What causes knots and stress when untwisting ropes?

[Aurelius120]

[Mentor Note -- thread moved from the schoolwork forums to GD as it seems like a more general question]

Homework Statement:: Topoisomerases help in relieving strain in the DNA ahead of the replication fork caused by the untwisting of the double helix (Topoisomerases are enzymes that participate in the over winding or underwinding of DNA).
The strain is same as caused when two ropes twisted around each other are untwisted from both ends.
Relevant Equations:: NA

As shown in the image the ropes develop supercoils on being unwound.
The knots caused due to untwisting develops tension enough to make it impossible to uncoil the rope further.

My question is :

What causes such unwanted stress(called torisonal stress maybe) and these knots?
Why does it happen only with coiled strands of rope?

All research has failed at providing the right solution to this problem(or even an incentive)

 

[DaveE]

I would guess that in untwisting the rope you are adding twist to the individual strands. I bet it doesn't happen if you comb it, i.e. allow the individual strands to twist freely.

It looks to me like the original twist in the rope is in the opposite direction from the larger twist shown.