Question Statement:
Consider the equation
2
aSV SbS c
Given a = 4, b = 1 and c = 9, the positive value of S at which V is maximum, will be _______.
Options:
-
(A) RSYRVA
-
(B) AVRYSR
-
(C) SRYVAR
-
(D) SVRRYA
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2016 Q.55)**
**1. Governing Concept & Question Classification**:
- **Section**: BT
- **Question Type**: **MCQ** (2 Marks)
- **Topic**: Biochemistry / Protein Chemistry (Peptide Sequencing by Enzymatic Cleavage)
**2. Detailed Step-by-Step Derivation**:
- We are given a hexapeptide (6 amino acids) with total composition:
$\{2\text{R}, \text{A}, \text{V}, \text{S}, \text{Y}\}$
- Let us analyze each enzymatic cleavage result:
1. **Carboxypeptidase A**: Cleaves from the C-terminus, but CANNOT cleave C-terminal basic residues (Arg, R, or Lys, K).
- Result: *“Digestion with carboxypeptidase A yields no cleavage product.”*
- This proves that the **C-terminal amino acid must be Arginine (R)**!
- Structure: $\text{X}_1\text{--X}_2\text{--X}_3\text{--X}_4\text{--X}_5\text{--R}$.
2. **Chymotrypsin**: Specifically cleaves on the carboxyl side of aromatic amino acids (Tyr, Y, Phe, Trp).
- Result: Yields two fragments with compositions **(A, R, V, Y)** and **(R, S)**.
- Because Chymotrypsin cuts after Y, the first fragment must end in Y: $(\text{A, R, V})\text{--Y}$.
- The second fragment is $(R, S)$. Since the C-terminal amino acid of the hexapeptide is R (deduced in Step 1), the remaining two amino acids at the C-terminus must be **S--R**!
- Structure: $[\dots]\text{--Y--S--R}$.
3. **Trypsin**: Specifically cleaves on the carboxyl side of basic residues (Arg, R, and Lys, K).
- Result: Yields two fragments: **(R, A, V)** and **(R, S, Y)**.
- Trypsin must cleave after the internal Arginine (R).
- Therefore, the N-terminal fragment ending in R must be $(\text{A, V})\text{--R}$.
- Between A and V: either $\text{A--V--R}$ or $\text{V--A--R}$.
- Combining these segments:
$\text{N-terminus}: \quad \text{A--V--R}$
$\text{C-terminus}: \quad \text{Y--S--R}$
$\text{Full sequence}: \quad \mathbf{\text{A--V--R--Y--S--R}}$
- Verification:
- Total composition: $\text{A}, \text{V}, \text{R}, \text{Y}, \text{S}, \text{R} = 2R, A, V, S, Y$. (Matches!)
- Trypsin cuts after R: $\text{AVR} + \text{YSR} \implies (A, V, R)$ and $(R, S, Y)$. (Matches!)
- Chymotrypsin cuts after Y: $\text{AVRY} + \text{SR} \implies (A, R, V, Y)$ and $(R, S)$. (Matches!)
- Carboxypeptidase A: C-terminal residue is R, so no cleavage occurs. (Matches!)
- The unique correct sequence is **AVRYSR**.
- **Option-by-Option Evaluation**:
- **Option (A) [INCORRECT]**: RSYRVA has C-terminal A, which would be cleaved by Carboxypeptidase A.
- **Option (B) [CORRECT]**: AVRYSR satisfies all four enzymatic cleavage rules and composition constraints.
- **Option (C) [INCORRECT]**: SRYVAR yields different Chymotrypsin fragments.
- **Option (D) [INCORRECT]**: SVRRYA has C-terminal A.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **B**
- **Scoring Criteria**: +2.0 Marks (Negative marking: -0.67 marks).