First order deactivation rate constants for soluble and immobilized amyloglucosidase
enzyme are 0.03 min-1 and 0.005 min-1, respectively. The ratio of half-life of the immobilized
enzyme to that of the soluble enzyme is (rounded off to the nearest integer) _________
Official Answer Key:
6 to
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2018 Q.62)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: BT
- **Question Type**: **NAT** (62 Marks)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Mathematical & Quantitative Formulation**:
- Problem Statement: *"First order deactivation rate constants for soluble and immobilized amyloglucosidase
enzyme are 0.03 min-1 and 0.005 min-1, respectively. The ratio of half-life of the immobilized
enzyme to that of the soluble enzyme is..."*
- 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**: **6 to**.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **6 to**
- **Scoring Criteria**: 62 Marks (Negative marking: -0.0 marks).
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