Optical Microscopy: Brownian motion and microscopy stability

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20.309: Biological Instrumentation and Measurement

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Brownian motion

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.

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).

M. Haw, Colloidal suspensions, Brownian motion, molecular reality: a short history, J. Phys. Condens. Matter (2002).

E. Frey and K. Kroy, Brownian motion: a paradigm of soft matter and biological physics, Ann. Phys. (2005).

Myosin XI and vesicle trafficking in plant cells

Nebenfuhr Lab: The Plant Myosin Page

Tominaga, et. al. Higher plant myosin XI moves processively on actin with 35 nm steps at high velocity. The EMBO Journal Vol. 22 No. 6 pp. 1263-1272, 2003

S. Bolte, C. Talbot, Y. Boutte, O. Catrice, N. D. Read, B. Satiat-Jeunemaitre. FM-dyes as experimental probes for dissecting vesicle trafficking in living plant cells. Journal of Microscopy 214(2): 159-173 (May 2004).

Avisar, et. al. Myosin XI-K Is Required for Rapid Trafficking of Golgi Stacks, Peroxisomes, and Mitochondria in Leaf Cells of Nicotiana benthamiana1. Plant Physiology 146:1098-1108 (2008)

Peremyslov, V., et. al. Two Class XI Myosins Function in Organelle Trafficking and Root Hair Development in Arabidopsis. Plant Physiology 146:1109-1116 (2008)

Experiment 1: tracking particles in suspension

Introduction and background[1]

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. J. 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.

Microscope stability for particle tracking

To verify that your system is sufficiently stable for accurate particle tracking, measure a dry specimen containing 1μ beads in bright field contrast. Chose a field of view in which you can see at least 3-4 beads. Using a 40x objective, track the beads for about 3 min. Use the bead tracking processing algorithm on two beads to calculate two trajectories. To further reduce common-mode motion from vibrations, calculate the differential trajectory from the individual trajectories of these two beads. Calculate the MSD from the differential trajectory. Your MSD should start out less than 10 nm2 at t = 1 sec. and still be less than 100 nm2 for t = 180 sec.

Estimating the diffusion coefficient by tracking suspended microspheres

According to theory,[2][3][4][5] 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.

  • Track some 3μm (Samples A & B) and 5μm (Samples C & D) microspheres.
  • Estimate the diffusion coefficient of these microspheres suspended in solutions of varying viscosities. For reference, Sample A contains 3μm spheres suspended in water.
  • Consider how many particles you should track and for how long. What is the uncertainty in your estimate?

See: this page for more discussion of Brownian motion and a Matlab simulation.

References

  1. taken from http://labs.physics.berkeley.edu/mediawiki/index.php/Brownian_Motion_in_Cells
  2. 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).
  3. 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.
  4. 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.
  5. M. Haw, Colloidal suspensions, Brownian motion, molecular reality: a short history, J. Phys. Condens. Matter (2002).