In biochemistry, an Eadie–Hofstee diagram (also Woolf–Eadie–Augustinsson–Hofstee or Eadie–Augustinsson plot) is a graphical representation of enzyme kinetics.

## Description

In the diagram the reaction rate is plotted as a function of the ratio between rate and substrate concentration:

$v=-K_{M}{v \over [S]}+V_{\max }$ where v represents reaction rate, KM is the Michaelis–Menten constant, [S] is the substrate concentration, and Vmax is the maximum reaction rate.

It can be derived from the Michaelis–Menten equation as follows:

$v={{V_{\max }{}[S]} \over {K_{M}+[S]}}$ invert and multiply with $V_{\max }$ :

${V_{\max } \over v}={{V_{\max }{}(K_{M}+[S])} \over {V_{\max }{}[S]}}={{K_{M}+[S]} \over {[S]}}$ Rearrange:

$V_{\max }={{{vK_{M}} \over {[S]}}+{{v[S]} \over {[S]}}}={{vK_{M}} \over {[S]}}+v$ Isolate v:

$v=-K_{M}{v \over {[S]}}+V_{\max }$ A plot of v against v/[S] will hence yield Vmax as the y-intercept, Vmax/KM as the x-intercept, and KM as the negative slope.

## Usage

Like other techniques that linearize the Michaelis–Menten equation, the Eadie–Hofstee plot was used historically for rapid identification of important kinetic terms like KM and Vmax, but has been superseded by nonlinear regression methods that are significantly more accurate and no longer computationally inaccessible. It is also more robust against error-prone data than the Lineweaver–Burk plot, particularly because it gives equal weight to data points in any range of substrate concentration or reaction rate. (The Lineweaver–Burk plot unevenly weights such points.) Both plots remain useful as a means to present data graphically.

## Drawback

One drawback from the Eadie–Hofstee approach is that neither ordinate nor abscissa represent independent variables: both are dependent on reaction rate. Thus any experimental error will be present in both axes. Also, experimental error or uncertainty will propagate unevenly and become larger over the abscissa thereby giving more weight to smaller values of v/[S]. Therefore, the typical measure of goodness of fit for linear regression, the correlation coefficient R, is not applicable.