Final Answer:
The superhelical density (σ) of eukaryotic DNA is approximately -0.053.
Step-by-step explanation:
Eukaryotic chromosomes are organized into nucleosomes, where 150 base pairs (bp) of DNA wrap around the nucleosome core proteins approximately 1.8 times, with about 100 bp of DNA between each nucleosome. To calculate the superhelical density (σ), we can assume that the DNA around the nucleosome experiences the same topological restrictions as a circular DNA molecule of the same length. The formula for superhelical density is given by:
σ =(Lk - Lk₀)/Lk₀
Where:
Lk is the linking number of the closed circular DNA.
Lk₀ is the linking number of the relaxed circular DNA.
The linking number can be calculated using the formula:
Lk = (Tw + Wr)/Delta
Where:
Tw is the twist number (number of turns of the helix).
Wr is the writhe number (number of superhelical turns).
Delta is the number of base pairs per turn (helical repeat).
Given that Tw = 1.8 turns (from the 150 bp wrapped around the nucleosome), Wr = -6 (since right-handed DNA has a negative writhe), and Delta = 10.4 (10.4 base pairs per turn for eukaryotic DNA), we can substitute these values into the formulas to calculate the linking numbers and subsequently the superhelical density.
Lk = (1.8 - 6)/10.4
Lk₀ = (0 - 6)/10.4
Finally, substituting these values into the formula for superhelical density:
σ =(1.8 - 6) - (0 - 6)/(0 - 6)
After the calculations, the superhelical density (σ) is approximately -0.053.