A Simple Confidence Band for the Michaelis-Menten Equation

Analysis of enzyme kinetic data requires more than just comparisons of Kms and Vmaxs using the corresponding error estimates of the parameters. This approach is often employed, but it can prompt contradictory and misleading inferences that might be avoided using a confidence band. We derive expressions for the confidence band for the Michaelis-Menten rate equation that rely on estimates and variances of Km and Vmax. These can be expressed in terms of the substrate concentration or the rate of reaction. While these equations are simple, they are nonlinear, which reinforces the need to consider both parameters simultaneously. The equations show that the amplitude of the confidence interval ( ) passes through a maximum if the variance of the Km is sufficently large compared with the variance of Vmax. We illustrate the value of the expressions by applying them to comparisons of the kinetics of enzymes involved in nitrogen metabolism in parasites. These examples confirm that (i) the variance of the estimate of the Km has a particularly significant effect on and (ii) comparisons among Kms and among Vmaxs are not necessarily sufficient to determine the significance of differences in activity.