What is linking number and how it is important for supercoiling?
Linking number is a topological property of DNA. Linking number is a sum of twists and writhes. Numbers of time one strand of DNA is turned around another strand is called as a twist and inter-coiling of the double helix is termed as a writhe. In a simple word, writhe is a number of a time DNA double helix is crossed, coiled over each other or the number of time one strand wrap around another strand.
As per the Watson and Cricks model, eukaryotic DNA is right handed and negatively supercoiled. It is very difficult to understand DNA topology in two-dimensional space because topology is a science which cannot be understood without three- dimensional property.
We can assume the telephone wire model for understanding topology. The same pattern DNA follows during packaging or supercoiling.
DNA writhe is more important, as it will help in an arrangement of DNA. Here writhe can be interwound or overwound. Interwound writhe is plectonemic which means it wraps around each other or over the axis.
While over-wound writhe is spiral. The classic example of spiral winding is histone and DNA assembly, dsDNA is wrapped around histone in a spiral manner during nucleosome formation.
The sum of the total number of twist and writhe is called as a linking number.
If both ends of DNA are joined, the linking number remains unchanged, (linking number is zero in case of circular DNA molecule). So if we want to change the linking number, we have to break the DNA strand and that function is performed by DNA topoisomerase.
Importantly, twist and writhe can be interconvertible, in cccDNA under some distortions conditions some of the twists can be converted into writhe and some of the writhes can be converted into the twist. However, the total of both remains same (because Lk= Tw + Wr).
Eukaryotic DNA is B form, right handed and under-wound which means it is negatively supercoiled. Left-handed DNA is positively supercoiled and over- wound (not prevalent in nature). We will discuss later in this part that why negative supercoiling is important.
In DNA supercoiling, writhe is also depended on the twist. As we know the writhe is depended on the axial stress of DNA, when a number of twist increase, it increases the torsional tension of the axis of DNA and ultimately the writhe will increase. This change makes DNA supercoiled and packed it even tighter on the chromosome.
In cccDNA, writhes remain zero as there is no inter-coiling between dsDNA is observed. here, if,
Lk= Tw + Wr
For cccDNA (writhe is equal to zero)
so, Lk= Tw.
Now imagine that the cccDNA is fully relaxed which means it does not have any supercoiling, in this condition the linking number becomes zero hence supercoiling in cccDNA is denoted as Lk0 .
As per the Watson and Crick model, the dsDNA has 10.5 bp per helix and is relaxed. The relaxed cccDNA has total 1050 bp so the total linking number is,
Linking number (Lk)= total number of base/basepair per helical turn
hence, Lk= 1050 bp / 10.5 (bp/turn)
Lk= +1000 (because the DNA is other than B form and left-handed)
Elaborately, it is indicated that if our DNA is left handed and has 10.5 bp per turn with 1050 bp length than one strand is cross or over-wound (positive supercoiling) to another strand 1000 times.
Attend class: Immunogenetics
However, it is just an assumed example because fully relaxed DNA (or positively supercoiled DNA) does not exist in nature. When we repeatedly decrease the twists and writhes by cutting with enzyme gradually linking number becomes zero.
Therefore, the difference between the linking number (Lk) and zero linking (Lk0) is called as linking difference ΔLk,
So, ΔLk = Lk – Lk0
If the value of ΔLk is different from zero ( >0 or <0 ) than the DNA is called as supercoiled. Additionally, Lk is lower than Lk0 (linking number is less than zero) than ΔLk is also <0 and the value which we get is negative so the DNA is called as negatively supercoiled.
Similarly, if Lk >Lk0 than ΔLk > 0, and the value obtained is positive so the DNA is called as positively supercoiled. Here the value of ΔLk is depended on the length of DNA. If the length increase, supercoiling will increase and vice versa.
Specific linking different is another important property of supercoiling. It is also called as superhelical density which is a difference between linking difference (ΔLk) and linking number of cccDNA (Lk0). so,
𝛔= 𝝙Lk /Lk0
- Human DNA is B type and right-handed with negative supercoiling. Majorly all the organism (from bacteria to eukaryotes) on earth are negatively supercoiled only some of the thermophilic bacteria are positively supercoiled.
- Negatively supercoiling stores energy, which is utilized during denaturation of dsDNA in replication or transcription. Positively supercoiling stores more energy hence even at higher temperature DNA does not denature. Even enzyme cannot recognize positively supercoiled DNA, and cannot cut it.
- The length of DNA from 46 chromosomes is approximate ~2 meters and it has to fit in ~10µM radium nucleus now imagine why supercoiling is important.
- If we stretch dsDNA from both the end it is approx. ~100km long.
- Globally, all living organisms are supercoiled on an average of approximately ~6%.
Identification of different forms of DNA
Agarose gel electrophoresis is a technique by which we can identify the different form of DNA molecules.
If we have four DNA molecules with the same length but different topology, each molecule migrates differently in agarose gel.
Suppose first DNA is closely circular with no supercoiling, second DNA molecule having both strands twisted around each other which means linear double-stranded DNA. The third DNA molecule is coiled around each other with some writhes and the fourth one is supercoiled.
In each case, DNA molecules migrate differently. The more compactly supercoiled DNA, the faster it will migrate in the gel. Hence the fourth one (which is supercoiled and compact) migrate faster than other DNA.
The first one, circular DNA do not have any supercoiling hence it migrates slower than any other DNA and remains last.
The more compact the DNA is, it can easily pass through agarose pores. So sequentially, circular DNA remains last, linear DNA cover more distance than circular DNA and coiled DNA covers more distance than linear DNA. At last supercoiled DNA cover more distance than any other, and run faster.
Attend class: Extrachromosomal inheritance
Topological properties are very important properties of DNA if it is not maintained properly in vivo, DNA cannot be packed properly on the chromosome which will result in epigenetic alteration and failure in replication.
Read article: DNA Topology class 1: Topoisomerase
Article Written by: Tushar Chauhan
Article reviewed by: Debayan baidya