# Calculate radius of curvature of DNA

• 150bp segment of DNA length wraps itself 1.7 times around a histone core.
• There are 0.34nm/bp
• DNA's persistence length l is 53 nm.

How can I use this data to calculate the radius of curvature of DNA?

According to the article, $$l = \frac{B}{k_BT}$$ ($$B$$ is bending modulus, $$k_B$$ is Boltzmann's constant, and $$T$$ is temperature). However, the only way the units cancel correctly is if $$l = \frac{k_BT}{B}$$. Which is the correct formula?

Assuming I know $$T, k_B, l$$, I can calculate $$B$$. Since DNA is a homogeneous isotropic rod, $$B$$ is equivalent to Young's modulus $$E$$. Is there a way I can use $$E$$ to calculate the radius of curvature? Or am I doing this completely wrong?

• According to the article E= Bl/2R^2. Does that help?
– bob1
Jun 7, 2022 at 21:30
• Yes, but I am then confused how to get E/I. Jun 8, 2022 at 1:14
• I'm no mathematician by any stretch of the imagination, but it seems from the paper that E~kbT, and l~B/kbT thus by substitution l~B/E and therefore E~B/l for a given temperature and if R=l. I get units for l as N.mm^-2.J^-1, but it should be just distance (nm in DNA's case) correct?
– bob1
Jun 8, 2022 at 2:08
• I don't think DNA has a particular radius of curvature any more than it has a particular length. It will depend on the situation. In the case of DNA wrapped around a histone, the radius will be half the diameter of the histone + half the diameter of the DNA. Jun 8, 2022 at 16:32