Question

In 30% ethanol, a 440 bp closed circular A-form DNA is in a relaxed form (no supercoil). What are the Lk, Tw and Wr values? (Please elaborate)

By transferring the above DNA from 30% ethanol solution to water solution, the structure of this DNA molecule converts from A-form to B-form helix (10 bp/turn) without breaking its backbone. What would the Lk, Tw and Wr be? (Please elaborate)

Answer 1

DNA supercoiling can be described numerically by changes in the linking numberLk. The linking number is the most descriptive property of supercoiled DNA. Lko, the number of turns in the relaxed (B type) DNA plasmid/molecule, is determined by dividing the total base pairs of the molecule by the relaxed bp/turn which, depending on reference is 10.4–10.5.

[Lk_o=bp/10.4]

Lk is merely the number of crosses a single strand makes across the other. Lk, known as the "linking number", is the number of Watson-Crick twists found in a circular chromosome in a (usually imaginary) planar projection. This number is physically "locked in" at the moment of covalent closure of the chromosome, and cannot be altered without strand breakage.

The topology of the DNA is described by the equation below in which the linking number 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'. If there is a closed DNA molecule, the sum of Tw and Wr, or the linking number, does not change. However, there may be complementary changes in TW and Wr without changing their sum.

[Lk=Tw+Wr]

Tw, called "twist", refers to the number of Watson-Crick twists in the chromosome when it is not constrained to lie in a plane. We have already seen that native DNA is usually found to be superhelical. If one goes around the superhelically twisted chromosome, counting secondary Watson-Crick twists, that number will be different from the number counted when the chromosome is constrained to lie flat. In general, the number of secondary twists in the native, supertwisted chromosome is expected to be the "normal" Watson-Crick winding number, meaning a single 10-base-pair helical twist for every 34 Å of DNA length.

Wr, called "writhe", is the number of superhelical twists. Since biological circular DNA is usually underwound, Lk will generally be less than Tw, which means that Wr will typically be negative.

For a form of the DNA linking number = 440/11 = 40

For relaxed DNA wr = 0 and Tw = 40

For b form DNA Lk = 440/ 10 = 44

Wr = 0 for relaxed form

Tw = 44