Problem-Based Learning for Calculating Kinetic Parameters from Michaelis-Menten Equation

Abstract

In “Advanced Enzymology” at the University of Barcelona, we teach various methods for identifying uni-uni irreversible reactions. Kinetic constants such as maximum velocity (Vmax) and Michaelis constant (Km) are calculated using non-linear regression with the Michaelis-Menten equation. However, if a computer is not available, students must calculate these kinetic parameters using linear regressions with Lineweaver-Burk, Eadie-Hofstee, and Hanes-Woolf plots. Michaelis-Menten equation: v = (Vmax [S]) / (Km + [S]), Lineweaver-Burk equation: 1/v = (Km/Vmax) (1/[S]) + 1/Vmax, Eadie-Hofstee equation: v = – Km (v/[S]) + Vmax, Hanes-Woolf equation: [S]/v = (1/Vmax) [S] + (Km/Vmax). The objective of this work was that students explore various methods for calculating kinetic constants and determine the most effective approach. A problem was prepared with data on substrate concentrations ([S]) and reaction rates (v). Data points with lower substrate concentration, and also with lower velocities had higher errors. The Michaelis-Menten plot provided only an approximate estimation of the kinetic constants, as it is not a linear graph. The Lineweaver-Burk plot generated maximum velocities that were too low due to the higher errors for low substrate concentrations, rendering impossible values of the kinetic parameters. The Eadie-Hofstee plot provided better results, as the values of v/[S] compensated their errors. Furthermore, kinetic constants were obtained directly from the slope and intersection of the line equation. The Hanes-Woolf plot also produced correct values for kinetic parameters, since high substrate concentrations were less erroneous than lower ones. After completing this computer class, students were very satisfied and learned the different methods for obtaining kinetic parameters. Non-linear regression is undoubtedly the most accurate method for obtaining kinetic parameters values. However, in the absence of computers, the Eadie-Hofstee plot is the best and most commonly used plot in kinetic papers.