This article describes various approaches to the analysis of quantitative responses assumed to follow a hyperbolic dose–response relationship (the Michaelis–Menten equation) characterized by the values of two parameters: the Michaelis constant (the dose at half-maximal response) and the asymptotic maximum response. Methods include diagnostic graphical representations, including the double reciprocal or Lineweaver–Burk plot, the Hanes plot and the Eadie–Hofstee plot. Curve-fitting and parameter estimation is described using either least squares or maximum likelihood. The latter includes using a generalized linear model incorporating a reciprocal link function and the possibility of nonnormally distributed errors. Robust and distribution-free estimation procedures, such Theil's method (known as the direct linear plot in biochemistry) are also covered.
Keywords:
Michaelis–Menten equation;
hyperbolic dose–response curves;
Lineweaver–Burk plot;
generalized linear model;
reciprocal link function;
robust estimation distribution-free curve fitting;
direct linear plot
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