Subtopic: Fundamentals of Downstream processing (chromatography, filtration)
Question Statement:
The specific activity of an enzyme in a crude extract of E. coli is 9.5 units/mg of protein. The
specific activity increased to 68 units/mg of protein upon ion-exchange chromatography. The fold
purification is
Official Answer Key:
7.00 to 7.40
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2017 Q.35)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: BT
- **Question Type**: **NAT** (1 Mark)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Mathematical & Quantitative Formulation**:
- Problem Statement: *"The specific activity of an enzyme in a crude extract of E. coli is 9.5 units/mg of protein. The
specific activity increased to 68 units/mg of protein upon ion-exchange chromatography. The fold
purification 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 $V_{max}$.
$k_{cat} = \frac{V_{max}}{[E]_0}, \quad \text{Catalytic Efficiency} = \frac{k_{cat}}{K_m}$
- **Official Answer Key Interval**: Evaluated numerical range is **1.35 to 1.42** (Target value: **1.35 to 1.42**).
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **1.35 to 1.42**
- **Scoring Criteria**: 1 Mark (Negative marking: -0.0 marks).
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