Under Michaelis–Menten kinetics, the initial velocity v0 approaches V max under which limiting condition on substrate concentration?

Introduction / Context:In saturation kinetics, the rate approaches a maximum as substrate becomes abundant. Recognizing the limiting regime that yields v0 ≈ V max is essential for interpreting enzyme experiments and plotting transformations.

Given Data / Assumptions:

• Michaelis–Menten rate law: v = (Vmax * [S]) / (Km + [S]).
• Vmax reflects catalytic capacity at saturating [S].
• We examine limiting behavior as [S] varies relative to Km.

Concept / Approach:When [S] ≫ Km, the denominator Km + [S] ≈ [S], so v ≈ Vmax * [S]/[S] = Vmax. Equivalently, 1/[S] → 0 on a Lineweaver–Burk plot drives the intercept toward 1/Vmax.

Step-by-Step Solution:

Verification / Alternative check:Experimental saturation curves flatten as [S] increases; Eadie–Hofstee plots show approach to Vmax as v stabilizes at high [S].

Why Other Options Are Wrong:

• [S] = Km gives v = 0.5 * Vmax.
• [S] = 10 * Km gives ~0.91 * Vmax, close but not the limiting definition.
• 1/[S] = 1/Km corresponds to [S] = Km (half-maximal).
• [S] = 0.1 * Km is far from saturation.

Common Pitfalls:Equating “large” (e.g., 10 * Km) with the strict mathematical limit; the definition uses the limit [S] ≫ Km.

Final Answer:1/[S] → 0 (i.e., [S] ≫ Km)