I am currently studying the supercoiling of DNA. I understand why overwinding would create additional strain for two attached strands of DNA, but I really don't get why underwinding would create strain and thus supercoiling. If anything it seems that the strands would just separate and strain would be relieved from any DNA helix. If someone would care to explain, that would be great!
The double helical structure of DNA with ~10.5 bp/turn is thermodynamically favorable. Any perturbation from this results in strain. Thus, if DNA is under wound, it is favourable for it to adopt a negative supercoil to return to ~10.5 bp/turn.
That said, negative supercoiling and DNA melting are in fact in some kind of equilibrium. This is important for processes such as transcription and replication which require ssDNA.
Good question! I didn't know the answer either, but I think I have a good idea after thinking of DNA as a normal rope.
This answer helped me put it into perspective: https://physics.stackexchange.com/questions/30871/what-prevents-a-natural-fibers-rope-from-untwisting-when-it-is-elongated
As well as the video linked to in this answer: What is positive and negative supercoiling?
Basically, imagine you have two long strings, then you twist them around each other (DNA helix structure), each twist is called a coil.
Now tie each end to opposing hooks (imagine the hooks located on each side of a doorframe at equal height) without allowing your two strings to untwist.
Once your double stranded rope is secure (the hooks it's tied to represent a point opposite the unwinding site on the circular DNA), pull the two intwined strings further and further apart from each other at the middle of the rope. (This is what underwinding does)
Because each end is secured, it can't untwist, so it supercoils. By pulling the strings apart in the middle, you didn't untwist the coils, you just pushed them closer together, squishing them 'tighter' (stressed) on each side.