The fundamental topological parametre of a covalently closed circular DNA is called the linking number (LK).
The linking number is the sum of all the inters section which is created by inter winding of the two strands .
Lk is always an integer and it can not be changed by any deformation of the DNA stand i.e it is topologycally invariant.
The only way to change linking number or LK is to both strands roated the two strands relative to each other to each other and seal the break or nick.This is precisely the role of DNA topoisomerases. Another characteretististic of circular DNA is called twist and it is the total number of helical turn under a given condition.Since dna is a right handed helix with 10.4 base pairs per helical turn.Twist is a large +ve number for any natural DNA.Writhe can be of any sign and its absolute value is always smaller than twist. The no. define the no. of times a strand of dna winds in the right handed direction around the helix axis when the axis is constrained to lie in a plane. For purpose a mathematical completation a right handed super helix is defined as having a negative no.of super helical turns ,and a left handed super helix define as leaving posetive no.of super helical turns.dna super coil can be described mathematically by change in the linking number [LK].
The linking no.is the most descriptive property of super coil DNA.LK is the no. Of turns in the relaxed (B type) DNA plasmid/molecule is determine by dividing the total base paris of the molecules by the relaxed bp by turn which depending on reference is 10.4,10.5,10.6.
For instance in a circular DNA of 5400base pairs and 10 is the base pairs called turns for types for type B- DNA.
The topology of DNA is describe by the equation below in which the linking number is equivalent to the sum, of Tw, which is the no. Of twist of the double helix, Wr which is the no. of coils or writhes.
If there is a close DNA molecules, the sum of Tw and Wk, or the linking no. does not change, however there may be complementary change without changing their sum.
LK = TW + WK
Tw called twist, refers to the no. of waston, crick. Twist in the DNA when it is not contain to lie in a plane.
We called writhe if the no. of super helical twist since biological circular DNA is underwound. LK will generally be less than Tw, which means that we will typically be negative.
The change in the linking number, ∆LK is the actual no.of turns in the plasmid/DNA (LK) minus the no. of turn in a relaxed plasmid/DNA (LKo).
LK = LK – LKo
If the DNA is -vely super coiled, ∆LK <O. The negatively super coiling implies that the DNA is underwound.
Since, the linking no. or inshort L of super coiled DNA is the no. Of times this two strands are interwound, L can not change. The reference state Lo of a circular DNA duplex in its relaxed state.