Magnetic Tweezers for the Measurement of Twist and Torque

The overall goal of this experiment is to directly measure torsional strains or changes in the twist of double stranded DNA molecules at the single molecule level. This is accomplished using two assays in the first assay called freely orbiting magnetic tweezers or thumped. A single functionalized DNA molecule is tethered between a magnetic bead and a glass surface.

While a cylindrically shaped magnet exerts a force stretching the DNA In this configuration, the beads angular position is only constrained by the tethered DNA, not by the magnet, allowing bead rotation as shown by the red arrow to report on changes in the twist of the DNA rotational thermal fluctuations of the bead cause. Its XY position to lie on A circular annulus or donut. Conversion of this XY position to rotation angle makes it possible to monitor changes in the twist of the tethered DNA in a second related assay called magnetic torque tweezers, or MTTA side magnet is added to the main cylindrical magnet to constrain the beads angular motion.

With this magnet configuration, external torques can be applied to the tethered DNA molecule through simple rotation of the magnet assembly, measurements of the deviation of the beads angular position after applying a number of turns compared to its initial torsionally relaxed configuration, together with calibration of stiffness of the magnetic trap that confines the beads, angular motion makes it possible to quantify the buildup of torque in the DNA. The main advantage of using font and MTT over conventional magnetic tweezers is that we can directly measure torque and changes in the twist of nucleic acids. This method can help answer key questions about the mechanics of DNA and RNA by allowing us to map out their responses to external forces and torques.

The implications of this technique extend to probing the interactions of DNA with proteins. For example, proteins responsible for DNA repair storage, or transcription Visual demonstration of this method illustrates how easily a conventional magnetic tweezer set up can be modified to give it new capabilities. The setup used for the following experiments is based on a conventional magnetic tweezers setup.

At its center is a flow cell illuminated from the top by an LED and imaged through a microscope objective and CCD camera from below. Above the flow cell is a magnet head that can be moved up and down and rotated using computer controlled motors. The images from the CCD camera are analyzed in real time by custom lab view software to determine the X, Y, and Z position of DNA tethered beads.

The custom lab view software is available from the authors upon request. After preparing a flow cell with DNA tethered magnetic beads, mounting it on the conventional magnetic tweezers and selecting both a surface immobilized to reference bead and a bead to which an individual DNA molecule of the proper length is tethered. The setup may be converted to the font mode.

Begin by manually unscrewing the complete magnet head that holds the magnet for the conventional tweezers configuration. Replace it with the magnet head that holds a cylindrical magnet for font. While placing the cylindrical magnet used for F in the magnet head, be sure to keep the selected DNA tether within the field of view.

The most difficult aspect of this procedure is to correctly align the magnets for the form geometry. A good alignment is achieved by systematically moving the magnets and testing the alignment after every step, which we will demonstrate. Now, Perform a course alignment of the magnet in the font using the position stages to manually move the magnets in the lab view software.

Click on the record button to measure the XY position fluctuations or excursions. The recorded traces are displayed on the screen in real time and saved as text files that contain the X, Y, Z position information. If the XY excursions follow an arc as shown here, the cylindrical magnet is not properly aligned, continue moving the cylindrical magnet in the appropriate direction and taking measurements until the XY fluctuations trace out a complete circular pattern, which indicates that the course alignment is achieved.Next.

If required for further experiments, perform a fine alignment in the font by using a high resolution automated stage to move the flow cell, aligning the cylindrical magnet within about 10 microns of the bead. Then as before, record the XY excursions. Continue moving the stage and recording excursions until the fluctuations on the circular annulus are nearly uniform.

To verify the final alignment, use a MATLAB script which is available from the authors upon request to plot the fluctuations in a histogram or a thermogram and inspect it for uniformity. To take measurements of DNA torque, remove the cylindrical magnet that is used for font and replace it with a cylindrical magnet plus a permanent side magnet. For the MTT, ensure that the selected DNA tether remains within the field of view.

Enter the number and rate of magnetic turns in the corresponding panel of the controlling lab view software.Here. The number of turns is set to five and the rate is set to 0.1 hertz. This will cause the magnets to rotate slowly during the measurement.

Next in matlab, use an angular tracking script based on monitoring the XY position, which is available from the author upon request. A plot that displays the angular fluctuations as a function of time, theta T will appear. Once everything is set up in lab view, click the record button.

The traces will appear in real time as before. In matlab, use the MATLAB script to produce plots of angle theta T and bead height Z of T trace on screen with a Gaussian fit to the angle signal to determine the standard deviation of the angular fluctuations. Sigma theta.

This script directly determines the stiffness of the torsional trap from the variance of the angular fluctuations. Sigma theta squared in radians. Using the formula shown here, Note that it is typical in the MTT to achieve rotational trap stiffness of 10 to 1000 pico newton nanometer per radian, which is much lower than in the conventional magnetic tweezers.

Here, for example, we've determined the rotational trap stiffness to be about 52 pig nanometer per radian. The rotational trap stiffness of the magnetic torque tweezers compared to the conventional magnetic tweezers renders it suitable for measurements of single molecule torque, but also means that the maximum torque that can be exerted is reduced. This implies that the MTT cannot counterbalance drag torques caused by rapid rotation.

Care must therefore be taken not to rotate too fast. We typically rotate at rates of about 0.1 hertz. Next, the DNA tether is overwhelmed by slowly rotating the magnets, a set number of turns, and by recording another trace of angular fluctuations, the number and rate of magnet turns is again entered in the corresponding panel of the controlling lab view software.

Here the number of turns is set to 40 and the rate is set to 0.1 hertz. This will cause the magnets to rotate slowly during the measurement to determine the torque accumulated in the nucleic acid tether. After N turns, we use the formula shown here where the angled brackets denote the average and theta zero.

And theta N are the angle at zero turns corresponding to a torsionally relaxed tether and turns respectively. Repeat the steps which the magnets are rotated and record a plateau of angular fluctuations as necessary in order to fully determine a molecule's toque response in a single measurement run. To measure changes in the twist of the DNA induced by the repair protein RAD 51 whose binding to double stranded DNA, both lengthens and unwind.

DNA rad 51 was added to a DNA molecule tethered in the font. As shown here, the bead traces out a spiraling trajectory. This motion can be decoupled into components that describe how the DNA lengthens and unwinds over time.

To measure the torque stored in DNA using the MTT, the molecule with systematically over and under wound and the angular fluctuations were measured for each number of applied turns. The standard deviation of the angular fluctuations, which reports on the angular trap stiffness should be independent of the number of applied turns. Here, the standard deviation is about nine degrees as shown here.

The mean of the angular positions systematically changes with the number of applied turns using the constant angular trap stiffness. The changes in the mean angle are converted to torque, yielding the torque stored in the DNA versus applied turns. The simultaneous recording of the beads Z position yields the length of the DNA versus applied turns.

Together these two curves yield the full mechanical response of DNA to over and under winding. After watching this video, you should have a good understanding of how to measure, twist and torque on biological molecules using the freely orbiting magnetic tweezers and the magnetic torque tweezers to novel single molecule assays to which conventional magnetic tweezers can readily be adapted. The development of these techniques paves the way for research in the field of biophysics, for example, to study the torsional properties of DNA or RNA and to observe processes such as DNA compaction and repair The font and MTT techniques can be enhanced by other methods like fluorescence detection in order to answer additional questions such as determining the particular location of a protein on a tethered DNA.