![21. An enzymatic reaction exhibits Michaelis-Menten kinetics. For this reaction, on doubling the concentration of enzyme while maintaining [S] >> [E0], (a) Both Km and Vmax will remain the same. (b) Km will remain the same but Vmax will increase. (c) Km will increase but Vmax will remain the same.](https://www.letstalkacademy.com/wp-content/uploads/2026/01/slide_21-14.png)
21. An enzymatic reaction exhibits Michaelis-Menten kinetics. For this reaction, on doubling the
concentration of enzyme while maintaining [S] >> [E0],
(a) Both Km and Vmax will remain the same.
(b) Km will remain the same but Vmax will increase.
(c) Km will increase but Vmax will remain the same.
Correct Answer
(b) Km will remain the same but Vmax will increase
Under classical Michaelis-Menten assumptions, when substrate concentration is saturating ([S] >> [E0]), doubling enzyme concentration increases total catalytic capacity while Km stays constant.
Michaelis-Menten Basics
Michaelis-Menten kinetics describes enzyme-driven reactions and uses the relationship:
v = (Vmax × [S]) / (Km + [S])
- v = reaction velocity
- Vmax = maximum velocity
- [S] = substrate concentration
- Km = Michaelis constant
The key proportionality is:
Vmax = kcat × [E0]
Vmax depends directly on total enzyme concentration ([E0]), but:
Km is independent of enzyme concentration because it reflects enzyme–substrate affinity.
Correct Answer Explanation
Doubling enzyme concentration provides twice as many active sites. Under saturating substrate conditions, every enzyme molecule is working at full capacity.
- Vmax doubles because it is proportional to total enzyme.
- Km stays unchanged because affinity does not depend on enzyme amount.
This conclusion follows the steady-state approximation where [S] >> [E0].
Option Analysis
Option (a)
Km and Vmax remain the same — Incorrect
Vmax must increase because adding enzyme increases maximum catalytic capacity.
Option (c)
Km increases, Vmax stays same — Incorrect
Km is an intrinsic constant and Vmax rises with increasing enzyme concentration.
Key Implications
| Parameter | Effect of Doubling [E0] | Reason | Condition |
|---|---|---|---|
| Vmax | Increases (doubles) | Vmax = kcat × [E0] | [S] >> [E0] |
| Km | No change | Affinity constant | Independent of [E0] |
In a Lineweaver–Burk plot, doubling enzyme shifts the y-intercept (1/Vmax) downward but leaves the x-intercept (−1/Km) unchanged.
