Enzyme kinetics data plotting: Why are Woolf–Augustinsson–Hofstee (v vs. v/[S]) and Eadie–Scatchard (v/[S] vs. v) plots often considered more reliable than reciprocal plots when measurement error in v is significant?

Introduction / Context:
In enzyme kinetics, transforming data to linear plots can aid parameter estimation. However, transformations also propagate measurement errors in different ways. Choosing a plot that minimizes error distortion improves reliability of Vmax and Km estimation.

Given Data / Assumptions:

• Measured variable v (initial rate) has experimental error.
• Lineweaver–Burk uses 1/v vs. 1/[S].
• Woolf–Augustinsson–Hofstee uses v vs. v/[S].
• Eadie–Scatchard uses v/[S] vs. v.

Concept / Approach:

Reciprocal transformations amplify relative error when the measured quantity is in the denominator. If v is small (low [S]) and noisy, 1/v becomes very large, spreading points and overweighting low-rate data. Hofstee and Eadie–Scatchard plots avoid placing v in the denominator, thus reducing error magnification and often giving more stable visual fits.

Step-by-Step Solution:

Verification / Alternative check:

Many biochemistry texts recommend direct nonlinear regression on the Michaelis–Menten equation as best practice, citing linear plots primarily for didactic use; among linear options, nonreciprocal plots are less distortionary.

Why Other Options Are Wrong:

(a) The premise states significant v error, so this is incorrect. (c) Reliability is affected by transformation. (d) Downplays the general advantage when v error is significant. (e) Incorrect: these plots avoid reciprocals of v.

Common Pitfalls:

Assuming any linearization is equally valid; over-reliance on Lineweaver–Burk can bias parameter estimates; forgetting homoscedasticity assumptions in linear regression.

Final Answer:

Because they avoid taking reciprocals of v, which magnify error when v has significant uncertainty