p = h/ λ

p = h/λ Slides from Yann Chemla— blame him if anything is wrong!

Optical Traps

Key points Light generates 2 types of optical forces: scattering, gradient Trap strength depends on light intensity, gradient Trap is harmonic: k ~ 0.1pN/nm

ΔP Pi Optical scattering forces – reflection 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

Pi ΔP Optical forces – Refraction Pi Pf

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

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

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

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

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, …) 2) Measurement – collection and detection optics (BFP interferometry) 3) Calibration – convert raw data into forces (pN), displacements (nm)

Laser Beam expander Photodetector Condenser Objective

1) Manipulation Want to apply forces – need ability to move stage or trap (piezo stage, steerable mirror, AOD…) DNA

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

BFP imaged onto detector Trap laser ∑ specimen Relay lens PSD BFP Conjugate image planes

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

Out1 P In1 N N In2 P Out2 Multiple rays add their currents linearly to the electrodes, where each ray’s power adds Wicurrent to the total sum. SIGNAL POSITION ΔX ~ (In1-In2) / (In1 + In2) ΔY ~ (Out1-Out2) /(Out1+Out2)

Calibration Want to measure forces, displaces – measure voltages from PSD – need calibration Δx = α ΔV F = kΔx = α kΔV

Calibrate with a known displacement Calibrate with a known force Glass water Glass Glass Move bead relative to trap Stokes law: F = γv

Drag force γ = 3πηd Brownian motion as test force kBT Langevin equation: Trap force Fluctuating Brownian force <F(t)> = 0 <F(t)F(t’)> = 2kBTγδ (t-t’) kBT= 4.14pN-nm

Δt Δt Δt Autocorrelation function

Brownian motion as test force Langevin equation: Exponential autocorrelation f’n FT → Lorentzian power spectrum Corner frequency fc = k/2πg

Power (V2/Hz) Frequency (Hz)

Reducing bandwidth reduces noise. The noise in position using equipartition theorem  you calculate for noise at all frequencies (infinite bandwidth). For a typical value of stiffness (k) = 0.1 pN/nm. <x2>1/2 = (kBT/k)1/2 = (4.14/0.1)1/2 = (41.4)1/2 ~ 6.4 nm 6.4 nm is a pretty large number. [ Kinesin moves every 8.3 nm; 1 base-pair = 3.4 Å ] If instead you collect data out to a lower bandwidth BW (100 Hz), you get a much smaller noise. (Ex: typical value of g (10-6 for ~1 mm bead in water). But (<x2>BW)1/2 = [∫const*(BW)dk]1/2= [(4kBTg100)/k]1/2 = [4*4.14*10-6*100/0.1]1/2 ~ 0.4 nm = 4 Angstrom!!

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

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

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.

p = h/ λ

p = h/ λ

Presentation Transcript