Consider a simple uni-substrate enzyme that follows Michaelis-Menten kinetics. When the
enzyme catalyzed reaction was carried out in the presence of 10 nM concentration of an
inhibitor, there was no change in the maximal velocity. However, the slope of the
Lineweaver-Burk plot increased 3-fold. The dissociation constant for the enzyme-inhibitor
complex (in nM) is _________
Official Answer Key:
5 to
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2018 Q.63)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: BT
- **Question Type**: **NAT** (52 Marks)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Mathematical & Quantitative Formulation**:
- Problem Statement: *"Consider a simple uni-substrate enzyme that follows Michaelis-Menten kinetics. When the
enzyme catalyzed reaction was carried out in the presence of 10 nM concentration of an
inhibitor, there was no change in the maxima..."*
- 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**: **5 to**.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **5 to**
- **Scoring Criteria**: 52 Marks (Negative marking: -0.0 marks).
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