How's the strain developed? I was reading about DNA supercoiling and stumbled upon the following:

DNAs derived from a given cellular source have a characteristic degree of supercoiling. Thus the DNA is strained.
  In most instance the strain is a result of underwinding of  the DNA double helix in the closed circle.


Here the author was talking about closed circular DNA (ccDNA) which has 10.5 bp per turn in relaxed state. When in relaxed state the ccDNA has no supercoils. But when the two strands are overcoiled or undercoiled, strain develops and the helix coils upon itself.
My question is how is this strain developed? How dose it cause tangling of the double helix/ supercoiling?
P.S. I've class XII Physics background.
 A: I'm not an expert, but here's my try:
As you probably already know, the torsional strain is imparted by decreasing or increasing the linking number number of the DNA molecule, relative to B-DNA (B-DNA is the most stable DNA form, contains 10.5 bp per turn, and is free of any constraints, stress or torsion). Linking number is a topological property because it does not vary when DNA is twisted or deformed in any way, as long as both strands remain intact. Also, it is always an integer. The changes in linking number are accomplished by a special group of enzymes called topoisomerase, and two forms of a given circular DNA that differ only in a topological property such as linking number are referred to as topoisomers.
Now, as for your question: how is this strain developed? 
Linking number can be broken down into two structural components called writhe ($W_r$) and twist ($T_w$), which may be thought as a measure of coiling of the helix axis ($W_r$) and as determining the local twisting or spatial relationship of neighboring base pairs (the total number of helical turns in circular
DNA under given conditions) ($T_w$). Maybe the picture will help to visualize them:

When a change in linking number ($L_k$) occurs, some of the resulting strain is usually compensated by writhe (supercoiling) and some by changes in twist, giving rise to the equation
$$L_k = T_w + W_r$$
Note that twist and writhe are geometric rather than topological properties, because they may be changed with changes in ambient conditions, temperature and during DNA functioning. Also, they do not need to be integers. For a relaxed molecule, its linking number is equal to its twist:
$$L_{k_0}=T_{w_0}$$
It is often convenient to express the change in linking number in terms of a length-independent quantity called the specific linking difference ($σ$), which is a measure of the turns added/removed relative to those present in B-DNA. The term σ is also called the superhelical density, defined as
$$σ=\frac{L_k-L_{k_0}}{L_{k_0}}≡\frac{\tau}{L_{k_0}}$$
where $L_{k_0}$ is the linking number of the B-DNA molecule. At a first approximation, $\sigma$ estimates the number of supercoils per helical turn of DNA.
Then, we can write the relationship between the linking difference and
twist and writhe, by combination of the preceding equations:
$$\tau=L_k-L_{k_0}=(T_w+W_r)-T_{w_0}=(T_w-T_{w_0})+W_r=\Delta{T_w}+W_r$$
Hence, topological stress caused by linking difference in a circular DNA both changes the twist from its optimal value and introduces writhe.
I think those changes in twist and writhe are directly related to the apparition of torsional strain in the molecule, but this is all I know. Maybe a more knowledgeable person will complete my answer.
For a more detailed treatment of DNA topology, see this. Also, you might enjoy reading this Quanta Magazine article on the whole subject. Hope some of this information is helpful.
