I am studying molecular biology from Lewin's Genes XII and got confused in the supercoiling topic. Since then I read from several other sources and so far understood the following. However, I can't seem to connect the dots. A bit of help in connecting the dots would be greatly appreciated.

So these are the stuff that I understand so far

1. Supercoiling is coiling of already coiled double helix
2. Positive supercoiling overwound the DNA (increase the number of turns thus decreasing the number of base pair per turn making it more twisted)
3. Negative supercoiling underwounds the DNA
4. Linking number is the sum of twist and writhe, twist is basically number of turns and writhe refers to the number of supercoil. It remains constant as long as phosphodiester bonds are not broken
5. unwinding DNA at replication fork results in positive supercoil downstream

Now coming to the confusion

In the diagram we can see that negative supercoiling has taken place. Twist value has gone up and to compensate that (to keep the linking number constant as no phosphodiester bond has broken in this case of cccDNA) six negative supercoils have been introduced.

All the books clearly mention that negative supercoil is something that underwounds the DNA resulting in less turns with more base pair per turn. But in this case it is clearly seen that the number of turns have increased (from 36 to 40) and to compensate that -4 supercoil is introduced. So here negative supercoil has resulted in over wounding instead of underwounding

similarly, from the linking number equation > Lk = Tw + Wr, If there is positive supercoiling (i.e., Wr is positive) the Tw (twist value) will go down to keep linking number constant. So, the statement saying positive supercoil wound overwound the DNA is not matching at all. shouldn't positive supercoil increase the Tw as well (I understand mathematically it is not possible because then linking number would change, but all I'm saying is that I fail to connect the concept that says positive supercoil overwounds the DNA (more twisted) with what I see in the equation i.e., twist number drops and only writhe goes up.

I am studying molecular biology from Lewin's Genes XII and got confused in the supercoiling topic. Since then I read from several other sources and so far understood the following. However, I can't seem to connect the dots. A bit of help in connecting the dots would be greatly appreciated.

So these are the stuff that I understand so far

1. Supercoiling is coiling of already coiled double helix
2. Positive supercoiling overwound the DNA (increase the number of turns thus decreasing the number of base pair per turn making it more twisted)
3. Negative supercoiling underwounds the DNA
4. Linking number is the sum of twist and writhe, twist is basically number of turns and writhe refers to the number of supercoil. It remains constant as long as phosphodiester bonds are not broken
5. unwinding DNA at replication fork results in positive supercoil downstream

Now coming to the confusion

In the diagram we can see that negative supercoiling has taken place. Twist value has gone up and to compensate that (to keep the linking number constant as no phosphodiester bond has broken in this case of cccDNA) six negative supercoils have been introduced.

All the books clearly mention that negative supercoil is something that underwounds the DNA resulting in less turns with more base pair per turn. But in this case it is clearly seen that the number of turns have increased (from 36 to 42) and to compensate that -6 supercoil is introduced. So here negative supercoil has resulted in over wounding instead of underwounding

similarly, from the linking number equation > Lk = Tw + Wr, If there is positive supercoiling (i.e., Wr is positive) the Tw (twist value) will go down to keep linking number constant. So, the statement saying positive supercoil wound overwound the DNA is not matching at all. shouldn't positive supercoil increase the Tw as well (I understand mathematically it is not possible because then linking number would change, but all I'm saying is that I fail to connect the concept that says positive supercoil overwounds the DNA (more twisted) with what I see in the equation i.e., twist number drops and only writhe goes up.