GATE BT 2026 • Q21
MCQ • 1 Mark
Section 2: General Biotechnology
Biomolecules, enzyme kinetics
Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
The catalytic efficiency of an enzyme following Michaelis -Menten kinetics is
defined by
Options:
-
(A) kCat
-
(B) Vmax / kCat
-
(C) kCat / KM
-
(D) kCat / Vmax
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2026 Q.21)**
**1. Governing Concept**:
- **Topic**: Enzyme Kinetics & Catalytic Efficiency ($k_{\text{cat}}/K_m$)
- For an enzyme obeying Michaelis-Menten kinetics:
$v_0 = \frac{k_{\text{cat}} [E]_t [S]}{K_m + [S]}$
- At low substrate concentrations ($[S] \ll K_m$):
$v_0 \approx \left(\frac{k_{\text{cat}}}{K_m}\right) [E]_t [S] = \left(\frac{k_{\text{cat}}}{K_m}\right) [E] [S]$
- The second-order rate constant **$\frac{k_{\text{cat}}}{K_m}$** represents the **catalytic efficiency** (or specificity constant) of the enzyme:
- Measures how efficiently the enzyme converts substrate into product when substrate is limiting.
- The theoretical upper physical limit is set by the diffusion-controlled collision rate of enzyme and substrate in aqueous solution ($10^8 - 10^9\text{ M}^{-1}\text{s}^{-1}$, "kinetic perfection").
**2. Option Analysis**:
- **Option (A) [$V_{\max} / K_m$] is INCORRECT**: Depends on total enzyme concentration $[E]_t$; catalytic efficiency is an intrinsic intensive constant ($k_{\text{cat}}/K_m$).
- **Option (B) [$k_{\text{cat}} \times K_m$] is INCORRECT**: Product of parameters is kinetically meaningless.
- **Option (C) [$k_{\text{cat}} / K_m$] is CORRECT**: Canonical biochemical definition of enzyme catalytic efficiency.
- **Option (D) [$K_m / k_{\text{cat}}$] is INCORRECT**: Reciprocal of catalytic efficiency.
**3. Final Answer**:
- **Correct Choice**: **C**
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