![Q.25 For an enzyme following Michaelis-Menten kinetics, when [S]=KM then, the velocity v is ([S] is substrate concentration, KM is Michaelis constant, Vmax is maximal velocity) (A) [S] × Vmax (B) 0.75 × Vmax (C) 0.5 × Vmax (D) KM × Vmax](https://www.letstalkacademy.com/wp-content/uploads/2025/12/slide_25-5.jpg)
Q.25 For an enzyme following Michaelis–Menten kinetics, when [S]=KM then, the
velocity v is
([S] is substrate concentration, KM is Michaelis constant, Vmax is maximal
velocity)
(A) [S] × Vmax
(B) 0.75 × Vmax
(C) 0.5 × Vmax
(D) KM × Vmax
Enzyme Kinetics: Velocity When [S]=KM in Michaelis-Menten Equation
✅ Correct Answer: (C) 0.5 × Vmax
For an enzyme following Michaelis-Menten kinetics, the velocity v equals half of the maximum velocity (Vmax) precisely when the substrate concentration [S] matches the Michaelis constant KM.
Michaelis-Menten Equation
The Michaelis-Menten equation describes enzyme kinetics:
\[ v = \frac{V_{\max} [S]}{K_M + [S]} \]
Substituting [S] = KM yields:
\[ v = \frac{V_{\max} K_M}{K_M + K_M} = \frac{V_{\max} K_M}{2K_M} = 0.5 V_{\max} \]
KM represents the substrate concentration at which v reaches half of Vmax, reflecting enzyme-substrate affinity.
Option Analysis
(A) [S] × Vmax
Incorrect, as this lacks dimensional consistency and ignores saturation kinetics; velocity depends on fractional enzyme occupancy, not a direct product.
(B) 0.75 × Vmax
Incorrect; this occurs at [S] ≈ 3KM, where:
\[ v = \frac{V_{\max} \cdot 3K_M}{K_M + 3K_M} = 0.75 V_{\max} \]
(C) 0.5 × Vmax
✅ Correct, as derived directly from the equation when [S] = KM.
(D) KM × Vmax
Incorrect; this mixes concentration and velocity units without relation to the hyperbolic curve behavior.
Core Equation Breakdown
The Michaelis-Menten equation \( v = \frac{V_{\max} [S]}{K_M + [S]} \) models hyperbolic enzyme saturation. At [S]=KM, half the enzyme active sites bind substrate, yielding v = 0.5 Vmax—a defining property of KM.
Practical Implications
-
- KM measures enzyme-substrate affinity: lower KM signals higher affinity.
- Useful for plotting Lineweaver-Burk graphs:
\[ \frac{1}{v} = \frac{K_M}{V_{\max}} \cdot \frac{1}{[S]} + \frac{1}{V_{\max}} \]
- In biotech, guides dosing for half-maximal activity in reactions.
CSIR NET Exam Tips
| [S]/KM Ratio | Velocity (% Vmax) | Key Concept |
|---|---|---|
| 0.5 | 33% | Sub-KM kinetics |
| 1.0 | 50% | KM definition |
| 3.0 | 75% | High saturation |
| 9.0 | 90% | Near Vmax |
