic data, described in the preceding paper (Eisenthal & Cornish-Bowden, 1974), are discussed for the case of the Michaelis-Menten equation. The plot is shown to lead directly to non-parametric confidence limits for the kinetic parameters, V and K(m), which depend on far less sweeping assumptions about the nature of experimental error than those implicit in the method of least squares. Median estimates of V and K(m) can also be defined, which are shown to be more robust than the least-squares estimates in a wide variety of experimental situations.
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Project description:The theoretical basis for the direct linear plot [Eisenthal & Cornish-Bowden (1974) Biochem. J. 139, 715-720], a non-parametric statistical method for the analysis of data-fitting the Michaelis-Menten equation, was reinvestigated in order to accommodate additional experimental designs and to provide estimates of precision more directly comparable with those obtained by parametric statistical methods. Methods are given for calculating upper and lower confidence limits for the estimated parameters, for accommodating replicate measurements and for comparing the results of two separate experiments. Factors that influence the proper design of experiments are discussed.
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