- Tethered particle motion
Tethered particle motion (TPM) is a biophysical method that is used for studying various
polymerssuch as DNAand their interaction with other entities such as proteins. The method allows to measure various physical properties on the substances, as well as to measure the properties of biochemical interactions with other substances such as proteins and enzymes.TPM is a single molecule experimentmethod.
TPM was first introduced by Schafer, Gelles, Sheetz and Landick in 1991 [ [http://www.nature.com/nature/journal/v352/n6334/pdf/352444a0.pdf Schafer, D.A., et al., "Transcription by single molecules of RNA polymerase observed by light microscopy." Nature, 1991. 352: p. 444-448.] ] . In their research, they attached
RNA polymeraseto the surface, and gold beads were attached to one end of the DNA molecules. In the beginning, the RNA polymerase "captures" the DNA near the gold bead. During the transcription, the DNA "slide" on the RNA polymerase so the distance between the RNA polymerase and the gold bead (the tether length)is increased. Using optical microscopethe area that the bead moves in was detected. The transcription rate was extracted from data.
Since then, a lot of TPM experiments were done, and the method was improved in many ways such as beads types, biochemstry techniques, imaging (faster cameras, different microscopy methods etc.) data analysis and combination with other single-molecule techniques (e.g. optical or magnetical tweezers).
Principle of the method
One end of a polymer is attached to a small bead (tens to hundreds of nanometer), while the other end is attached to a surface.Both the polymer and the bead stay in an aquaneos environment, so the bead moves in
Brownian motion. Because of the tether, the motion is restricted. Using optical microscopeand CCD camera, one can track the bead position in a time series. Although the bead is usually small 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.
right|thumb|250px|TPM simulation. The simulation done by
MATLAB, using Freely Jointed Chainmodel of polymer. The green points represent the projection of the end-to-end vector of the polymer on the XY plane.]
In order that the motion would be polymer dominated, and not bead dominated, one should notice that the exrusion number [ [http://dx.doi.org/10.1103/PhysRevLett.96.088306 Segall, D.E., et al., "Volume-exclusion effects in tethered-particle experiments: bead size matters." Physical Review Letters, 2006. 96: p. 088306-1-4.] ] will be less than 1:
where is the bead radius, is the
contour lengthof the polymer and is the persistence length(50nm in physiological conditions) of the polymer. (It is possible to work also when , but it should treated carefully.)
* Metal beads: The metalic beads (usually gold) scatter light with high intensity, so one can use very small beads (~40nm diameter), and still have a good picture. From the other hand, metallic beads are not the appropiate tool for
* Polystyrene beads: The
polystyrenebead scatter light weaker than metallic (in order to get the same intensity as getting from 40nm gold bead, the polystyrene bead should be ~125nm! [Paul R. Selvin, Taekjip Ha, "Single Molecule Techniques (Chapter 19)", Cold Spring Harbor Laboratory Press, 2008] ), but it has the advantage tat it can be combined with optical tweezers experiments.
* Fluorospheres: The major advantage of fluorospheres is that the excitation
wavelengthand the emission wavelength are not the same, so dichroic filtercan use in order to have cleaner signal. The disadvantage of the fluorospheres is photobleaching.
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.
Chip and Tether Assembly
A chip can be made of two coverslips. One of them should be drilled to make two holes so it would be possible to inject the reagents into the flowcell. The slides should be cleaned to remove dirt. A bath sonicator is a good tool for that, 15 minutes in Isopropanol should do the trick. Next, the a channel should be made. One way of doing so is to cut parafilm in the center, leaving a frame of parafilm that would be used as a spacer between the slides. The slides should be assembled one on the other with the cut parafilm between them. The final step would be to hit 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 pleanty of blocking reagents available (BSA, alpha-casein, etc) and one should find what fits best for him.Next, the surface should be coated with a steroid (such as anti-
digoxigenin) that will bind to an antibody ( digoxigenin) at one end of the polymer. After an incubation of about 45min, the excess antibody has to be washed away.After washing the excess antibody, the polymer should be injected into the chip and incubated for about the same time. The polymer had been modified before at the ends. One end has a biotin tail and the other has a digoxigenin tail. After incubation, unbound polymer has to be washed out from the cell. Then, anti- biotincoated beads should be injected to the flowcell and incubate for about 30-45min. Excess beads should be washed out.
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 pixelsize 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. It can be done with good resolution using two different techniques, both based on spot characteristics. The light intensity in the focal planedistributed as airy disk, and has circular symmetry.
Gaussian fitting: A 2-dimensional
Gaussian functionis a good approximation for airy disk. By fitting this function to the spot one can find the parameters and that are the coordinates of the center of the spot, and of the end-to-end vector.
"Center of mass": The second technique is to find the center of intensity [ [http://www.biophysj.org/cgi/reprint/89/2/1272.pdf Blumberg, S., et al., "Three-dimensional characterization of tethered microspheres by total internal reflection fluorescence microscopy." Biophysical Journal, 2005. 89: p. 1272-1281.] ] , using the definition of
center of mass:
where is the center of mass coordinate, is the number of the pixels in the spot, and and are the intensity and coordinate of the "k"-th pixel. Because of the circular symmetry, the coordinate of the center of intensity is the coordinate of the center of the bead.
Both techniques let us the coordinate of the end-to-end vector in a resolution better than pixel size.
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.
Usually, the whole system drifts during the measuring. There are several methods to correct the drift, generally can divided to 3 gruops:
Frequency: The Brownian motion frequency is much larger than the drift frequency, so one can use
high-pass filterin order to remove the drift. Similar effect can achieve by smoothing the data, and subtraction of the smoothed from the data (see figure).
Averaging over few beads: If few beads are showed in the frame, because evevry 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).
Immobilized bead: If immobilized bead are showed in the frame, we can take its position as a reference, and correcting the data by the immobilized bead's position. (Another advantage of looking at immobilized bead, is the fact that the motion of it can tell us about the accuracy of the measure.)
Of course one can use more than one method.
It is common to fit
random walkstatistics to the end-to-end vector of the polymer [Rubinstein, M. & Colby, R.H., "Polymer Physics (chapter 2.5 – Distribution of end-to-end Vector)", OXFORD University Press (2003).] . For 1-dimensional we'll get the Normal distribution, and for 2-dimensional the Rayleigh distribution:
where is the contour length and is the persistence length.
After collecting the data of time series, one should fitting the
histogramof the data to the distribution function (one or two dimensional). If the contour length of the polymer is known, the only fitting parameter is the persistence length.
entropic force, the polymer acts like [http://en.wikipedia.org/wiki/Statistical_mechanics#Random_walks_in_space Hookian spring.] According to Boltzmann distribution, the distribution is proprtional to exponent of the ratio between the elastic energyand the thermal energy:
where is the
spring constant, is Boltzmann constantand is the temperature. By taking the logarithmof the disribution and fitting it to a parabolashape, one can get the spring constant of the polymer [ [http://dx.doi.org/10.1117/12.699040 Dietrich, H.R.C., et al., "A new optical method for characterizing single molecule interactions based on dark field microscopy." Proceedings of the SPIE, 2007.] ] :
where is the coefficient of from the parabola fit.
Advantage and disadvantage
* Simple setup system.
* Not expensive.
* Observations are made in the polymer's natural environment (no external forces are being used).
* Suitable to various microscopy method (e.g.
TIRFM, Dark field, Differential interference contrast microscopy, etc.).
* Can be combined and manipulated using other methods.
* High variety of applications.
* Low spatial resolution (~30nm).
* Fits to
in vitroexperiments only.
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