Calculate persistence length of a single dsDNA molecule

[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.

Homework 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 $2\sqrt{\frac{P}{k_BT}}$.

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

 

[epenguin]

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.

Homework 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 $2\sqrt{\frac{P}{k_BT}}$.

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

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.

 

[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.

 

[epenguin]

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

 

[DeeNos]

elope


Hello Penelope,

Thank you for sharing your problem and your attempt at a solution. From your description, it seems like you have followed the correct steps to calculate the persistence length of a single dsDNA molecule. However, the calculated value of 2.9 nm is significantly lower than the expected value of 50 nm. There could be a few reasons for this discrepancy:

1. Experimental error: It is possible that there were errors in the experimental setup or data collection that led to inaccurate force and extension measurements. This could be due to factors such as equipment calibration, external disturbances, or human error. It would be helpful to repeat the experiment and see if you get similar results.

2. Assumptions and limitations: The formula you used to calculate the persistence length assumes a linear relationship between force and extension, and it is only applicable for a specific force range of 5-15 pN. If the force range used in your experiment was outside of this range, it could have affected the accuracy of your calculations. Additionally, the formula assumes a worm-like chain model and does not account for the complexity of DNA structure. It is possible that these assumptions and limitations could have contributed to the discrepancy in your results.

3. Other factors: There could be other factors that affect the persistence length of a single dsDNA molecule, such as temperature, salt concentration, and DNA sequence. These factors may need to be controlled or taken into account in your calculations.

In conclusion, while your approach to calculating the persistence length seems correct, there could be various reasons for the discrepancy in your results. It would be helpful to carefully evaluate and control for potential sources of error and limitations in your experiment, and perhaps consult with other experts in the field for further insights. Good luck with your research!

Best regards,