Subtopic: Fundamentals of Biomolecules, enzyme kinetics
Question Statement:
Determine the correctness or otherwise of the following Assertion [a] and the Reason [r]:
Assertion [a]: The association constant in water for the G-C base pair is three times lower than that for the A-T base pair.
Reason [r]: There are three hydrogen bonds in the G-C base pair and two in the A-T base pair.
Options:
(A) Both [a] and [r] are true and [r] is the correct reason for [a]
(B) [a] is false but [r] is true
(C) Both [a] and [r] are false
(D) Both [a] and [r] are true and [r] is not the correct reason for [a]
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2018 Q.41)**
**1. Governing Concept & Question Classification**:
- **Section**: BT
- **Question Type**: **MCQ** (2 Marks)
- **Topic**: Biochemistry / Biophysics (Nucleic Acid Thermodynamics & Base Pairing)
**2. Detailed Step-by-Step Analysis**:
- **Assertion [a]**: *“The association constant in water for the G-C base pair is three times lower than that for the A-T base pair.”*
- This assertion is **FALSE**. Guanine-Cytosine (G-C) base pairing involves **three** intermolecular hydrogen bonds, whereas Adenine-Thymine (A-T) base pairing involves only **two** hydrogen bonds.
- The extra hydrogen bond and superior base stacking energy make the G-C association constant ($K_a$) **higher** (not lower) than that of A-T. Hence, DNA duplexes rich in G-C pairs exhibit higher thermal stability ($T_m$) and greater association affinity. Assertion [a] is demonstrably false.
- **Reason [r]**: *“There are three hydrogen bonds in the G-C base pair and two in the A-T base pair.”*
- This reason is **TRUE**. According to the Watson-Crick base-pairing model, G-C pairs form three hydrogen bonds ($O^6\cdots H-N^4$, $N^1-H\cdots N^3$, and $N^2-H\cdots O^2$), while A-T pairs form two hydrogen bonds ($N^6-H\cdots O^4$ and $N^1\cdots H-N^3$).
- Therefore, **[a] is false but [r] is true**.
- **Option-by-Option Evaluation**:
- **Option (A) [INCORRECT]**: [a] is false.
- **Option (B) [CORRECT]**: [a] is false because G-C has a higher (not lower) association constant, while [r] is true regarding the number of hydrogen bonds (3 vs 2).
- **Option (C) [INCORRECT]**: [r] is an established chemical fact.
- **Option (D) [INCORRECT]**: [a] is incorrect.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **B**
- **Scoring Criteria**: +2.0 Marks (Negative marking: -0.67 marks).
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