Question

A 5250 base-pair long plasmid with 10 negative supercoils would have a linking number of _______, considering 10.5 base pairs per turn for B DNA. (Answer in integer)

Hint:

The linking number is a topological property that remains constant under certain conditions and is crucial in understanding DNA topology and its biological implications.

Answer 1

The linking number (\( Lk \)) of a circular DNA molecule is defined as the total number of times one strand of DNA winds around the other. The linking number can be calculated using the formula: \[ Lk = Tw + Wr \]

where:

• \( Tw \) is the twist, the number of helical turns in the DNA,
• \( Wr \) is the writhe, the number of supercoils.

Step 1: Calculating Twist (\( Tw \)).

Given that the DNA is 5250 base pairs long and there are 10.5 base pairs per turn of the DNA helix:

\[ Tw = \frac{5250}{10.5} = 500 \] Step 2: Considering Supercoils (\( Wr \)).

The plasmid has 10 negative supercoils:

\[ Wr = -10 \] Step 3: Calculating Linking Number (\( Lk \)). \[ Lk = Tw + Wr = 500 - 10 = 490 \] Conclusion:

Explanation: The linking number for this plasmid is **490**, accounting for the number of helical turns and the negative supercoiling present. This value represents the total number of times the strands are intertwined, including both twists and supercoils.