Supercoil

In a "relaxed" double-helical segment of DNA, the two strands twist around the helical axis once every 10.6 base pairs of sequence. To add or subtract twists, as some enzymes can do, is to impose a strain. If a DNA segment under twist strain were to be closed into a circle by joining its two ends and then allowed to move freely, the circular DNA would contort into new shape, such as a simple figure-eight. Such a contortion is a supercoil.

The simple figure eight and its topological equivalents is the simplest supercoil, and is the shape a circular DNA assumes to accommodate one too many or one too few helical twists. The two lobes of the figure eight will appear rotated either clockwise or counterclockwise with respect to one another, depending on whether the helix is over or underwound. For each additional helical twist being accommodated, the lobes will show one more rotation about their axis.

In fact the noun form "supercoil" is rarely used in the context of DNA topology. Instead, global contortions of a circular DNA, such as the rotation of the figure-eight lobes above, are referred to as writhe. The above example illustrates that twist and writhe are interconvertable. "Supercoiling" is an abstract mathematical property, and represents the sum of twist and writhe. The relationship of twist, writhe and supercoiling is expressed as the equation

S = T + W

Extra helical twists are positive and lead to positive supercoiling, while subtractive twisting causes negative supercoiling. Many topoisomerase enzymes sense supercoiling and either generate or dissipate it as they change DNA topology.

In part because chromosomes may be very large, segments in the middle may act as if their ends are anchored. As a result, they may be unable to distribute excess twist to the rest of the chromosome or to absorb twist to recover from underwinding--the segments may become supercoiled, in other words. In response to supercoiling, they will assume an amount of writhe, just as if their ends were joined.