What is positive and negative supercoiling?
According to this powerpoint from the SIU School of Medicine:

Right handed supercoiling = negative supercoiling (underwinding)
Left handed supercoiling = positive supercoiling

And from this Boston University webpage:

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.

And finally from wikibooks:

Positive and Negative Supercoilings

Positive supercoiling is the right-handed, double helical form of DNA. It is twisted tightly in a right handed direction until the helix creates knot.

Negative supercoiling is the left-handed, double helical form of DNA.


Although the helix is underwound and has low twisting stress, negative supercoil's knot has high twisting stress. Prokaryotes and Eukaryotes usually have negative supercoiled DNA. Negative supercoiling is naturally prevalent because negative supercoiling prepares the molecule for processes that require separation of the DNA strands. For example, negative supercoiling would be advantageous in replication because it is easier to unwind whereas positive supercoiling is more condensed and would make separation difficult.
Topoisomerases unwind helix to do DNA transcription and DNA replication. After the proteins have been made,the DNA template supercoils by the force to make chromatin. RNA polymerase also influence DNA strand to have two different supercoiled directions. The region RNA polymerase has passed forms negative supercoil while the region RNA polymerase that have not passed forms positive supercoil. By these processes, supercoils are generated.

In the following image from web-books:

 (a) Positive supercoils (the front segment of a DNA molecule cross over the back segment from left to right). (b) Negative supercoils. 
This video, titled &quot;super coil (positive and negative) formation of DNA&quot; should help you visualize this.