Closed circular (B form) DNA with one turn of double helix per 10.5 bp (base pair) is relaxed. An 84 bp segment of a circular DNA in the relaxed state would contain 8 double helical turns or 1 for every 10.5 bp. If one of these turns were removed, there would be 84 bp/7 = 12 bp/turn rather than 10.5 bp/turn in B-DNA. This would result in a thermodynamically strained DNA. So, the strain is a result of the unwinding of DNA double helix in the closed circle. This strain introduced by underwinding is generally accommodated by supercoiling rather than strand separation because coiling the axis of DNA usually requires less energy than breaking the hydrogen bonds. So, supercoiling is a result of underwinding. However, underwinding represent a form of stored energy and makes separation of DNA strands easier. Linking number can be defined as a number of times the 2nd strand pierces the surface of the 1st strand which is visualized as a circle. It is defined as positive (+ve) if strands are interwound in right handed helix and (-ve) in left handed helix. So linking number is the number of turns. Superhelical density or specific linking difference (σ) is a measure of a number of turns removed relative to the number present in relaxed DNA. It is independent of the length of the DNA molecule. The negative sign indicates that the change in linking number is due to the underwinding of DNA. So, the supercoiling induced by underwinding is called negative supercoiling. Overwinding results in positive supercoiling. Topoisomerase I breaks one of the 2 strands, change the linking number in increments of 1. Topoisomerase II breaks both DNA strands and changes the linking number in increments of 2.