An uncompetitive inhibitor interacts with the enzyme-substrate complex, but not with the enzyme alone. For uncompetitive inhibition, the double-reciprocal equation is as follows:
1/V_{0} = α’/V_{max} + K_{m}/V_{max} • 1/[S]
where α’ = 1+[I]/K’_{I}
This equation shows that a double-reciprocal plot of enzyme kinetic data with varying concentrations of an uncompetitive inhibitor should give a straight line with varying y-intercepts, but with the same slopes (Figure 1). In enzyme kinetic assays with an uncompetitive inhibitor, the apparent K_{m} and V_{max} will change with increasing inhibitor concentrations [1].
Figure 1: a) Lineweaver-Burk plot showing the uncompetitive inhibition. b) y-intercepts of each linear regression plotted against the inhibitor concentration.
When working with an uncompetitive inhibitor, no parameters can be calculated from the initial Lineweaver-Burk plots. To calculate the different parameters, the ‘’y-intercepts’’ of these plots must be plotted against the inhibitor concentration:
y-intersect_{uncompettive} = α’/V_{max} = 1/V_{max} + 1/V_{max} • 1/K_{I} • [I]
This plot should, therefore, result in a straight line with the intercept 1/max and slope 1 / (V_{max} • K_{I} ). K_{I} can, therefore, be calculated by dividing the slope of this straight line with the intercept. V_{max} can also be calculated from this fit, by taking the reciprocal to the y-intercept. Because the initial Lineweaver-Burk plots had the same slopes, K_{m} / V_{max}, K_{m} can now be calculated by multiplying these slopes with V_{max} obtained from the plot of y-intercepts against inhibitor concentrations.
Prepare Lineweaver-Burk plots of the kinetic data and fit the data using linear regression (1 fit per inhibitor concentration).
Plot the y-intercepts of each of these fits as a function of the inhibitor concentration.
To calculate V_{max}, take the reciprocal of the y-intercept of this plot.
To calculate K_{I}, divide the y-intercept of this plot with the slope.
To calculate K_{m}, go back to the first Lineweaver-Burk plots, take the slope from 1 of these plots (the slope should be the same, or close, for all the plots), and multiply it with V_{max}.