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I am using this article to calculate the radius of curvature of DNA. I know that

  • 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?

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  • $\begingroup$ According to the article E= Bl/2R^2. Does that help? $\endgroup$
    – bob1
    Jun 7, 2022 at 21:30
  • $\begingroup$ Yes, but I am then confused how to get E/I. $\endgroup$ Jun 8, 2022 at 1:14
  • $\begingroup$ 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? $\endgroup$
    – bob1
    Jun 8, 2022 at 2:08
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    $\begingroup$ 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. $\endgroup$
    – timeskull
    Jun 8, 2022 at 16:32

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