DNA Supercoiling & Topoisomerase Simulator

Replication Fork

Fork speed 1.0×

Topoisomerases

Topo I rate (relieves 1 turn) 0.6/s

Topo II rate (relieves 2 turns) 0.3/s

Torsional State

Torque ahead of fork

low

ΔLk (linking number)

0.0

Supercoil density σ

0.000

Fork position

Stall events

How it works

Closed circular (or anchored, loop-domain) DNA obeys the topological identity Lk = Tw + Wr — linking number equals twist plus writhe. As a replication fork (or RNA polymerase) tracks along the double helix, it cannot rotate the whole downstream chromosome fast enough, so it spins the DNA in place: this is the twin supercoiled-domain model (Liu & Wang, 1987).

ahead of fork:  ΔLk → positive (over-wound, (+) supercoils)
behind fork:    ΔLk → negative (under-wound, (-) supercoils)
relaxed target: σ = ΔLk / Lk0 ≈ 0  (B-form DNA)

Left unchecked, the accumulating positive torque ahead of the fork stalls replication entirely — this is where topoisomerases act:

Topoisomerase I nicks one strand, lets it swivel around the intact strand, and reseals it — relieving ±1 turn per catalytic cycle, ATP-independent.
Topoisomerase II (DNA gyrase in bacteria) passes one intact duplex through a transient double-strand break in another, changing Lk by ±2 turns per cycle, and can actively introduce negative supercoiling using ATP hydrolysis.

This simulator renders the double helix ahead of the fork with tighter, over-wound turns as positive torque builds (σ rising), and looser, under-wound turns behind it (σ falling below zero) — turn on either enzyme to watch the local twist relax back toward σ ≈ 0 in real time. If σ ahead of the fork exceeds the stall threshold with both enzymes off, the fork halts, exactly as replication does in a topoisomerase inhibitor (e.g. a fluoroquinolone acting on gyrase, or a camptothecin acting on Topo I).

Relaxed duplex (σ≈0) Positive supercoil (ahead) Negative supercoil (behind) Replication fork

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