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If a DNA segment under twist strain is closed into a circle by joining its two ends, and then allowed to move freely, it takes on different shape, such as a figure-eight. This shape is referred to as a supercoil. (The noun form "supercoil" is often used when describing DNA topology.) The DNA of most organisms is usually negatively supercoiled.
Contrary to intuition, a topological property, the linking number, arises from the geometric properties twist and writhe according to the following relationship: L k = T + W, where L k is the linking number, W is the writhe and T is the twist of the coil. The linking number refers to the number of times that one strand wraps around the other.
DNA is said to be positively supercoiled if Lk of it is higher than Lk 0 for the relaxed state (Lk-Lk o = ΔLk, ΔLk>0); that means that Tw and/or Wr are increased relative to the relaxed molecule. Conversely, DNA is negatively supercoiled if Lk of the molecule is lower than the Lk 0 (ΔLk<0).
First, the single-stranded DNA binds domain III and I. The catalytic tyrosine cleaves the DNA backbone, creating a transient 5' phosphotyrosine intermediate. The break is then separated, using domain II as a hinge, and a second duplex or strand of DNA is passed through. Domain III and I close and the DNA is re-annealed.
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DNA in cells is negatively supercoiled and has the tendency to unwind. Hence the separation of strands is easier in negatively supercoiled DNA than in relaxed DNA. The two components of supercoiled DNA are solenoid and plectonemic. The plectonemic supercoil is found in prokaryotes, while the solenoidal supercoiling is mostly seen in eukaryotes.