Download FA15Lec17 Optical Traps.Two

Announcements
Midterm grades: online by 5pm today
HW: VMD (primarily) due Thursday Oct 29th.
Optical Traps/Tweezers
Physics: use lasers and optical traps to control individual
molecular motors.
Biology: can study how forces operate on these motors.
Cartoon of kinesin walking in cell
(Optical Traps primarily used for in vitro motion)
Optical Traps
Hold bead with some force, F.
Have the molecular motor pull against it.
How does motor act as a function of force? ATP? Mutation?
For an Optical Trap to work
• Gradient of laser beam (trapping):
bead attracted to brightest spot
• Generate optical trap force ~ motor force
• Laser beam is altered and position measured.
Optical Traps (Tweezers)
Z
Dielectric objects are attracted to the center (x-y) of the beam where
light is brightest. (Slight deviation in z-direction due to reflection.)
Depends on gradient of beam, index of refraction of bead vs. water.
Vary ktrap with laser intensity such that ktrap ≈ kbio (k ≈ 0.1pN/nm)
~ to stiffness of motor.
Can measure pN forces and (sub-) nm steps!
http://en.wikipedia.org/wiki/Optical_tweezers
Lateral (x-y) gradient force (leads to trapping in x-y)
(Snell’s law twice: two surfaces)
Bright ray
Dim ray
Z 
Object feels a force toward brighter light
Axial (z-axis) gradient force: leads to trapping in z
How so?
ΔP
Pi
Focused
light
Pf
Pi
Z 
Object feels a force toward focus
Force ~ gradient intensity
What about: Optical scattering forces – reflection
(Not of interest, here)
Pf
Pi = h/λ
ΔP
θ
Pi
Z 
F = ΔP/Δt = (Pf-Pi)/Δt
Newton’s third law – for every action there is an equal and opposite reaction
Estimate size of trapping force
Want: Force (pN) as a function of Laser Power (mW)
F= Dp/Dt = 2 pphoton/Dt ≈ Qpphoton/Dt
Convert pphoton into Energy/time = Power
Photon in vacuum: Energy = f( pphoton ) = pphotonc
Photon in index of refraction n: goes with speed v
E = pphotonv = pphotonc/n
E/Dt = pphotonc/nDt = Power = P
F = Qpphoton/Dt =
QPn/c
pphoton/Dt = Power n/c
Incident momentum/sec =
Power P in medium of
refractive index.
Estimating Trap Force/Stiffness
F = QPn/c
Q spherical particle radius ~ l ~ 0.1
This is approximately correct:
Vary ktrap with laser intensity such that ktrap ≈ kbio (k ≈ 0.1pN/nm)
How to detect movement of bead?
Measuring the position of a trapped bead
As bead moves to side,
so does trapping light
Want a Position
Sensitive Detection to
measure
How you get parallel light?
Recall Len’s Maker’s Equation
Put object at the focal length of lens.
Then image is at infinity.
Position sensitive detector (PSD)
Out1
Plate resistors separated by reversebiased PIN photodiode
P
In1
N
N
In2
P
Out2
Opposite electrodes at same potential
– no conduction with no light
Multiple rays add their currents linearly to the electrodes, where each ray’s power
adds Wi current to the total sum.
SIGNAL
Out1
P
In1
N
N
In2
POSITION
P
Out2
ΔX ~ (In1-In2) / (In1 + In2)
ΔY ~ (Out1-Out2) /(Out1+Out2)
Linear signal with position.
Can just read off signal, get position
Laser
Beam expander
Photodetector
Condenser Objective
Optical Traps
How small can you see? 1 base-pair (3.4 Å)?
• Get rid of (noise) sources of vibration.
• Get rid of KBT of thermal vibration
Basepair Resolution—Yann Chemla @ UIUC
Eliminate (floor) noise
Limit BW—noise
Take difference & sum.
Diff: no shaking of floor!
comes in at all
frequencies
3.40
1bp = 3.4Å
1
PNAS
2
3
1
2
2.04
4
3
5
4
1.36
5
6
6
0.68
7
7
8
UIUC - 02/11/08
0.00
0
2
Probability (a.u.)
Displacement (nm)
2.72
4
6
Time (s)
8 9
9
3.4 kb DNA
8
10
0.00
0.68
1.36
2.04
Distance (nm)
2.72
F ~ 20 pN
f = 100Hz, 10Hz
What is noise in measurement?.
The noise in position using equipartition theorem
[For a typical value of stiffness (k) = 0.1 pN/nm; kBT= 4.1pN-nm
<x2>1/2 = (kBT/k)1/2 = (4.14 pN-nm/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 ]
How to decrease noise?
Hint: Equipartion Theorem calculates for noise at all frequencies
(infinite bandwidth).
Reduce bandwidth.
Also: Operate at high force less noise due to finite Temp.
Also be clever about how to differentiate noise from signal.
Solve Langevin’s Equation,
Get power spectrum of bead in an optical trap.
Noise is not distributed evenly
across all frequencies in an
optical trap. Most noise at low f.
fc 
k
= trap stiffness
2 γ = 6πηr (for sphere)
Bandwidth = infinite:
limit to ~6 nm.
If use BW = 100 Hz
~ 0.4 nm = 4 Angstrom!!
Also, know how to cut out noise.
Take out frequencies where signal isn’t
Class evaluation
1. 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.