Q.46 Topological winding number of a 2.0 kb covalently closed circular DNA was found to be 191 with
a writhing number of -4. Hence, its LINKING NUMBER and the NUMBER OF BASE PAIR PER
TURN when the molecule is laid flat on the surface is _______ and_________, respectively.
(A) 187, 10.69 (B) 195, 10.25 (C) 200, 10.00 (D) 187, 10.50
DNA Topology: Linking Number, Twist, Writhe in 2 kb Circular DNA
In DNA topology, the linking number (Lk) quantifies how strands interwind in covalently closed circular DNA, remaining invariant. The topological winding number here refers to twist (Tw), given as 191, while writhing number (Wr) is -4. Using the fundamental equation Lk = Tw + Wr, the linking number calculates directly, and base pairs per turn emerges when the molecule relaxes flat on the surface.
## Correct Answer
The correct option is (A) 187, 10.69.
Linking number Lk = Tw + Wr = 191 + (-4) = 187. For a 2.0 kb (2000 base pairs) DNA laid flat, twist equals total helical turns, so Tw = 2000 / (bp/turn). Thus, bp/turn = 2000 / 191 ≈ 10.69.
## Option Analysis
Each option tests understanding of Lk = Tw + Wr and relaxed twist calculation.
| Option | Lk Calculation | bp/turn (2000 bp / 191) | Why Incorrect/Correct |
|---|---|---|---|
| (A) 187, 10.69 | 191 – 4 = 187 | 2000/191 ≈ 10.69 | ✅ Matches exactly: Lk from topology equation; bp/turn from relaxed flat state |
| (B) 195, 10.25 | 191 + 4? | ~195 turns | ❌ Wrong Lk (ignores negative Wr sign); bp/turn mismatches |
| (C) 200, 10.00 | Assumes Lk=2000/10 | 2000/200=10 | ❌ Ignores given Tw/Wr; assumes standard 10 bp/turn without data |
| (D) 187, 10.50 | Lk correct | 2000/190.48≈10.5 | ⚠️ Lk right, but bp/turn uses ~10.5 (B-DNA average) instead of given Tw=191 |
## Key Concepts Explained
- Linking Number (Lk): Topological invariant for closed DNA; Lk = Tw + Wr.
- Twist (Tw): Helical turns of strands; when flat/relaxed, Tw = Nbp / (bp/turn).
- Writhe (Wr): Supercoiling of helix axis; negative for right-handed supercoils in bacteria.
Understanding these resolves supercoiling in plasmids, vital for replication and gene regulation in biotechnology.
