Introduction: What is supercoiling?

Double helical DNA exhibits two levels of coiling. One is the helical coiling of the double helix, that is, the number of turns that one polynucleotide strand makes about the duplex axis. This number is known as the twist (T). The second type of coiling, which is known as supercoiling, is the number of turns that the duplex DNA’s helix axis makes around the superhelix axis. This is called the writhing number (W).The sum of the twist and the writhing number is the number of times that one DNA strand winds about the other, a quantity called the linking number (L). Thus, L = T + W. In covalently closed circular DNA, the linking number is invariant; it can’t be changed without cleaving at least one strand of the duplex DNA.

Electron micrographs of circular DNA

The chromosomes of many viruses and bacteria are circular molecules of duplex DNA. In electron micrographs, some of these molecules have a peculiar twisted appearance, a phenomenon known as supercoiling. In order to be transcribed and replicated, DNA must maintain the proper level of supercoiling. This is controlled by  the actions of enzymes known as topoisomerases.

Telephone cord analogy

You may not realize it, but I’m sure you’re familiar with the distinction between twists and writhing number.

"Hey, Dustin, can I borrow the phone? Thanks."

Here the helical twist of the telephone cord is analogous to the twist of the DNA double helix. The relaxed state of the telephone cord is like that of circular DNA without any supercoiling. As I twist the cord, the cord begins to develop a supercoil because the helical cord has a natural twist that mechanically resists changing. Continuing to twist the cord creates additional writhes until we arrive at the standard state of most domestic phones, a compact entangled mess. To disentangle the cord, you can just disconnect one end and the writhes dissipate as the cord untwists. This is analogous to cutting a closed circular duplex DNA and changing its linking number.

[Note: The telephone cord analogy is used differently in this video than in Fig. 23-8. In Fig. 23-8, the cord itself represents the DNA double helix and the coil of the telephone cord represents the superhelix, whereas in this video, the coil of the telephone cord represents the DNA double helix and the writhing of this coil represents the DNA’s supercoiling. In terms of Fig. 23-8, the twisted up telephone cord is a super-superhelix (its superhelical axis is also coiled).]

Belt analogy

It's easier to demonstrate the equivalency of twist and writhe on a simpler analog. Let's use a belt.

"Hey, Dustin, I need a belt."

Here the white and red edges of the belt represent the two antiparallel strands of duplex DNA. You can count the number of twists by counting the number of times the white or red edge changes from up to down. Let's put a twist in the belt. When the belt is laid flat, we count one twist. The white edge starts up, twists to down, and back to up. Now, if we introduce a writhe by coiling the belt, the twist disappears. The edges never change sides. I can also make the twist disappear by forming a figure 8. Again, the white edge is always on top.

Lets try two twists. Notice that I have to unlatch the belt to introduce more twists, that is, change the belt’s linking number. Laying the belt flat on the table, we can count the two twists. One - two. Making a single figure 8, that is, one writhe, reduces the twist to one. Up - down - up. A second writhe reduces the twist to zero. Removing a writhe adds a twist. No writhes recovers the original 2 twists. 1 writhe - 1 twist. 2 writhes - zero twists.

Cool.