Optical Microscopy Part 4: Particle Tracking

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20.309: Biological Instrumentation and Measurement

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In this part of the lab, you will follow microscopic objects throughout a series of movie frames: first small, fluorescent microspheres diffusing in purely viscous solutions of glycerol-water, next small fluorescent bacteria cells swimming in salt water. 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 diffusive vs. ballistic travel as a function of aerotactic stimuli.

Contextual background

Background references

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.

Instructions

Estimating the diffusion coefficient by tracking suspended microspheres

Imaging chamber for fluorescent microspheres diffusing in water:glycerol mixtures

1. Track some 0.84μm Nile Red Spherotech polystyrene beads in water-glycerin mixtures (Samples A, B and C contain 0%, 30% and 50% glycerin, respectively).

Notes: Fluorescent microspheres have been mixed for you by the instructors into water-glycerin solutions A, B, C, and D. (a) Vortex the stock Falcon tube, and then (b) transfer the bead suspension into its imaging chamber (consisting of a microscope slide, double-sided tape delimiting a 2-mm channel, and a 22x40mm No. 1.5 coverslip, and sealed at both ends nail polish).
Tip: Do not choose to monitor particles that remain stably in focus: these are likely to be 'sitting on the coverslip' and their motion will not be representative of diffusion in the viscous water-glycerol fluid.

2. Estimate the diffusion coefficient of these samples: $ \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. Use Sample A to verify that your algorithm correctly calculates the viscosity of water at the lab temperature (check the temperature on the clock on the wall or by other means).

  • Consider how many particles you should track and for how long. What is the uncertainty in your estimate?
  • From the viscosity calculation, estimate the glycerin/water weight ratio. (This chart is a useful reference.)
  • See: this page for more discussion of Brownian motion and a Matlab simulation.

Describing Vibrio alginolyticus behavior with transport equation

Snapshot of Vibrio alginolyticus swimming in water. The bacteria were stained with the FM 4-64 membrane dye.
Microfluidic slide designed to study bacterial response to aerotaxis. When air (20% oxygen) gets supplied to the "top" (red flag) channel and nitrogen (0% oxygen) to the "bottom" (blue flag) channel, Vibrio responds to varying levels of oxygen across the central channel.
Regulators and flow meters used for gas supply control in the bacterial aerotaxis experiment.

Let's ramp it up a notch and monitor living creatures this time! Instructors have dyed a sample of Vibrio alginolyticus, a Gram-negative marine bacterium approximately 2-3-microns in size (length of their ellipsoidic body) with the FM 4-64 [5] membrane dye and resuspended them in marine broth 2216 [6].

  1. Introduce < 10 μL V. alginolyticus in the central channel of the microfluidic chamber provided.
    • The channel is 600 μm in width and 100 μm in height.
    • It is typically easier to "suck" rather than "inject" the bacteria into the channel, by first pipetting a drop onto one of its extremities and next aspirating (by means of an empty pipet tip), from the other end, the solution through the microchannel and outward.
  2. Place the slide on your epi-fluorescence microscope equipped with a 40X objective.
    • Adjust the stage height to achieve focus on an actively swimming plane of bacteria.
    • In Matlab imaqtool, work at a Gain value (0-24) that allows image collection with Exposure Time Abs = 100,000 μs and Acquisition Frame Rate = 10 fps.
  3. Record three 1-minute movies of swimming V. alginolyticus at distinct coordinates across the central microchannel:
    • movie_rest_bottom: one movie with field of view (FOV) adjacent to the "bottom" channel (blue flag),
    • movie_rest_middle: one movie with FOV toward the center of the middle microchannel (~ 300 μm away, or halfway between the "bottom" and "top" outer channels), and
    • movie_rest_top: one movie with FOV adjacent to the "top" channel (red flag).
  4. Now let's observe and quantify aerotaxis on V. alginolyticus.
    • Prepare the gas supply:
      • Start with the slide disconnected (Tygon tubing tagged with red or blue tape).
      • Prepare both the air and nitrogen supply lines with (i) the nitrogen tank open, (ii) the air valve open, (iii) their two regulators only open to < 50 PSI, and (iv) their two flow meters only open to 10-15 (gradations).
    • Verify your FOV is still dwelling around a portion of the sample near the "top" channel (red flag).
    • Get ready!
      • You're about to record data during the short (~ 1-minute long) transient state of bacterial response to aerotaxis.
      • You are going to start recording bacterial motion for 1 minute in a movie encompassing pre- and post-application of an oxygen gradient across the central microchannel.
      • You are going to start acquiring a 1-minute movie, and right away, after a few seconds only, you are going to connect the "top" (red flag) and "bottom" (blue flag) channels to the air (20% oxygen) and nitrogen (0% oxygen), respectively.
    • Record Vibrio's travel during the short transient state of bacterial adaptation to the newly applied presence of oxygen:
      • Start acquiring a 1-minute movie, and right away, connect the "top" (red flag) channel to the air source, and the "bottom" (blue flag) channel to the nitrogen source: movie_transient_top
  5. Repeat the three 1-minute movies of swimming V. alginolyticus, now in the presence of a steady-state gradient of oxygen across the central microchannel:
    • movie_gradient_top: one movie with FOV adjacent to the "top" channel (red flag, air, 20% oxygen),
    • movie_gradient_middle:one movie with FOV toward the center of the middle microchannel, and
    • movie_gradient_bottom:one movie with FOV adjacent to the "bottom" channel (blue flag, nitrogen, 0% oxygen).

At the end of your lab session,

  • Make sure to turn all gas tanks off and degas their lines,
  • Purge the central channel of your microfluidic slide with deionized water, discarding the bacteria sample in a beaker of bleach.

Report

  1. Viscosity
    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 all glycerin samples (A, B, C, and D); 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, B, C, and D).
      • 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.
  1. Particle Tracking in Cells
    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 for untreated and Cyto 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.

Optical microscopy lab

Code examples and simulations

Background reading

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).
  5. ↑ See Life Technologies' website and 20.309 staining protocol
  6. ↑ See 2216 composition
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