Hanes–Woolf plot explained

In biochemistry, a Hanes–Woolf plot, Hanes plot, or plot of

a/v

against

is a graphical representation of enzyme kinetics in which the ratio of the initial substrate concentration
a

to the reaction velocity
v

is plotted against
a

. It is based on the rearrangement of the Michaelis–Menten equation shown below:

{a\overv}={a\overV}+{K_m\overV}

where

K_m

is the Michaelis constant and

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 to Barnet 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

1/v

, rather than

Starting from the Michaelis–Menten equation:

v={{Va}\over{K_m+a}}

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

{1\overv}={1\overV}+{K_m\overV} ⋅ {1\overa}

which can be multiplied on both sides by

{a}

to give

{a\overv}={1\overV} ⋅ a+{K_m\overV}

Thus in the absence of experimental error data a plot of

{a/v}

against

{a}

yields a straight line of slope

1/V

, an intercept on the ordinate of

{K_m/V}

and an intercept on the abscissa of

-K_m

Like other techniques that linearize the Michaelis–Menten equation, the Hanes–Woolf plot was used historically for rapid determination of the kinetic parameters

K_m

and

K_m/V

, but it has been largely superseded by nonlinear regression methods that are significantly more accurate and no longer computationally inaccessible.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.

Notes and References

The term maximum rate is often used, but not recommended by the IUBMB; see Cornish-Bowden . A . Persp. Sci. . 2014 . 1 . 74–87 . Current IUBMB recommendations on enzyme nomenclature and kinetics . 10.1016/j.pisc.2014.02.006. free .
Book: Haldane . John Burdon Sanderson . J. B. S. Haldane . Stern . Kurt Günter . Allgemeine Chemie der Enzyme . Theodor Steinkopff . Dresden and Leipzig . 28 . . 1932 . 119-120 . 964209806.
Haldane . John Burdon Sanderson . J. B. S. Haldane . Graphical methods in enzyme chemistry . . 179 . 4564 . 832-832 . 10.1038/179832b0 . 1957 . 1957Natur.179R.832H . 4162570 . free.
Hanes, Charles Samuel . Studies on plant amylases: The effect of starch concentration upon the velocity of hydrolysis by the amylase of germinated barley . Biochemical Journal . 26 . 5 . 1406-1421 . 10.1042/bj0261406 . 1932 . 16744959 . 1261052.

Hanes–Woolf plot explained

See also

Notes and References