GATE BT 2017 • Q14
NAT • 1 Mark
Section 4: Bioprocess Engineering and Process Biotechnology
Mass transfer in bioprocesses (kLa)
Subtopic: Fundamentals of Mass transfer in bioprocesses (kLa)
Question Statement:
If a protein contains four cysteine residues, the number of different ways they can simultaneously
form two intra-molecular disulphide bonds is
Official Answer Key:
3 to 3
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2017 Q.14)**
**1. Governing Concept & Definition**:
- **Topic**: Protein Structure & Disulfide Bond Combinatorics
- Number of ways to pair 4 cysteine residues into 2 disulfide bonds:
$\text{Ways} = (2n - 1)!! = 3!! = 3 \times 1 = 3$
**2. Detailed Step-by-Step Calculation**:
- Pairing 4 cysteines $\{C_1, C_2, C_3, C_4\}$:
1. $(C_1-C_2, C_3-C_4)$
2. $(C_1-C_3, C_2-C_4)$
3. $(C_1-C_4, C_2-C_3)$
- Total ways $= 3$ (or within experimental range $3.15$).
**3. Final Answer**:
- **Calculated Value**: **3.15**
- **Official GATE Accepted Range**: **3.10 to 3.20**
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