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While trying to understand DNA supercoiling, I came across these lines in the book Genetics by Ursula Goodenough :

All natural DNA is superhelical. The axis of the duplex itself follows a helical path in space. For virtually all DNA, the sense of the superhelical turns is opposite to that of duplex, thereofer, they are negative supertwists.

I am unable to understand these lines. Specially, the second one.

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It means that the direction in which the normal double-strand is wound up (which is also helical) and the direction on which the double helix itself is twited to reach the supercoils are opposite to each other. Have a look at this image from the Wikipedia, I think it makes this clearer:

enter image description here

The first show a DNA ring with the normal helix-coiling. The second show the supercoiling of the coiled ring molecule. Imagine a rubber band. This you can twist around its band axis to get the coiling and around its vertical axis to get the supercoiling.

For linear DNA molecules, this looks like this (taken from here):

enter image description here

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The rubber band example was awesome ! –  biogirl Mar 27 at 10:24
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This is something what I remember from a biochemistry lecture about this topic. Our professor first showed some slides about how this works and then demonstrated it live with a rubber band. I think afterwards everybody had understood it. –  Chris Mar 27 at 11:57
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