# Calculate persistence length from force extension data of a single DNA

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1. Aug 29, 2014

### pen

Hello!

From a data set of F-x measurements of a single dsDNA molecule I want to calculate the persistence length $P$. So I plotted $\frac {1} {\sqrt{(F)}}$ vs. $x$ and fitted these data points (linear).

According to an interpolation formula the extension $x$ of a worm like chain with contour length $L_0$ (Bustamante et al.,1994) is:

$\frac{FP}{k_BT}= \frac{1}{4} \Big( 1-\frac{x}{L_0}\Big)^{-2} -\frac{1}{4} + \frac{x}{L_0}$, applicable for extensions $\frac{x}{L_0}<0.97$

Thus the y-intercept of the straight line fitted to the data as described above is $2\sqrt{\frac{P}{k_BT}}$.

When I calculate $P$ this way, I get values between ~2.7 nm (when I choose a force range beween ~6-17pN, which is roughly linear, and the dsDNA molecule behaves as a Hookean spring). However these values are far below the expected value for the persistence length of dsDNA (50nm).

Does anyone see what' s wrong with my approach ?

Thanks a lot for help

Pen

P.S. please find attached the F-x-graph and the 1/sqrt(F)-x-graph

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Last edited: Aug 29, 2014
2. Aug 30, 2014

### Staff: Mentor

I find your 1/√F plot to have a y-intercept of 1.4

3. Aug 31, 2014

### pen

then unfortunately the plot was for a different force range, however in case the intercept is 1.4, the persistence length would be ~2nm (still much too low).