Hanes-Woolf plot
Encyclopedia
In biochemistry
, a Hanes–Woolf plot is a graphical representation of enzyme kinetics
in which the ratio of the initial substrate concentration [S] to the reaction velocity v is plotted against [S]. It is based on the rearrangement of the Michaelis–Menten equation shown below:
where Km is the Michaelis–Menten constant and Vmax is the maximum reaction velocity. It was first described by Barnet Woolf. Charles Samuel Hanes subsequently pointed out 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 1/v, rather than v.
The equation can be derived from the Michaelis–Menten equation as follows:
invert and multiply by [S]:
Rearrange:
As is clear from the equation, perfect data will yield a straight line of slope 1/Vmax, a y-intercept of Km/Vmax and an x-intercept of −Km.
Like other techniques that linearize the Michaelis–Menten equation, the Hanes–Woolf plot was used historically for rapid determination of the important kinetic parameters Km, Vmax and Vmax/Km, but it has been superseded by nonlinear regression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.
One drawback of the Hanes–Woolf approach is that neither ordinate
nor abscissa
represent independent variable
s: both are dependent on substrate concentration. As a result, the typical measure of goodness of fit, the correlation coefficient R, is not applicable.
Biochemistry
Biochemistry, sometimes called biological chemistry, is the study of chemical processes in living organisms, including, but not limited to, living matter. Biochemistry governs all living organisms and living processes...
, a Hanes–Woolf plot is a graphical representation of enzyme kinetics
Enzyme kinetics
Enzyme kinetics is the study of the chemical reactions that are catalysed by enzymes. In enzyme kinetics, the reaction rate is measured and the effects of varying the conditions of the reaction investigated...
in which the ratio of the initial substrate concentration [S] to the reaction velocity v is plotted against [S]. It is based on the rearrangement of the Michaelis–Menten equation shown below:
where Km is the Michaelis–Menten constant and Vmax is the maximum reaction velocity. It was first described by Barnet Woolf. Charles Samuel Hanes subsequently pointed out 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 1/v, rather than v.
The equation can be derived from the Michaelis–Menten equation as follows:
invert and multiply by [S]:
Rearrange:
As is clear from the equation, perfect data will yield a straight line of slope 1/Vmax, a y-intercept of Km/Vmax and an x-intercept of −Km.
Like other techniques that linearize the Michaelis–Menten equation, the Hanes–Woolf plot was used historically for rapid determination of the important kinetic parameters Km, Vmax and Vmax/Km, but it has been superseded by nonlinear regression
Nonlinear regression
In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables...
methods that are significantly more accurate and no longer computationally inaccessible. It remains useful, however, as a means to present data graphically.
One drawback of the Hanes–Woolf approach is that neither ordinate
Ordinate
In mathematics, ordinate refers to that element of an ordered pair which is plotted on the vertical axis of a two-dimensional Cartesian coordinate system, as opposed to the abscissa...
nor abscissa
Abscissa
In mathematics, abscissa refers to that element of an ordered pair which is plotted on the horizontal axis of a two-dimensional Cartesian coordinate system, as opposed to the ordinate...
represent independent variable
Independent variable
The terms "dependent variable" and "independent variable" are used in similar but subtly different ways in mathematics and statistics as part of the standard terminology in those subjects...
s: both are dependent on substrate concentration. As a result, the typical measure of goodness of fit, the correlation coefficient R, is not applicable.