Transcript Document

Using Optical Tweezers as a Tool in Undergraduate Labs.
Paul Ingram, Ido Braslavsky and David F. J. Tees
Dept of Physics and Astronomy, Ohio University, Athens OH 45701
Optical Tweezers
Fig 5. IDL based
particle
tracking
software. The upper
image shows the
unfiltered video with
red dots on particles
that
the
input
parameters identify.
The lower screen
shows the filtered
image
as
the
program sees it.
• Optical trapping using a device called Optical Tweezers was
developed in the 1980s from work on laser trapping of atoms.
• It was realized that a focused laser could be used to trap and
manipulate micrometer-sized particles, such as latex beads.
• Researchers have used optical tweezers to study molecular motors1
and the physical properties of DNA2.
• Trap is made by directing a laser through the objective lens of a
microscope.
• In our Tweezer the beam is split into multiple traps and manipulated
using a Holographic Optical Trap (HOT) plate made by Arryx Inc.
•HOT plate software allows students to move traps manually, create
preprogrammed trap movements, change the depth of traps relative to
the focus of the microscope and take distance measurements.
Beam Intensity
Beam Intensity
Fig 4. Sequential images of
magnetic streptavidin coated
bead burning in the laser. A
gas bubble appears and rapidly
expands. In the last image the
stage is being moved and a
path is burnt into the slide.
The beads had settled to the
surface of the slide.
in
out
Force
Force
change
Fig 6. Graph of the mean
squared displacement <r²> vs
time t of thirty-one 2µm beads.
Video was taken through the
40x air objective. For this value
of the diffusion coefficient D
we get 1.3x10-23 ± .1 for
Bolzmann’s constant.
7
r 2  4 Dt
6
MSD = 0.8098t
5
MSD (μm²)
• Beads can be attached to either end of a strand of DNA allowing it to
be manipulated with the tweezers.
Fig 2. 2µm beads in buffer solution. Fig 3. Multiple traps of 2µm
polystyrene beads. The bottom two
The bead in the lower center of the
beads are trapped, the dichroic used
screen is trapped.
in this image does not allow the
student to see glare from the laser.
4
3
2
1
0
0
1
1
1
2
U ( x)  k x ( x  x0 )   k BT
2
2
2
3
4
time (s)
5
6
7
Eqn 2. Modeling the trap as
a potential well we calculate
the stiffness of the trap as
spring constant kx. The
right side is the energy from
the equipartition theorem.
Results and Conclusions
At the end of the lab students have used the Optical Tweezer setup to:
Fig 1. For objects larger than the laser wavelength the trap can be explained
using ray optics. From Newton’s 3rd law the change in momentum as the ray
enters and exits the bead forces it back to the center of the beam.
Methods
•Students first observe the Brownian motion of 2µm beads under the
microscope to familiarize them with the equipment, programs and
principles required to calculate the trap stiffness later on.
•Students then manipulate the beads to gain a basic understanding of
the fundamentals of optical trapping.
•Students create multiple traps and can use different concentrations
and types of beads such as silica, magnetic or polystyrene.
Analysis
• Gain a basic understanding of the fundamentals of optical trapping.
•Analysis of trap videos is done with Rytrack, one of several freely
available particle tracking routines.
• Gain a basic understanding of the fundamentals of particle tracking.
•The routine outputs the x and y position in pixels and the frame
number for each particle.
•This data is used to calculate the diffusion coefficient and then
Boltzmann’s constant from video of untrapped beads.
• Students calculate the trap stiffness using statistical analysis of the
beads position.
k BT
D
6 R
Eqn 1. Equation relates the diffusion
coefficient D to Boltzmann’s constant kB by
the temperature T, radius R and viscosity η.
• Calculate Boltzmann’s constant.
• Explain trap stiffness and calculate it.
• Learn how to operate basic programs in IDL.
Citations
1. Svoboda, K., et al., Direct observation of kinesin stepping by optical
trapping interferometry. Nature. 365:721-727, 1993.
2. Wang, M.D., et al. Stretching DNA with optical tweezers.Biophysical J.
72:1335-1346, 1997.
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