What Happens When the Wrong Equation is Fitted to Data?

A common variant of the Michaelis-Menten model of enzyme kinetics involves inhibition by excess substrate. This phenomenon is known as substrate inhibition and the mathematical description of it requires an inhibition constant (Ki) as well as the usual kinetic parameters (Km and Vmax). Fitting the 3-parameter substrate inhibition expression to data that might reasonably be described by the 2-parameter Michaelis-Menten model yields biased estimates of Km and Vmax. Numerical simulations demonstrate that the extent of the bias is related to the magnitude of the estimated Ki. The quality of the data is particularly important in determining the size of Ki and, therefore, in the bias of the other parameters. Consideration of the residuals, statistical justification of the inclusion of extra parameters and reporting of the estimated values should be matters of routine. The estimates of Km and Vmax obtained from a three-parameter substrate inhibition model can only be compared with the corresponding estimates from the two-parameter Michaelis-Menten model with caution.