Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
An enzyme (E) catalyzes the biochemical reaction
AB→ with
catk equal to
1500 s-
. If the initial reaction velocity (
0V ) is
110 . Ms - at the total enzyme
concentration [
tE ] of
30 nM and substrate concentration [A] of
40 M , the
value of
mK (in
M ) is ____________.
Official Answer Key:
20 to 20
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2023 Q.54)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: BT
- **Question Type**: **NAT** (2 Marks)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Mathematical & Quantitative Formulation**:
- Problem Statement: *"An enzyme (E) catalyzes the biochemical reaction
AB→ with
catk equal to
1500 s-
. If the initial reaction velocity (
0V ) is
110 . Ms - at the total enzyme
concentration [
tE ] of
30 nM and substrate concentration..."*
- Identifying governing bioprocess / mathematical relation:
- Following standard Michaelis-Menten enzyme kinetics:
$v = \frac{V_{max}[S]}{K_m + [S]}$
where $K_m$ is the substrate concentration at which reaction rate is half of $V_{max}$.
$k_{cat} = \frac{V_{max}}{[E]_0}, \quad \text{Catalytic Efficiency} = \frac{k_{cat}}{K_m}$
- **Calculated Quantitative Value**: **20 to 20**.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **20 to 20**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.0 marks).
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