- Hanes–Woolf plot
In
biochemistry , a Hanes-Woolf plot is a graphical representation ofenzyme kinetics in which the ratio of the initial substrate concentration [S] to thereaction velocity "v" is plotted against [S] . It is based on the rearrangement of the Michaelis-Menten equation shown below::S] over v } = { [S] over V_{max} } + { K_m over V_{max} }
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:
:v = V_{max} [S] } over {K_m + [S]
invert and multiply with S] :
:S] over v} = [S] (K_m+ [S] )}over{V_{max} [S] = K_m+ [S] }over{V_{max}
Rearrange:
:S] over v} = [S] *{1 over V_{max + {K_m over V_{max
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historically for rapid determination of the important kinetic parameters "Km", "Vmax" and "Vmax/Km", but it has been superseded bynonlinear regression methods that are significantly more accurate and no longer computationally inaccessible.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 norabscissa representindependent 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.ee also
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Michaelis–Menten kinetics
*Lineweaver–Burk plot
*Eadie-Hofstee diagram References
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