In both cases, the molecule is locally strained or tense, because it is away from the most stable conformation, i.e. B-DNA with one turn per 10.4 bp.
Therefore:
Esta página está disponible también en español.
The "B" conformation of double-stranded DNA is the reference, as the most stable conformation.
Its value of twist is calculated as
Tw0 = number of turns = number of bp / number of bp per turn = Nbp / 10.4
Example: for a molecule with 1024 bp, Tw0 = 1024/10.4 = 98 approx.
This is done for example by topoisomerases, by either unwinding or overwinding the DNA — i.e., reducing the number of turns or increasing it, respectively.
| unwinding | overwinding |
|---|---|
|
|
In both cases, the molecule is locally strained or tense, because it is away from the most stable conformation, i.e. B-DNA with one turn per 10.4 bp. Therefore: |
|
| less turns | more turns |
| lower torsion Tw | higher torsion Tw |
| more bp/turn | less bp/turn |
The molecule resolves its strain or tension, to reach "normal" torsion value Tw0, by adopting supercoils or superhelices. (See the videos of the piece of rope.)
Remember: Lk = Tw + Wr
| unwinding | overwinding |
|---|---|
Initial state: molecule in a flat plane (relaxed, no writhe, Wr=0) but locally tense. |
|
| Lk1 = Tw1 + 0 with Tw1 lower than Tw0 |
Lk1 = Tw1 + 0 with Tw1 higher than Tw0 |
| Final state: supercoiled molecule, no local strain/tension; hence Tw2 = Tw0 | |
| Lk2 = Tw0 + Wr2 | Lk2 = Tw0 + Wr2 |
| The change while going from state 1 to state 2 is: | |
| ΔLk = Lk2 − Lk1 = (Tw0 − Tw1) + (Wr2 − 0) | ΔLk = Lk2 − Lk1 = (Tw0 − Tw1) + (Wr2 − 0) |
| But ΔLk=0 because this was a change in conformation without any covalent bonds being broken (no action of topoisomerases). Therefore: |
|
| since Tw1 was lower than Tw0 , Wr2 must be <0 | since Tw1 was higher than Tw0 , Wr2 must be >0 |
| so, ΔTw>0 produced ΔWr<0, by convention called negative supercoiling (Wr2<0) | so, ΔTw<0 produced ΔWr>0, by convention called positive supercoiling (Wr2>0) |
As an example, a molecule with 1024 bp that, without any supercoils, is currently adopting Tw=96 (in other words, a molecule with 1024 bp the strands of which cross each other 96 times — this situation may be the result of a topoisomerase acting on the DNA)
will spontaneously evolve to reach the reference, stable, B-DNA conformation such as:
0 = ΔLk = (Tw0 − Tw1) + (Wr2 − 0) = (98−96) + Wr2
and so the final writhe Wr2 = −2 , the molecule will form two negative supercoils