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Calculate persistence length of a single dsDNA molecule

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  1. Aug 30, 2014 #1

    pen

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    Hello!

    1. The problem statement and all variables

    AIM: Calculating persistence length [itex]P[/itex] of a single dsDNA molecule from a data set of force [itex]F[/itex] (to the molecule) vs. extension [itex]x[/itex] 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 [itex]P[/itex], I get values of about 2.9 nm, which is far below the expected value for [itex]P[/itex] of dsDNA, which is about 50nm.

    2. Relevant equations

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

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

    [itex]\frac{FP}{k_BT}=\frac{1}{4}(1−\frac{x}{L_0})−2−\frac{1}{4}+\frac{x}{L_0}[/itex],

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

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

    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 [itex]F^{-1/2}-x[/itex] 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. jcsd
  3. Aug 30, 2014 #2

    epenguin

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    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.
     
  4. Aug 31, 2014 #3

    pen

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    Hello Epenguin!

    Sorry, my mistake: it should be [itex] \big(1-\frac{x}{L_0}\Big)^{-2}[/itex] instead of [itex] \big(1-\frac{x}{L_0}\Big)[/itex] in the equation.
     
  5. Aug 31, 2014 #4

    epenguin

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