# Homework Help: Calculate persistence length of a single dsDNA molecule

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1. Aug 30, 2014

### pen

Hello!

1. The problem statement and all variables

AIM: Calculating persistence length $P$ of a single dsDNA molecule from a data set of force $F$ (to the molecule) vs. extension $x$ measurements. Experimental background: pN forces were applied to a single dsDNA molecule spanned between two μm-beads using an optical tweezer.

PROBLEM: When I calculate $P$, I get values of about 2.9 nm, which is far below the expected value for $P$ of dsDNA, which is about 50nm.

2. Relevant equations

The calculation was done as follows: For a chosen force range the $F$-data were converted to $F^{-1/2}$ and plotted vs. $x$. The data points were fitted linearly.

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

$\frac{FP}{k_BT}=\frac{1}{4}(1−\frac{x}{L_0})−2−\frac{1}{4}+\frac{x}{L_0}$,

applicable for a force range of ~5-15pN, where the molecule reveals a linear $F-x$ relationship (like a Hookean spring).

From that follows that the y-intercept of the straight line fitted to the data points is $2\sqrt{\frac{P}{k_BT}}$.

3. The attempt at a solution

The problem is (as I think) that the slope of the fitted straight line is too low. So I chose different force-ranges, as I thought, that the chosen force range might be wrong. But that didnt work. In the attachement of the thread "Calculate persistence length from force extension data of a single DNA" one can find the force curve and a $F^{-1/2}-x$ graph, plotted for a force range of 6-16pN, with the linear fit: slope of -1.5151, the y-intercept at 1.6931 and a calculated persistence length of 2.9455 nm

I really would appreciate some help

Pen

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

### epenguin

I know approximately nothing about this subject, but the equation quoted relating F and x which I gather are your experimental parameters is linear so I don't understand how a square root could enter your calculation of an intercept. I wonder at a formula that contains 1/4 - 1/4.

3. Aug 31, 2014

### pen

Hello Epenguin!

Sorry, my mistake: it should be $\big(1-\frac{x}{L_0}\Big)^{-2}$ instead of $\big(1-\frac{x}{L_0}\Big)$ in the equation.

4. Aug 31, 2014

### epenguin

Too much guessing needed now, maybe if you quoted the equation and showed the plot something might become apparent.