DNA supercoiling can be described numerically by changes in the linking number $L_k$, it's the most descriptive property of supercoiled DNA.
The linking number $L_k$ is equivalent to the sum of $Tw$, which is the number of twists or turns of the double helix, and $Wr$ which is the number of coils or writhes.
$$L_k = Tw + Wr$$
[...] If there is a closed DNA molecule, the sum of $Tw$ and $Wr$, or the linking number, does not change. [...] Since the linking number L of supercoiled DNA is the number of times the two strands are intertwined (and both strands remain covalently intact), L cannot change.
I don't know how to explain it more but I think the main idea is represented in the image below.
From DNA Topology: Fundamentals :
There are two important features of the $L_k$:
- $L_k$ is always an integer.
- $L_k$ cannot be changed by any deformation of the DNA strands, i.e. it is topologically invariant. The only way to change it is to introduce a break in one or both DNA strands, rotate the two DNA strands relative to each other and seal the break. This is precisely the role of DNA
Related question: Reason behind formation of positive supercoils during DNA replication/transcription.
Sources : DNA supercoil and DNA Topology.