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.
Attribution to Woolf is often omitted, because although Haldane and Stern[1] 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:[2]In 1932, Dr. Kurt Stern published a German translation of my book Enzymes, with numerous additions to the English text.
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
, the first plot being most convenient unless inhibition is being studied.The simplest equation for the rate
of an enzyme-catalysed reaction as a function of the substrate concentration
is the Michaelis-Menten equation, which can be written as follows: in which
is the rate at substrate saturation (when
approaches infinity, or limiting rate, and
Eadie[3] and Hofstee[4] transformed this into straight-line relationship.
gives: This can be directly rearranged to express a straight-line relationship: which shows that a plot of
is a straight line with intercept
In the Eadie plot the axes are reversed: with intercept
These plots are kinetic versions of the Scatchard plot used in ligand-binding experiments.
The plot is occasionally attributed to Augustinsson[5] and referred to the Woolf–Augustinsson–Hofstee plot[6][7][8] or simply the Augustinsson plot.
[9] However, although Haldane, Woolf or Eadie were not explicitly cited when Augustinsson introduced the
equation, both the work of Haldane[10] and of Eadie[3] are cited at other places of his work and are listed in his bibliography.
[5]: 169 and 171 Experimental error is usually assumed to affect the rate
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[12][13][14] have compared the suitability of the various plots for displaying and analysing data.
Like other straight-line forms of the Michaelis–Menten equation, the Eadie–Hofstee plot was used historically for rapid evaluation of the parameters
, but has been largely superseded by nonlinear regression methods that are significantly more accurate when properly weighted and no longer computationally inaccessible.
As the ordinate scale spans the entire range of theoretically possible
one can see at a glance at an Eadie–Hofstee plot how well the experimental design fills the theoretical design space, and the plot makes it impossible to hide poor design.
By contrast, the other well known straight-line plots make it easy to choose scales that suggest that the design is better than it is.
Faulty design, as shown in the right-hand diagram, is common with experiments with a substrate that is not soluble enough or too expensive to use concentrations above
(left-hand diagram) is less common but not unknown, as for example in a study of nitrate reductase.
