Tethered particle motion

Tethered particle motion (TPM) is a biophysical method that is used for studying various polymers such as DNA and their interaction with other entities such as proteins.

In the beginning, the RNA polymerase "captures" the DNA near the gold bead.

data analysis and combination with other single-molecule techniques (e.g. optical or magnetical tweezers).

Using an optical microscope and CCD camera, one can track the bead position in a time series.

Although the bead is usually smaller than the diffraction limit, so the image is a spot which is larger than the bead itself (point spread function), the center of the spot represents the projection on the X-Y plane of the end of the polymer (end-to-end vector).

Analyzing the distribution of the bead position can tell us a lot of information about the polymer.

From the other hand, metallic beads are not the appropriate tool for optical tweezers experiments.

All of the bead types and diameters (with the biochemistry marker, look at the tether assembly section) are manufactured by commercial companies, and can purchased easily.

One of them should be drilled to make two hole, allowing the reagents to be injected into the flowcell.

A bath sonicator is a good tool for that, 15 minutes in Isopropanol should do the trick.

The final step is to heat the chip so that the parafilm will melt and glue the slides together.

First, the chip has to be passivated so that the polymer won't stick to the glass, there are plenty of blocking reagents available (BSA, alpha-casein, etc.)

and one should find what works best for the specific situation Next, the surface should be coated with an antibody or other reactive molecule (such as anti-digoxigenin) that will bind to an antigen (digoxigenin) at one end of the polymer.

After washing the excess antibody, the polymer should be injected into the chip and incubated for about the same time.

As mentioned above, the image doesn't show the bead itself but a larger spot according to its PSF (Point spread function).

In addition, the pixel size on the camera may reduce the resolution of the measure.

In order to extract the exact bead's position (that corresponds to the end-to-end vector), the center of the spot should be found as accurate as possible.

The light intensity in the focal plane distributed as airy disk, and has circular symmetry.

Both techniques give us the coordinate of the end-to-end vector in a resolution better than pixel size.

If few beads are shown in the frame, because every bead moving randomly, averaging over the position of them for every frame should give us the drift (it should subtracted from the data for having clean data).

(Another advantage of looking at immobilized bead, is the fact that the motion of it can tell us about the accuracy of the measure.)

It is common to fit random walk statistics to the end-to-end vector of the polymer.

Due to entropic force, the polymer acts like Hookian spring.

Advantages include a simple setup, cost, the fact that observations are made in the polymer's natural environment (no external forces are used), it is suitable for various microscopy methods (e.g. TIRFM, dark field, differential interference contrast microscopy, etc.

Disadvantages include low spatial resolution (~30 nm) and that it fits to in vitro experiments only.

TPM - the bead diffuses in the solution, but because of the tethering, it can move only in restricted volume.
TPM simulation . The simulation done by MATLAB , using the freely-jointed chain model of polymers . The green points represent the projection of the end-to-end vector of the polymer on the XY plane.
Video taken from TPM experiment, using darkfield microscope. The green framed beads are tethered beads, and the red framed are immobilized beads.
TPM drift: top: The green graph is the data of the TPM experiment, the black curve is smoothing of the data (the drift). bottom: Subtraction of the drift from the data.