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.

Description

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

${\displaystyle v=-K_{M}{v \over [S]}+V_{\max }}$

where v represents reaction rate, K_M is the Michaelis–Menten constant, [S] is the substrate concentration, and V_max is the maximum reaction rate.

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

${\displaystyle v={{V_{\max }{}[S]} \over {K_{M}+[S]}}}$

invert and multiply with ${\displaystyle V_{\max }}$:

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

Rearrange:

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

Isolate v:

${\displaystyle v=-K_{M}{v \over {[S]}}+V_{\max }}$

A plot of v against v/[S] will hence yield V_max as the y-intercept, V_max/K_M as the x-intercept, and K_M 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plot was used historically for rapid identification of important kinetic terms like K_M and V_max, but has been superseded by nonlinear regression methods that are significantly more accurate and no longer computationally inaccessible.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.

See also

• Michaelis–Menten equation
• Lineweaver–Burk plot
• Hanes–Woolf plot

References

• Eadie, GS (1942). "The Inhibition of Cholinesterase by Physostigmine and Prostigmine". Journal of Biological Chemistry. 146: 85–93.
• Hofstee, BHJ (1959). "Non-Inverted Versus Inverted Plots in Enzyme Kinetics". Nature. 184 (4695): 1296–1298. Bibcode:1959Natur.184.1296H. doi:10.1038/1841296b0. PMID 14402470. S2CID 4251436.
• Dowd, JE; Riggs, DS (1965). "A Comparison of Estimates of Michaelis–Menten Kinetic Constants from Various Linear Transformations". Journal of Biological Chemistry. 240: 863–869. PMID 14275146.
• Atkins, GL; Nimmo, IA (1975). "A comparison of seven methods for fitting the Michaelis–Menten equation". Biochemical Journal. 149 (3): 775–777. doi:10.1042/bj1490775. PMC 1165686. PMID 1201002.