Post on 23-Dec-2015
Light transfers momentum to matter
p = h/λ
Slides from Yann Chemla—blame him if anything is wrong!
Optical Traps
Key points
Trap strength depends on light intensity, gradient
Trap is harmonic: k ~ 0.1pN/nm
Light generates 2 types of optical forces: scattering, gradient
Optical scattering forces – reflection
Pi = h/λ
Pf
ΔP
Newton’s third law – for every action there is an equal and opposite reaction
F = ΔP/Δt = (Pf-Pi)/Δt
Pi
θ
Optical forces – Refraction
Pi
Pf
Pi
ΔP
Lateral gradient force
Bright ray
Dim ray
Object feels a force toward brighter light
Axial gradient force
Pi
Pf
PiΔP
Force ~ gradient intensity
Object feels a force toward focus
Focused light
IR traps and biomolecules are compatible
Neuman et al. Biophys J. 1999
Biological scales
www.alice.berkeley.eduwww.cnr.berkeley.edu/~hongwang/Project
www.scripps.edu/cb/milligan/projects.html
Force: 1-100 picoNewton (pN)Distance: <1–10 nanometer (nm)
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
ObjectiveCondenser
Photodetector
1) Manipulation
DNA
Want to apply forces – need ability to move stage or trap (piezo stage, steerable mirror, AOD…)
2) Measurement
Want to measure forces, displacements – need to detect deflection of bead from trap center
1) Video microscopy2) Laser-based method – Back-focal plane interferometry
BFP imaged onto detector
Trap laser
BFP
specimen
PSD
Relay lens
Conjugate image planes
∑
N
P
N
P
In1 In2
Out1
Out2
Position sensitive detector (PSD)
Plate resistors separated by reverse-biased PIN photodiode
Opposite electrodes at same potential – no conduction with no light
N
P
N
P
In1 In2
Out1
Out2
ΔX ~ (In1-In2) / (In1 + In2)
ΔY ~ (Out1-Out2) /(Out1+Out2)
POSITION
SIGNAL
Multiple rays add their currents linearly to the electrodes, where each ray’s power
adds Wi current to the total sum.
Calibration
Want to measure forces, displaces – measure voltages from PSD – need calibration
Δx = α ΔVF = kΔx = α kΔV
Glass
Glass
water
Glass
Calibrate with a known displacement
Calibrate with a known force
Move bead relative to trap Stokes law: F = γv
)(tFkxx
Brownian motion as test force
Langevin equation:
Drag forceγ = 3πηd
Fluctuating Brownian force
Trap force
<F(t)> = 0<F(t)F(t’)> = 2kBTγδ (t-t’)
kBT
kBT= 4.14pN-nm
ΔtΔtΔt
)()( txtx
Autocorrelation function )()( txtx
)()( txtx ΔtΔtΔt
Autocorrelation function )()( txtx
)(tFkxx
Brownian motion as test forceLangevin equation:
22 1
14
c
Bx
ffk
TkfS
FT → Lorentzian power spectrum
Corner frequencyfc = k/2π
k
Tkx B 2ttkB e
k
Tktxtx )()(
Exponential autocorrelation f’n
Po
we
r (V
2/H
z)
Frequency (Hz)
22
4 k
TkB
222
f
TkB
2
kfc
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
Reducing bandwidth reduces noise.
But (<x2>BW)1/2 = [∫const*(BW)dk]1/2= [(4kBT100)/k]1/2 = [4*4.14*10-6*100/0.1]1/2
~ 0.4 nm = 4 Angstrom!!
If instead you collect data out to a lower bandwidth BW (100 Hz), you get a much smaller noise.
(Ex: typical value of (10-6 for ~1 m bead in water).
6.4 nm is a pretty large number.
[ Kinesin moves every 8.3 nm; 1 base-pair = 3.4 Å ]
0.00 0.68 1.36 2.04 2.72
Probability (a.u.)
Distance (nm)0 2 4 6 8 10
0.00
0.68
1.36
2.04
2.72
3.40
Dis
plac
emen
t (n
m)
Time (s)
3.4 kb DNA
F ~ 20 pN
f = 100Hz, 10Hz
1bp = 3.4Å1
2
3
4
5
6
7
8 9
12
34
5
6
78
9UIUC - 02/11/08
Basepair Resolution—Yann Chemla @ UIUC
unpublished
Kinesin
Asbury, et al. Science (2003)
Step size: 8nm
Observing individual steps
Motors move in discrete steps Detailed statistics on kinetics of stepping & coordination
Class evaluation1. 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.