Preliminary Conclusions

1
The Design and Construction of Optical Tweezers 
 to Measure Piconewton Scale Biological Forces  
Chlamydomonas reinhardtii
Chlamydomonas reinhardtii
R.P. McCord, J.N. Yukich, and K.K. Bernd,
Davidson College, Davidson, North Carolina
Abstract
Experimental technique
Optical tweezers have many applications in
measuring biological forces due to their ability
to exert piconewton scale forces and to
manipulate biological material with minimal
damage.  This research involves the construction
and calibration of a dual-beam optical tweezers
laser trap apparatus and the use of this trap to
measure the swimming force exerted by the
unicellular flagellated algae Chlamydomonas
reinhardtii.  The data presented will demonstrate
the efficacy of this technique of force
measurement by comparing the force exerted by
wild type Chlamydomonas cells to that exerted by
oda1 cells, a mutant strain lacking the entire
dynein outer arm of the flagella.  This work will
both contribute to knowledge of optical tweezers
and their applications to investigations of
living biological systems. 

• The swimming force of Chlamydomonas reinhardtii
  cells is measured as follows
• The laser power is set to 1.0 W and the polarizer
  is adjusted so that all of the light travels
  through one path creating a maximum power trap
  spot at the microscope.
• A single swimming Chlamydomonas cell is trapped
  in a sample on a microscope slide.
• Using the polarizer, the laser power, and thus
  the trap force, is decreased until the swimming
  cell can just escape the trap
• This escape power is recorded as directly
  related to the swimming force exerted by the
  Chlamydomonas flagella.

Background
Preliminary data
Origin of Trapping Force
Lens Arrangement to Obtain Tight Focus
L2
L3
L1
Objective Lens
f1 f2
f3
16 cm
Figure from Svoboda and Block, 1994.
Image created from Physlet at http//webphysics.da
vidson.edu/Course_Material/Py230L/optics/lenses.ht
m Physlet by Dr. Wolfgang Christian and Mike Lee

• A dielectric particle is trapped by optical
  tweezers due to opposing scattering and gradient
  forces.
• The scattering force occurs in the direction of
  the laser beam and is caused by the collision of
  photons with the trapped object
• The gradient force (shown in diagram) is caused
  by the refraction of the laser light ray through
  the object. The force is equal and opposite to
  the change in momentum of the beam. As shown, an
  object will be pushed toward the brightest part
  of the beam and held in place at a tight focus.

• The best trap is obtained when the maximum
  light gradient is obtained. This corresponds to
  a very tight focus, which is obtained with four
  lenses.
• L1 and L2 form a telescope to expand the laser
  beam to fill the back of the microscope.
• L3 focuses the beam 16 cm away from the back of
  the objective lens.
• The objective lens has a high numerical aperture
  which creates a tight focus of the beam.

This graph shows a preliminary calibration
of the optical trap. Dead Chlamydomonas cells
were dragged with the piezoelectric stage through
the viscous fluid. The velocity at which the
viscous drag force caused the cell to escape from
the trap is directly proportional to the optical
force at that corresponding optical power. The
data follow a linear trend.

This graph shows the distribution of escape
powers recorded for mutant oda1cells and wild
type Chlamydomonas cells. The table below the
graph gives the sample size and average escape
power for each strain.
Preliminary Conclusions

• The force exerted on a Chlamydomonas cell by the
  optical trap is linearly related to the laser
  power.
• As expected for a living system, the swimming
  force exerted by individual Chlamydomonas cells
  is highly variable.
• Despite this variation, the average measured
  swimming forces and distribution of swimming
  forces demonstrate a clear difference between the
  dynein deficient oda1 mutant strain and the wild
  type strain. The mutant oda1 cells, which lack
  an important component of their flagella, exert a
  smaller swimming force than do wild type cells.

Apparatus
 
 
Future Work

• This optical method of force measurement will be
  used to examine whether flagella regenerated by
  Chlamydomonas after acid-induced deflagellation
  or flagella resorbtion are functionally
  equivalent to the original flagella in force
  production.
• This force measurement may be used to investigate
  the phenomenon of chemotaxis or phototaxis and
  the swimming forces exerted by cells attracted to
  such stimulants.
• The dual beam optical trap may be used for other
  Chlamydomonas investigations, such as a
  measurement of the adhesive forces between the
  cells during mating agglutination.

Active Layer
References
Laser Trap Setup

• Ashkin, A. (1997). Optical trapping and
  manipulation of neutral particles using
  lasers.Proc Natl Acad Sci U S A. 94, 4853-60.
• Konig, K., Svaasand, L., Liu, Y., Sonek, G.,
  Patrizio, P., Tadir, Y., Berns, M.W., Tromberg,
  B.J. (1996). Determination of motility forces of
  human spermatozoa using an 800 nm optical trap.
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  42, 501-9.
• Mammen, M., Helmerson, K., Kishore, R., Choi, S.
  (1996). Optically controlled collisions of
  biological objects to evaluate potent polyvalent
  inhibitors of virus-cell adhesion. Chemistry and
  Biology 3, 757-763.
• Minoura, I., Kamiya, R. (1995). Strikingly
  Different Propulsive Forces Generated by
  Different Dynein-Deficient Mutants in Viscous
  Media. Cell Motil. Cytoskel. 31, 130-139.
• Smith, S.P., Bhalotra, S.R., Brody, A.L., Brown,
  B.L., Boyda, E.K., Prentiss, M. (1999).
  Inexpensive Optical Tweezers for Undergraduate
  Laboratories. Am. J. Phys. 67, 26-34.
• Svoboda K., and Block S. (1994) Biological
  applications of optical forces. Ann. Rev.
  Biophys. Biomol. Struct. 23, 247-285.

This photograph of the optical tweezers setup
shows the 1.0 W NdYAG laser in the foreground.
The lenses and mirrors that direct and modify the
beam are seen behind this laser, followed by the
microscope for sample manipulation and the camera
and television screen which are used to view the
trapped samples.
This schematic diagram of the apparatus shows the
splitting of the laser beam with the combination
of a polarizer and two beam-splitting cubes.
This creates two independently manipulable traps.
The diagram also shows the path of the beam
through the lenses and microscope.
Acknowledgements
This work has been supported by Davidson
College, The National Institute of Standards and
Technology, and The Duke Foundation