Optical Tweezers

Fscatt

Fgrad

1

Velocity autocorrelation function from the Langevin model

0

/

0

0 dtem

kTdttvv mt

kinetic propertyproperty of equilibrium fluctuations

,300

Ddtt

vv

For 3-dimensional model

Green-Kubo relationship

D

2

kT

Fluctuation – Dissipation Theorem

x-axis

F(x)

Periodic asymmetric potential(Randomly fluctuating)

A simple Brownian ratchet

Random diffusion of protein(Gaussian probability distribution)

Probability for protein to move across the potential barrier to the right (+x) is higher than to move to the left

0 a-b

3

Manipulating single molecules

• Attach molecule to magnetic particle and use magnetic fieldMagnetic tweezers

• Attach molecule to dielectric particle and use laser lightOptical tweezers

mirror

AFM tip

photodiode position detector

cantilever

laser

imaging surface

sample

laser beam

focus of optical trap

trapF externalF

optical trap force balances the external force

magnetic bead

external magnets

DNA

surface

Atomic Force Microscope Optical Tweezers Magnetic Tweezers

objective

F

1

The physics behind optical tweezers

The change in momentum can be calculated by the difference of momentum flux between entering and leaving a dielectric object

BES

0

1

is the Poynting vector for an electromagnetic waveS

Momentum flux of photons is given by

dAScndtPdd

)/()/(

5

Optical Trapping - a>> Conditions for Mie scattering when the particleradius a is larger than the wavelength of the light .

We can use a ray optics argument andlook at the transfer of momentum

a

6

Optical TweezersLateral gradient force in non-uniform light

High intensity low intensity

7

Axial gradient forces towards focus of laser light

Force due to reflection

8

Scattering force and gradient force are separable

nm = refractive index trapping mediumnp= refractive index particlem = np/nm (in the Fscatt, Fgrad equation)

Optical Trapping - a<<

Condition for Rayleigh scattering when the particleradius a is smaller than the wavelength of the light .

Fgrad > Fscatt requires tight focusing

a

9

The scalesCan trap 0.1 to 10’s m

1m is…..…the same as 1/100th diameter of a hair.

In water, you can move a particle at about 20-30m per sec.

Sensitivity ~ 1 – 100pN

Require 10mW per trap.

Can rotate at 100’s of Hz.

10

Optical Trap Dynamics

Equation of motion of particle in a potential well

restoring force

Brownian motion

Newtonian force

drag force

11

Particle in fluid

Solution is of exponential decay

Damping provided by water

12

Particle in ideal trap

Spring constant or trap stiffness)

13

Solution is a simple harmonic motion

t

Trapped particle in fluid

14

Solution is of damped simple harmonic motion

t

The whole picture

Time averaged effect is 0

Stochastic events introduce fluctuations in the particle’s position

Add in the effect of Brownian motion

15

Trap dynamics

Look at the movement of the particle in x and y

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Collecting data

How can we collect this data?

Moving 100s nm at a few kHz!!!

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Quadrant Photodiode

Quadrant Photodiode

Intensity distribution signals Dx and Dy

Quadrant Photodiode

linear response for small displacements

Quadrant Photodiode

Quadrant photodiode collects the laser light transmitted through the condenser lens.

Small changes in the transmitted and scattered light are measured.

Advantages

• Large bandwidth 100s kHz• Very fast compared to f0

•High light level as collecting laser light

Disadvantages

• Complex arrangement• Single particle

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sample

microscoop lens

dichroic mirror

position sensitive detector

Camera

lamp

laser

microscoop lens

dichroic mirror

Trap strength or stiffness

Fourier transform to get the power spectrum

Lorenzian

Calibration using the Power spectrum22

Real data

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Calibration (viscous drag force calibration)

Vibrate container with liquid with known amplitude xo and frequency

A

)sin( txx o

)cos( txv o

avvFvis 6

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Calibration (viscous drag force calibration)

AA

Double frequency

Signal is )cos( tAS Get A from fitting A against for different ’s.

A

ax

S

F o6calibration constant

25

Bio-applications

The size of particles that can be trapped is ~0.1m to 10’s m

Approximately the same size asmany biological specimen.

e.g. Blood cells, stem cells, DNA molecules

Either trapped directly, or beads used as handles to reduce optical damage.

Ashkin et al. Nature. 330, 768 (1987)

Block et al. Nature. 338, 514 (1989)

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Measuring force/motion

Molloy et al. Biophys J. 68, S298 (1995)

biologicalobject

trapped bead

quadrant detector

imaging lens

• Image trapped bead (handle) onto quadrant detector

• Measure movement of shadow– nm accuracy!– kHz response

• Adjust trap to maintain position gives measurement of force– pN accuracy!

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RNA Polymerase

http://www.stanford.edu/group/blocklab/RNAP.html

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RNA-Polymerase

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e.g. Stretching/twisting of DNA

Perkins et al. Science. 264, 822 (1994)

Wang et al. Science. 282, 902 (1998)

• Attach handles to ends of DNA molecule

• Pull, let go and observe what happens!– understanding of

protein folding

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DNA mechanics

Unzipping a DNA double strand

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