Eadie–Hofstee diagram on arvau

Wikipedia / Eadie–Hofstee diagram

In biochemistry, an Eadie–Hofstee plot (or Eadie–Hofstee diagram) is a graphical representation of the Michaelis–Menten equation in enzyme kinetics. It has been known by various different names, including Eadie plot, Hofstee plot and Augustinsson plot. Attribution to Woolf is often omitted, because although Haldane and Stern credited Woolf with the underlying equation, it was just one of the three linear transformations of the Michaelis–Menten equation that they initially introduced. However, Haldane indicated in 1957 that Woolf had indeed found the three linear forms:In 1932, Dr. Kurt Stern published a German translation of my book Enzymes, with numerous additions to the English text. On pp. 119–120, I described some graphical methods, stating that they were due to my friend Dr. Barnett Woolf. [...] Woolf pointed out that linear graphs are obtained when is plotted against , against , or against , the first plot being most convenient unless inhibition is being studied.

Derivation of the equation for the plot

is the Michaelis-Menten equation, which can be written as follows:

approaches infinity, or limiting rate, known as the Michaelis constant. Eadie and Hofstee transformed this into straight-line relationship gives:

This can be directly rearranged to express a straight-line relationship:

(Hofstee plot).

In the Eadie plot the axes are reversed:

These plots are kinetic versions of the Scatchard plot used in ligand-binding experiments.

Attribution to Augustinsson

The plot is occasionally attributed to Augustinsson and referred to the Woolf–Augustinsson–Hofstee plot or simply the Augustinsson plot. equation, both the work of Haldane and of Eadie are cited at other places of his work and are listed in his bibliography.

Effect of experimental error

is the dependent variable. are subject to experimental error, and so the deviations that occur due to error are not parallel with the ordinate axis but towards or away from the origin. As long as the plot is used for illustrating an analysis rather than for estimating the parameters, that matters very little. Regardless of these considerations various authors have compared the suitability of the various plots for displaying and analysing data.

Use for estimating parameters

, but has been largely superseded by nonlinear regression methods that are significantly more accurate when properly weighted and no longer computationally inaccessible.

Making faults in experimental design visible

one can see at a glance at an Eadie–Hofstee plot how well the experimental design (left-hand diagram) is less common but not unknown, as for example in a study of nitrate reductase.