Using Optical Tweezers as a Tool in Undergraduate Labs. Paul Ingram, Ido Braslavsky and David F. J....
1
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 •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. Methods •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 motors 1 and the physical properties of DNA 2 . •Beads can be attached to either end of a strand of DNA allowing it to be manipulated with the tweezers. •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. Optical Tweezers 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. Beam Intensity Force in out change Beam Intensity Force •Analysis of trap videos is done with Rytrack, one of several freely available particle tracking routines. •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. Analysis 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. Fig 2. 2µm beads in buffer solution. The bead in the lower center of the screen is trapped. Fig 3. Multiple traps of 2µm polystyrene beads. The bottom two beads are trapped, the dichroic used in this image does not allow the student to see glare from the laser. •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. 6 B kT D R Eqn 1. Equation relates the diffusion coefficient D to Boltzmann’s constant k B by the temperature T, radius R and viscosity η. 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 the filtered image as the program Results and Conclusions At the end of the lab students have used the Optical Tweezer setup to: • Gain a basic understanding of the fundamentals of optical trapping. • Gain a basic understanding of the fundamentals of particle tracking. • Calculate Boltzmann’s constant. • Explain trap stiffness and calculate it. • Learn how to operate basic programs in IDL. 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. Citations 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. 2 0 1 1 () ( ) 2 2 x B Ux k x x kT Eqn 2. Modeling the trap as a potential well we calculate the stiffness of the trap as spring constant k x . The right side is the energy from the equipartition theorem. M SD = 0.8098t 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 8 tim e (s) M SD (μm ²) 2 4 r Dt
-
Upload
polly-kelley -
Category
Documents
-
view
216 -
download
1
Transcript of Using Optical Tweezers as a Tool in Undergraduate Labs. Paul Ingram, Ido Braslavsky and David F. J....
Using Optical Tweezers as a Tool in Undergraduate Labs.Paul Ingram, Ido Braslavsky and David F. J. TeesDept of Physics and Astronomy, Ohio University, Athens OH 45701
•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.
Methods
• 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.
• Beads can be attached to either end of a strand of DNA allowing it to be manipulated with the tweezers.
• 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.
Optical Tweezers
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.
Beam Intensity
Force
in
out
change
Beam Intensity
Force
•Analysis of trap videos is done with Rytrack, one of several freely available particle tracking routines.
•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.
Analysis
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.
Fig 2. 2µm beads in buffer solution. The bead in the lower center of the screen is trapped.
Fig 3. Multiple traps of 2µm polystyrene beads. The bottom two beads are trapped, the dichroic used in this image does not allow the student to see glare from the laser.
•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.
6Bk T
DR
Eqn 1. Equation relates the diffusion coefficient D to Boltzmann’s constant kB by the temperature T, radius R and viscosity η.
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.
Results and Conclusions
At the end of the lab students have used the Optical Tweezer setup to:
• Gain a basic understanding of the fundamentals of optical trapping.
• Gain a basic understanding of the fundamentals of particle tracking.
• Calculate Boltzmann’s constant.
• Explain trap stiffness and calculate it.
• Learn how to operate basic programs in IDL.
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.
Citations
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.
20
1 1( ) ( )
2 2x BU x k x x k T 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.
MSD = 0.8098t
0
1
2
3
4
5
6
7
0 1 2 3 4 5 6 7 8time (s)
MS
D (
μm
²)
2 4r Dt
