Eadie-Hofstee diagram

In biochemistry, an Eadie-Hofstee diagram (also Woolf-Eadie-Augustinsson-Hofstee or Eadie-Augustinsson plot) is a graphical representation of enzyme kinetics in which reaction velocity is plotted as a function of the velocity vs. substrate concentration ratio:


 * $$v = -K_m { v \over [S] } + V_{max}$$

where v represents reaction velocity, Km is the Michaelis-Menten constant, [ S ] is the substrate concentration, and Vmax is the maximum reaction velocity.

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 vs v/[S]will yield Vmax at the intercept with the X-axis and the slope is -Km. 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plot was used historically for rapid identification of important kinetic terms like Km and Vmax, but has been superseded by nonlinear regression methods that are significantly more accurate and no longer computationally inaccessible.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 velocity. (The Lineweaver-Burk plot unevenly weights such points.) Both plots remain useful as a means to present data graphically.

One drawback from the Eadie-Hofstee approach is that neither ordinate nor abscissa represent independent variables: both are dependent on reaction velocity. Thus any experimental error will be present in both axes. Furthermore, the typical measure of goodness of fit, the correlation coefficient R, is not applicable.