Section 4: Bioprocess Engineering and Process Biotechnology
Mass transfer in bioprocesses (kLa)
Subtopic: Fundamentals of Mass transfer in bioprocesses (kLa)
Question Statement:
You have purified an enzyme using a series of chromatographic methods. It was
observed that a 10 µg mL-1 of this purified enzyme converted 10 mM substrate per
hour at 25°C and pH 7. Its specific activity is _______ IU µg -1. (rounded off to
three decimal places)
Official Answer Key:
0.016 to 0.017
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2026 Q.35)**
**1. Governing Concept & Definition**:
- **Topic**: Biochemistry & Enzyme Specific Activity
- Specific activity is defined as units of enzymatic activity per mass of enzyme ($\text{IU }\mu\text{g}^{-1}$), where:
$1\text{ IU} = 1\text{ }\mu\text{mol substrate converted per minute}$
**2. Detailed Step-by-Step Calculation**:
- **Given**:
- Enzyme concentration = $10\text{ }\mu\text{g mL}^{-1}$
- Substrate converted = $10\text{ mM} = 10\text{ }\mu\text{mol mL}^{-1}$ in $1\text{ hour} = 60\text{ min}$
- **Step 1: Activity per mL of solution**:
$\text{Rate of conversion} = \frac{10\text{ }\mu\text{mol mL}^{-1}}{60\text{ min}} = \frac{1}{6}\text{ }\mu\text{mol min}^{-1}\text{mL}^{-1} = 0.1667\text{ IU mL}^{-1}$
- **Step 2: Specific Activity**:
$\text{Specific Activity} = \frac{0.1667\text{ IU mL}^{-1}}{10\text{ }\mu\text{g mL}^{-1}} = \frac{0.1667}{10} \approx 0.01667\text{ IU }\mu\text{g}^{-1} \approx 0.017\text{ IU }\mu\text{g}^{-1}$
**3. Final Answer**:
- **Calculated Value**: **0.017 IU µg⁻¹**
- **Official GATE Accepted Range**: **0.016 to 0.017**
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