Assignment 5 Overview

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20.309: Biological Instrumentation and Measurement

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Particle tracking

In this part of the lab, you will follow microscopic objects throughout a series of movie frames: small, fluorescent microspheres first diffusing in purely viscous solutions of glycerol-water, and next moving in fibroblast cells after endocytosis. Calculating the mean squared displacement of their motion as a function of time interval will allow you to characterize their physical environment and behavior, first in terms of diffusivity and viscosity coefficients of the glycerol-water mixtures, next recognizing other material or transport properties in fibroblast cells.

Contextual background

Brownian motion

This section was adapted from http://labs.physics.berkeley.edu/mediawiki/index.php/Brownian_Motion_in_Cells.

If you have ever looked at an aqueous sample through a microscope, you have probably noticed that every small particle you see wiggles about continuously. Robert Brown, a British botanist, was not the first person to observe these motions, but perhaps the first person to recognize the significance of this observation. Experiments quickly established the basic features of these movements. Among other things, the magnitude of the fluctuations depended on the size of the particle, and there was no difference between "live" objects, such as plant pollen, and things such as rock dust. Apparently, finely crushed pieces of an Egyptian mummy also displayed these fluctuations.

Brown noted: [The movements] arose neither from currents in the fluid, nor from its gradual evaporation, but belonged to the particle itself.

This effect may have remained a curiosity had it not been for A. Einstein and M. Smoluchowski. They realized that these particle movements made perfect sense in the context of the then developing kinetic theory of fluids. If matter is composed of atoms that collide frequently with other atoms, they reasoned, then even relatively large objects such as pollen grains would exhibit random movements. This last sentence contains the ingredients for several Nobel prizes!

Indeed, Einstein's interpretation of Brownian motion as the outcome of continuous bombardment by atoms immediately suggested a direct test of the atomic theory of matter. Perrin received the 1926 Nobel Prize for validating Einstein's predictions, thus confirming the atomic theory of matter.

Since then, the field has exploded, and a thorough understanding of Brownian motion is essential for everything from polymer physics to biophysics, aerodynamics, and statistical mechanics. One of the aims of this lab is to directly reproduce the experiments of J. Perrin that lead to his Nobel Prize. A translation of the key work is included in the reprints folder. Have a look – he used latex spheres, and we will use polystyrene spheres, but otherwise the experiments will be identical. In addition to reproducing Perrin's results, you will probe further by looking at the effect of varying solvent molecule size.

Diffusion coefficient of microspheres in suspension

According to theory,[1][2][3][4] the mean squared displacement of a suspended particle is proportional to the time interval as: $ \left \langle {\left | \vec r(t+\tau)-\vec r(t) \right \vert}^2 \right \rangle=2Dd\tau $, where r(t) = position, d = number of dimensions, D = diffusion coefficient, and $ \tau $= time interval.

Assignment details

This assignment has 2 parts:

  1. Part 1: Estimating the diffusion coefficient by tracking suspended microspheres;
  2. Part 2: Live cell particle tracking of endocytosed beads.

Submit your work in on Stellar in a single PDF file with the naming convention <Lastname><Firstname>Assignment5.pdf.


Pencil.png Here is a checklist of all things you have to turn in:

For Part 1:

  1. Procedure
    • Document the samples you prepared and used and how you captured images (camera settings including frame acquisition rate, number of frames, number of particles in the region of interest, choice of sample plane, etc)
  2. Data
    • Include a snapshot of the 0.84 μm fluorescent beads monitored.
    • Plot two or more example bead trajectories for each of the glycerin samples. (Hint: If you subtract the initial position from each trajectory, then you can plot multiple trajectories on a single set of axes.)
  3. Analysis and Results
    • Plot the average MSD vs τ results for the two glycerin samples (A and B); use log-log axes. Use the minimum number of axes that can convey your results clearly.
    • Include a table of the diffusion coefficient, viscosity and glycerin/water ratio for each of the samples (A and B)
    • Provide a bullet point outline of all calculations and data processing steps.
  4. Discussion
    • How do your viscosity calculations compare to your expectations? (This chart is a useful reference.)
    • Include a thorough discussion of error sources and the approaches to minimize them. It may be helpful to list out the error sources in a table, including a category for the error source, type of error (random, systematic, fundamental, technical, etc.), the magnitude of the error, and a description and way to minimize each one.

For Part 2:

  1. Procedure
    • Document the samples you prepared and used and how you captured images (camera settings including frame acquisition rate, number of frames, number of particles in the region of interest, choice of sample plane, etc)
  2. Data
    • Include a snapshot of the 0.84 μm fluorescent beads monitored.
    • Plot two or more example bead trajectories for each of the samples. (Hint: If you subtract the initial position from each trajectory, then you can plot multiple trajectories on a single set of axes.)
  3. Analysis and Results
    • Combine your data with others from the class to increase your sample size
    • Plot the average MSD (from the difference trajectories) for untreated and cytochalasin D treated cells on a single set of log-log axes.
  4. Discussion
    • What kind of motion do you see described by your MSD vs τ results?
    • What differences do you see between the untreated and Cyto D treated MSD curves?
    • Please suggest an interpretation of the behavior of your cells based on your data.
    • Include a discussion of your error sources.


Code examples and simulations

Navigation

Back to 20.309 Main Page

References

  1. A. Einstein, On the Motion of Small Particles Suspended in Liquids at Rest Required by the Molecular-Kinetic Theory of Heat, Annalen der Physik (1905).
  2. E. Frey and K. Kroy, Brownian motion: a paradigm of soft matter and biological physics, Ann. Phys. (2005). Published on the 100th anniversary of Einstein’s paper, this reference chronicles the history of Brownian motion from 1905 to the present.
  3. R. Newburgh, Einstein, Perrin, and the reality of atoms: 1905 revisited, Am. J. Phys. (2006). A modern replication of Perrin's experiment. Has a good, concise appendix with both the Einstein and Langevin derivations.
  4. M. Haw, Colloidal suspensions, Brownian motion, molecular reality: a short history, J. Phys. Condens. Matter (2002).