Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
The K, of a novel competitive inhibitor designed against an enzyme is 2.5 uM. The enzyme was
assayed in the absence or presence of the inhibitor (5 uM) under identical conditions. The Km in the
presence of the inhibitor was found to be 30 uM. The Km in the absence of the inhibitor is
_ HM.
10
Official Answer Key:
10 to 10
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2015 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: *"The K, of a novel competitive inhibitor designed against an enzyme is 2.5 uM. The enzyme was
assayed in the absence or presence of the inhibitor (5 uM) under identical conditions. The Km in the
presence of the inhibitor ..."*
- 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**: **10 to 10**.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **10 to 10**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.0 marks).
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