The Michaelis–Menten Equation and Its Linear Transformations Revisited

Twelve published enzyme kinetic datasets were fitted with the Michaelis-Menten equation via non-linear regression and with linear transformations (Lineweaver-Burk, Eadie-Hofstee, and Hanes-Woolf) via linear regression to compare parameter estimates (V_max and K_M). Model performances were compared based on the sum of squared error values calculated on the untransformed scale. The best method to obtain V_max and K_M was to fit the Michaelis-Menten equation via nonlinear regression. Among linear transformations, the Hanes-Woolf yielding the closest estimates to the non-linear fit in seven out of 12 datasets, and the Eadie-Hofstee in five out of 12. Lineweaver-Burk, despite its widespread use, consistently performed the poorest, providing no closest estimates in any dataset. We concluded that the Lineweaver-Burk transformation may be utilized for data visualization; however, it is not recommended for estimating kinetic parameters, at least without weighted linear regression. If simple linear regression is to be employed for the determination of V_max and K_M, Hanes-Woolf transformation presents a preferable alternative, albeit with certain inherent limitations that must be considered. It can also be used for educational purposes (Excel solutions of this study are available at https://drive.google.com/drive/u/0/folders/1KfyvXTGG-3Hgc9MVlXiKQH1YHbpAYwNm for further reference). Researchers should apply non-linear regression to obtain V_max and K_M.