Topoisomerase Action and DNA Linking Number

Topoisomerases are essential enzymes that manage DNA supercoiling. DNA supercoiling is the coiling of a DNA double helix upon itself, which is crucial for processes like DNA replication, transcription, and packaging.

One important topological property of DNA, especially closed circular DNA, is the linking number (Lk).

• Linking Number (Lk): This is a topological invariant for closed circular DNA. It represents the total number of times one strand of the DNA double helix crosses the other strand when the DNA is constrained to lie flat on a plane. Lk is always an integer.
• Twist (Tw): The number of helical turns of one strand around the other in B-DNA (approximately 10.5 base pairs per turn).
• Writhe (Wr): The number of superhelical turns or the coiling of the DNA axis itself.

These three properties are related by the equation:

\( \text{Lk} = \text{Tw} + \text{Wr} \)

For linear DNA molecules, the linking number is not a fixed topological property because the ends can rotate freely. The linking number is primarily defined and relevant for closed circular DNA molecules (like plasmids or mitochondrial DNA) or linear DNA segments whose ends are constrained (like domains in chromosomal DNA).

Topoisomerases work by temporarily breaking the phosphodiester backbone of DNA strands (either one strand for Type I topoisomerases or both strands for Type II topoisomerases) and then rejoining them. This breaking and rejoining process allows the DNA strands to pass through each other, thereby changing the supercoiling of the DNA and, consequently, the linking number (Lk).

Let's look at the options provided:

• Option 1: Linking number of linear single stranded DNA. Linking number is defined for double-stranded DNA, and typically for closed molecules or constrained domains. Linear DNA doesn't have a fixed linking number.
• Option 2: Linking number of double stranded linear DNA. Similar to single-stranded linear DNA, linear double-stranded DNA lacks a fixed linking number because the ends are free to rotate.
• Option 3: Linking number of closed circular single stranded DNA. Topoisomerases primarily act on double-stranded DNA to manage supercoiling related to the double helix. While single-stranded circles exist, topoisomerase activity is centered around the topology of the double helix.
• Option 4: Linking number of closed circular double stranded DNA. This fits the definition of linking number as a topological invariant relevant to DNA supercoiling and the known action of topoisomerases. Topoisomerases change Lk by relaxing or introducing supercoils in closed circular double-stranded DNA.

Therefore, the action of topoisomerase directly leads to a change in the linking number of closed circular double stranded DNA.