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50-60 60-70 70-80 80-90 90-100. Optical Traps (Tweezers) con’t. Dielectric objects are attracted to the center of the beam, slightly above the beam waist. This depends on the difference of index of refraction between the bead and the solvent (water).

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50-60 60-70 70-80 80-90 90-100

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  1. 50-60 60-70 70-80 80-90 90-100

  2. Optical Traps (Tweezers) con’t Dielectric objects are attracted to the center of the beam, slightly above the beam waist. This depends on the difference of index of refraction between the bead and the solvent (water). Vary ktrap with laser intensity such that ktrap ≈ kbio (k ≈ 0.1pN/nm) Can measure pN forces and (sub-) nm steps! http://en.wikipedia.org/wiki/Optical_tweezers

  3. Key points Light generates 3 types of optical forces: absorption, reflection (scattering), refraction. Absorption: along direction of incident photons minimize– use IR light. Reflection/Scattering: along direction of incident photons. Try to minimize. Refraction – bending of light. Change in momentum, produces force. Trap strength depends on light intensity, gradient Trap is harmonic: k ~ 0.1pN/nm

  4. Pi Pi Optical forces: absorption Reaction of sphere = forward motion Minimize by IR light (where protein & bead doesn’t absorb) Pi= h/λ Absorption– along direction of incident photons

  5. IR traps and biomolecules & water are compatible Neuman et al. Biophys J. 1999

  6. ΔP Pi Optical scattering forces – reflection ~along direction of incident photons Try to minimize: small compared to refraction Pf Pi = h/λ θ F = ΔP/Δt = (Pf-Pi)/Δt Newton’s third law – for every action there is an equal and opposite reaction

  7. Pi ΔP Optical forces – Refraction Pi Pf

  8. Bright ray Dim ray Lateral gradient force Object feels a force toward brighter light

  9. ΔP Pi Axial gradient force Focused light Pf Pi Object feels a force toward focus Force ~ gradient intensity

  10. Biological scales Force: 1-100 picoNewton (pN) Distance: <1–10 nanometer (nm) www.scripps.edu/cb/milligan/projects.html www.cnr.berkeley.edu/~hongwang/Project www.alice.berkeley.edu

  11. Why does index of refraction of bead nbead > nwater for trap to work? Beam doesn’t change at all No scattering, no bending nbead = nwater Regular, stable trap. Force towards most intense light. Scattering, Bending. nbead > nwater Unstable trap. Force towards least intense light. Scattering, Bending, wrong way. nbead < nwater

  12. = 2p/Dt Dp/Dt Force on material = Slightly more general: F = Dp/Dt = Qp/Dt Q = (dimensionless) efficiency factor (not a perfect reflector so Dp= 2p Now we want to convert momentum/time into something more convenient like energy/time = power of incident light.

  13. For light (in vacuum) E = pc (E= energy; p = momentum) For light in material with index of refraction n E= pv = pc/n energy/photon E/Dt = pc/nDt = Power Incident momentum per sec of a ray of Power in a medium of refractive index n p/Dt = (n/c) Power Force = Qp/Dt = Q Power (n/c) Q for spherical particle radius ~ l Q ~ 0.1 P = 1 mW = 1 mJ/sec = 10-3 N-m/s F ~ (0.1) (10-3 N-m/s) (~1.3)/ 3 x 108m/sec) Force of molecular motors : ~1-10, occasionally 60 pN F ~ (0.5 pN/mW of laser power

  14. Motors move in discrete steps: Kinesin moves 8.3 nm per ATP How much force do they generate? 7pN Efficiency? 8 nm x 7 pN = 56 pN–nm per step ATP ~ 80-100 pN-nm 75% efficient! By comparison: Car = 20% efficient!

  15. Observing individual steps Motors move in discrete steps Detailed statistics on kinetics of stepping & coordination Kinesin Step size: 8nm Asbury, et al. Science (2003)

  16. Basic Optical Trap set-up

  17. 1 2 3 1 2 4 3 5 4 5 6 6 7 7 8 9 9 8 Basepair Resolution—Yann Chemla @ UIUC unpublished 1bp = 3.4Å UIUC - 02/11/08 3.4 kb DNA F ~ 20 pN f = 100Hz, 10Hz

  18. Requirements for a quantitative optical trap: 1) Manipulation – intense light (laser), large gradient (high NA objective), moveable stage (piezo stage) or trap (piezo mirror, AOD, …) [AcoustOptic Device- moveable laser pointer] 2) Measurement – collection and detection optics (BFP interferometry) 3) Calibration – convert raw data into forces (pN), displacements (nm)

  19. Laser Beam expander Photodetector Condenser Objective

  20. 1) Manipulation Want to apply forces – need ability to move stage or trap (piezo stage, steerable mirror, AOD…) (Acouto Optic Device: variable placement of laser) DNA By using two beads, and taking difference, capable of removing floor movement! Get to Angstrom level!

  21. 2) Measurement Want to measure forces, displacements – need to detect deflection of bead from trap center 1) Video microscopy 2) Laser-based method – Back-focal plane interferometry

  22. 2) Measurement: BFP imaged onto detector Trap laser ∑ specimen Relay lens PSD BFP (Image at point P will get imaged to point P’) Conjugate image planes

  23. Out1 P In1 N N In2 P Out2 Position sensitive detector (PSD) Plate resistors separated by reverse-biased PIN photodiode Opposite electrodes at same potential – no conduction with no light

  24. Class evaluation • What was the most interesting thing you learned in class today? • 2. What are you confused about? • 3. Related to today’s subject, what would you like to know more about? • 4. Any helpful comments. Answer, and turn in at the end of class.

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