When the DNA helix has the normal number of base pairs per helical turn it is in the relaxed state. Changing this normal amount of twist can be demonstrated by grasping both ends of a short linear model (one to two complete turns) and twisting the ends in opposite directions. If the helix is overtwisted so that it becomes tighter, the edges of the narrow groove move closer together. If the helix is undertwisted, the edges of the narrow groove move further apart. Notice that changing the twist from the relaxed state requires adding energy and increases the stress along the molecule.
If DNA is in the form of a circular molecule, or if the ends are rigidly held so that it forms a loop, then overtwisting or undertwisting leads to the supercoiled state. Supercoiling occurs when the molecule relieves the helical stress by twisting around itself. Overtwisting leads to postive supercoiling, while undertwisting leads to negative supercoiling. Twist can be altered in a circular model by breaking the circle, over or undertwisting and then reconnecting the ends. In the illustration above of a negatively supercoiled molecule, part of the helix is yellow to show how the molecule twists around itself. If you attempt to unwind this molecular twist, the helix will become further undertwisted.
Although supercoiling relieves some stress in the molecule, when there is negative supercoiling, further stress can be relieved by partial strand separation. The hydrogen bonds (holding together complementary bases) break and part of the double helix separates. Strand separation is required for transcription (copying DNA to RNA) and replication (copying DNA to DNA). In the figure below, the yellow strands have separated allowing the molecule to relax and assume a circular configuration.