Inbiochemistry, aHanes–Woolf plot,Hanes plot, orplot of${\displaystyle a/v}$ against${\displaystyle a}$ is a graphical representation ofenzyme kinetics in which the ratio of the initial substrate concentration${\displaystyle a}$ to thereaction velocity${\displaystyle v}$ is plotted against${\displaystyle a}$. It is based on the rearrangement of theMichaelis–Menten equation shown below:

${\displaystyle \frac{a}{v}=\frac{a}{V}+\frac{K_{\mathrm{m}}}{V}}$

where${\displaystyle K_{\mathrm{m}}}$ is theMichaelis constant and${\displaystyle V}$ is the limiting rate.^[1]

J. B. S. Haldane stated, reiterating what he and K. G. Stern had written in their book,^[2] that this rearrangement was due toBarnet Woolf.^[3] However, it was just one of three transformations introduced by Woolf. It was first published by C. S. Hanes, though he did not use it as a plot.^[4] Hanes noted that the use of linear regression to determine kinetic parameters from this type of linear transformation generates the best fit between observed and calculated values of${\displaystyle 1/v}$, rather than${\displaystyle v}$.^[4]: 1415

Starting from the Michaelis–Menten equation:

${\displaystyle v=\frac{Va}{K_{\mathrm{m}}+a}}$

we can take reciprocals of both sides of the equation to obtain the equation underlying theLineweaver–Burk plot:

${\displaystyle \frac{1}{v}=\frac{1}{V}+\frac{K_{\mathrm{m}}}{V}\cdot \frac{1}{a}}$

which can be multiplied on both sides by${\displaystyle a}$ to give

${\displaystyle \frac{a}{v}=\frac{1}{V}\cdot a+\frac{K_{\mathrm{m}}}{V}}$

Thus in the absence of experimental error data a plot of${\displaystyle a/v}$ against${\displaystyle a}$ yields a straight line of slope${\displaystyle 1/V}$, an intercept on the ordinate of${\displaystyle K_{\mathrm{m}}/V}$and an intercept on the abscissa of${\displaystyle -K_{\mathrm{m}}}$.

Like other techniques that linearize the Michaelis–Menten equation, the Hanes–Woolf plot was used historically for rapid determination of the kinetic parameters${\displaystyle K_{\mathrm{m}}}$,${\displaystyle V}$ and${\displaystyle K_{\mathrm{m}}/V}$, but it has been largely superseded bynonlinear regression methods that are significantly more accurate and no longer computationally inaccessible. It remains useful, however, as a means to present data graphically.

• Michaelis–Menten kinetics
• Lineweaver–Burk plot
• Eadie–Hofstee plot
• Direct linear plot

• Plots (graphics)
• Enzyme kinetics
• Eponyms in biology
• Eponymous diagrams of chemistry

• Articles with short description
• Short description matches Wikidata