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/V0 = α’/Vmax + Km/Vmax • 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 Km and Vmax will change with increasing inhibitor concentrations [1].

To the left is a Lineweaver-Burk plot with 1 divided by V on the y-axis and 1 divided by the concentration of substrate on the x-axis. The plot is showing the uncompetitive inhibition as three different lines in the color green, blue, and red. These lines represent different plots with varying uncompetitive inhibitor concentrations and the lines have the same slopes. However, the three lines intersect at varying spots on the y-axis. The green line intersects with the y-axis at a higher value than the other two lines. The blue line intersects at a lower value on the y-axis than the green line, however, its intersection with the y-axis is higher than the red line, which is the line with the lowest y-intersect. To the right is another plot, showing the y-intersects of each linear regression plotted against the inhibitor concentration. The plot shows that as the inhibitor concentration increases, so do the y-intersect of the linear regression line

Figure 1: a) Lineweaver-Burk plot showing the uncompetitive inhibition. b) y-intercepts of each linear regression plotted against the inhibitor concentration.

Calculating K’I, Km and Vmax

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-intersectuncompettive = α’/Vmax = 1/Vmax + 1/Vmax • 1/KI • [I]

This plot should, therefore, result in a straight line with the intercept 1/max and slope 1 / (Vmax • KI ). KI can, therefore, be calculated by dividing the slope of this straight line with the intercept. Vmax 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, Km / Vmax, Km can now be calculated by multiplying these slopes with Vmax obtained from the plot of y-intercepts against inhibitor concentrations.

Steps of calculating the kinetic parameters when using an uncompetitive inhibitor

  • 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 Vmax, take the reciprocal of the y-intercept of this plot.

  • To calculate KI, divide the y-intercept of this plot with the slope.

  • To calculate Km, 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 Vmax.

References

  1. Lehninger, Albert L.; Nelson, David L.; Cox, Michael M. (2008). Principles of Biochemistry (5th ed.). New York, NY: W.H. Freeman and Company. ISBN 978-0-7167-7108-1.

Inhibitors

Theory overview