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Using Tethered Particle Motion Experiments in Statistical Mechanics or Biophysics Labs Adam D. Smith, Obinna A. Ukogu, and Ashley R. Carter We propose the adoption of a biophysics lab for undergraduate education in either the modern or advanced laboratory. Biophysics is a field that is rapidly growing at many institutions, and biophysics labs like the one described here will develop a student’s ancillary skills in biochemistry, microscopy, and computational analy- sis, in addition to providing an opportunity to sample physics research. This biophysics lab is based on teth- ered particle motion (TPM). In our case, tethered particle motion involves using video microscopy to track the 2-D position of a polystyrene particle tethered to the surface by a DNA molecule. The particle will be undergo- ing Brownian motion, and the standard deviation of that Brownian motion over time is correlated to the length of the tether. First, students will prepare the single-molecule assay using molecular biology techniques, im- portant in interdisciplinary research. Then they will use video microscopy to record the position of the particle over time, use a program to analyze the data, and experimentally determine the length of their DNA tether. Tethered particle motion has a wide variety of research applications ranging from rheology to the mechanics of DNA compaction, and is relatively simple for undergraduate students to set up and execute. We used tethered particle motion to determine the length of a DNA molecule. Students perform- ing this lab will learn about biochemistry, microscopy, and computer vision, which are important skills for indisciplinary research. This laboratory could serve as the introductory laboratory in a biophysics class or could be combined with an applied research project on tethered particle motion (see “Tethered Particle Motion Experiments as a Gateway to Biophysics Research” by Obinna Ukogu). Department of Physics, Amherst College, Amherst, MA 01002 [1] Schafer, Dorothy A., Gelles, Jeff, Sheetz, Michael P., Landick, Robert. (1991). Transcription by single mole- cules of RNA polymerase observed by light microscopy. Nature, 352. [2] Catipovic, Marco A., Tyler, Paul M., Trapani, Josef G., Carter, Ashley R. (2012). Improving the quantification of Brownian motion. American Journal of Physics, 81. [3] Beausang, J.F., Zurla, C., Finzi, L., Sullivan, L. & Nelson, P.C. Elementary simulation of tethered Brownian motion. American Journal of Physics, 75. Abstract What is Tethered Particle Motion? Part II - Image Modification & Computational Analysis Part I - Biochemical Prep. & Particle-Tracking Microscopy Conclusion References Figure 2 (above): Using a model [3], we can simulate TPM for different DNA lengths (blue) and fit the points to a polynomial curve (black). The fit allows students to easily calculate the DNA length from the standard deviation. Goal: Learn how to use computer vision to track a particle Time Required: 2 hrs Goal: Learn molecular biology lab techniques and microscopy Time Required: 1 hr prep, 2 hrs wait Questions for Students: 1) How will we know if a particle we’re looking at has bound itself to two DNA molecules? 2) What would an x vs. t graph look like for a 200 nm piece of DNA? What about 1000 nm? 10000 nm? Why would it be imprudent to use TPM to determine the exact length of an extremely long DNA fragment? Questions for Students: 1) What could go wrong if we attached digoxigenin to both ends of the DNA and anti-digoxigenin to the slide and the particle? 2) What would the video look like if the particle were not tethered to the sample chamber? ● Sample Chamber Preparation ● Biochemical Assay Preparation ● Image Capture ● Image Modification ● Track Particle & Calculate Standard Deviation ● DNA Length from Standard Deviation is ~1100 nm Goal: Use tethered particle motion to experimentally mea- sure the length of a DNA molecule Polynomial fit to data yields L(σ) DNA Length, L (nm) Figure 1 (above): Differences between free motion of a particle and tethered particle motion (TPM). (A) In TPM [1], a particle is tethered to a sample chamber via a DNA molecule, and does not undergo diffusion like a free particle. (B) The mean squared displacement <x 2 > of a free parti- cle undergoing Brownian motion increases linearly over time and can be easily measured in the lab [2]. The mean squared displacement for a tethered particle remains constant, but increases with the tether length. And because the square root of the mean squared displacement is the stan- dard deviation of displacement, we know that standard deviation increases as tether length in- creases. t 1 A B t 2 t 3 t 4 Cover Slip Tethered Particle DNA Molecule Free Particle Epoxy Slide Streptavidin Biotin Digoxigenin Anti-Digoxigenin DNA Molecule -500 0 500 x (nm) 200 150 100 50 0 t (s) Cover Slip Double-sided tape x y z x y z Standard Deviation, σ (nm) σ = 267 nm -500 0 500 y (nm) -500 0 500 Free particle follows Einstein’s equation < x 2 (t) > = 2Dt < x 2 > (μm 2 ) t (s) x (nm) 0 0.2 0.4 0.6 0.8 1 1 2 1.5
