Hanes–Woolf plot

In biochemistry, a Hanes–Woolf plot, Hanes plot, or plot of ${\displaystyle a/v}$ against ${\displaystyle a}$ is a graphical representation of enzyme kinetics in which the ratio of the initial substrate concentration ${\displaystyle a}$ to the

${\displaystyle v}$

${\displaystyle a}$

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

where ${\displaystyle K_{\mathrm {m} }}$ is the

${\displaystyle V}$

Hanes said that the use of linear regression to determine kinetic parameters from this type of linear transformation is flawed, because it generates the best fit between observed and calculated values of ${\displaystyle 1/v}$, rather than ${\displaystyle v}$.

Starting from the Michaelis–Menten equation:

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

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

${\displaystyle {1 \over v}={1 \over V}+{K_{\mathrm {m} } \over V}}$ · ${\displaystyle {1 \over a}}$

which can be rearranged to express a different straight-line relationship:

${\displaystyle {a \over v}={{a(K_{\mathrm {m} }+a)} \over {Va}}={{(K_{\mathrm {m} }+a)} \over {V}}}$

which can be rearranged to give

${\displaystyle {a \over v}={1 \over V}}$ · ${\displaystyle a+{K_{\mathrm {m} } \over V}}$

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K_{\mathrm {m} }}$, ${\displaystyle V}$ and '${\displaystyle V/K_{\mathrm {m} }}$, but it has been largely superseded by nonlinear regression methods that are significantly more accurate and no longer computationally inaccessible. It remains useful, however, as a means to present data graphically.

See also

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

References