consisting of Lk = 200:

1. DNA undergoes positive supercoiling with Lk = 202
2. DNA undergoes positive supercoiling with Lk = 198
3. DNA undergoes negative supercoiling with Lk = 202
4. Structure does not change

   Correct Answer: DNA undergoes positive supercoiling with Lk = 202

   Adding +2 to the linking number (Lk) of relaxed DNA (Lk₀ = 200) creates positive supercoiling. Relaxed DNA has Lk = Lk₀ with ΔLk = 0; increasing Lk above Lk₀ (ΔLk > 0) overwinds the helix, causing positive supercoils—key DNA topology concept for GATE Life Sciences.

   Detailed Option Analysis

   1. DNA undergoes positive supercoiling with Lk = 202 (Correct)

   Lk formula: Lk = Tw + Wr (Twist + Writhe). Relaxed: Lk = Lk₀ = 200, ΔLk = 0.
   After +2: Lk = 202, ΔLk = +2 > 0 → positive supercoiling (overwound helix). Positive writhe forms right-handed plectonemes.

   2. DNA undergoes positive supercoiling with Lk = 198 (Incorrect)

   Lk = 198 gives ΔLk = -2 < 0 → negative supercoiling (underwound), not positive. Math error confuses direction of change.​

   3. DNA undergoes negative supercoiling with Lk = 202 (Incorrect)

   Lk = 202 is positive ΔLk (+2), not negative. Trap tests supercoiling sign convention: +ΔLk = positive supercoils.​

   4. Structure does not change (Incorrect)

   ΔLk = +2 introduces torsional stress; DNA adopts superhelical conformation to minimize energy. Never relaxed unless topoisomerases act.​

   Linking number positive supercoiling DNA questions test DNA topology fundamentals crucial for GATE Life Sciences. Relaxed circular DNA (Lk = Lk₀ = 200) becomes positively supercoiled when linking number increases to 202 (ΔLk = +2), overwinding the double helix. This guide solves the MCQ with topology equations and exam strategy.

   DNA Topology Formula

   text

   Lk = Tw + Wr (Linking = Twist + Writhe)
   ΔLk = Lk - Lk₀ (Linking Difference)

   Relaxed: Lk = Lk₀, ΔLk = 0, Wr = 0
Supercoiled: ΔLk ≠ 0 → Wr adjusts


   Given: Lk₀ = 200 (relaxed) → Lk = 202 yields ΔLk = +2 = positive supercoiling.

   Supercoiling Decision Tree

   ΔLk Sign	Supercoiling Type	Helix State	Biological Context ​
   +ΔLk	Positive	Overwound	Replication stress, thermophiles
   -ΔLk	Negative	Underwound	Transcription, bacteria (~-0.06σ)
   ΔLk = 0	Relaxed	Natural B-DNA	Topoisomerase relaxed

   Visual Supercoil Types

   text

   Negative Supercoiling (ΔLk < 0): ←←← Toroidal left-handed writhe
Relaxed DNA (ΔLk = 0): → Straight helix
Positive Supercoiling (ΔLk > 0): →→→ Right-handed plectonemes


   GATE Exam Strategy

   High-Yield Calculations (Molecular Biology: 15-20% weightage):

   text

   Lk₀ ≈ Nbp / 10.5 (Nbp = base pairs)
σ = ΔLk / Lk₀ (Superhelical density, bacterial σ ≈ -0.06)
Topo I: ΔLk = +1 per cycle
Topo II: ΔLk = +2 per cycle


   Common Traps:

   • Sign confusion: +ΔLk = positive (overwound)

   • Lk vs Lk₀ mixup: relaxed = Lk = Lk₀ only

   • Units: always integer changes

   Mnemonic: “Positive = Plus ΔLk = Packed tight overwinding**

   Pro Tip: Natural DNA is negatively supercoiled (ΔLk < 0) to facilitate strand separation; positive supercoiling arises transiently during replication/repair.​