Effect of Changing Kinetic Parameters: For an enzyme with Km = 10 mM and Vmax = 100 mmol/min, at [S] = 100 mM, which statements about velocity changes are correct?

Introduction:
This problem applies the Michaelis–Menten equation to assess how changes in Vmax and Km affect reaction velocity at a fixed substrate concentration. It tests quantitative intuition at saturating and near-saturating conditions.

Given Data / Assumptions:

• Km = 10 mM.
• Vmax = 100 mmol/min.
• [S] = 100 mM.
• Single-substrate Michaelis–Menten kinetics.

Concept / Approach:

Use v = Vmax * [S] / (Km + [S]). At [S] ≫ Km, velocity approaches Vmax, so changes in Vmax have roughly proportional effects. Decreasing Km at fixed [S] increases the fraction [S]/(Km + [S]), raising v but with diminishing returns as [S] greatly exceeds Km.

Step-by-Step Solution:

Verification / Alternative check:

Limiting case logic: as [S] → ∞, v → Vmax; thus scaling Vmax scales v. Reducing Km increases saturation fraction toward 1, raising velocity until limited by Vmax.

Why Other Options Are Wrong:

D: Increasing Vmax cannot decrease v; it raises the upper limit. E: Contradicts calculations showing both effects increase v.

Common Pitfalls:

Assuming that once [S] ≫ Km, changing Km has no effect; it still slightly increases v unless saturation is complete.

Final Answer:

Both (a) and (b)