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OPTICAL TWEEZERS: PRINCIPLES AND SELECTED

APPLICATIONS

Matti Kinnunen, Adjunct Professor

University of Oulu

University of Oulu University of Oulu

Content ‒ Basics of optical trapping

‒ Optical tweezers setup

‒ Calibration of tweezers

‒ Light matter interaction/elastic light

scattering

‒ Force measurements

‒ Conclusions

‒ Acknowledgments


Principles of optical trapping

Scattering force:

- In the direction of light

propagation

Gradient force:

- In the direction of the spatial light

gradient

Microscope

objective

Matti Kinnunen

[email protected]

Optical trap can be estimated

as a spring with stiffness k


Example setup

REQUIREMENTS:

• Laser

• Beam expander

• Dichroic mirror

• Microscope objective

(high NA)

• Sample illumination

• Camera


Calibration methods

- Viscous drag force method

- High-speed camera imaging

- Quadrant Photo Diode

University of Oulu

Evaluation of trapping efficiency

‒ Viscous drag method

‒ Viscous drag force and transverse trapping force of optical tweezers are in balance just before the particle escapes from the trap

‒ Viscous drag method is applicable for rigid particles

‒ Forces induce stretching and deformation of red blood cell which induces variation in trapping efficiency

rvF 6

Qc

PnF

Motorized xy-stage Stage movement

Transverse trapping

force

Matti Kinnunen

[email protected]

Stock`s

force

Trapping

force

Direction of flow

University of Oulu

Evaluation of trapping efficiency

‒ Viscous drag method

‒ Viscous drag force and transverse trapping force of optical tweezers are in balance just before the particle escapes from the trap

‒ Viscous drag method is applicable for rigid particles

‒ Forces induce stretching and deformation of red blood cell.

rvF 6

Motorized xy-stage

M. Collins, M. Kinnunen, R. Myllylä, A. Karmenyan, A. Priezzhev, “Measurement of forces

affecting red blood cells in optical tweezers”. International Conference on Laser Application

in Life Sciences “LALS-2008”, December 4-6, 2008, Taipei, Taiwan, Poster.

Qc

PnF

?

Trapping Force

0

5

10

15

20

25

30

35

40

5 10 15 20 25 30 35 40 45

P [mW]

F [p

N]

P.S.

RBC (s.i. modified Stokes')

RBC (surface area modified Stokes')

Stage movement

Transverse trapping

force

Matti Kinnunen

[email protected]


‒ We used a model for calculating viscous drag force for non-

spherical objects

sndrag rvrvF3

26

3

16

rn is the radius for a sphere with equivalent cross sectional

area than that of the object, and rs is the radius for a

sphere with the same surface area than the effective

surface area of the object (effective

area is the area affected by flow).

P.Puhakka, ” Punasolun venyminen optisessa pinsetissä ja pinsetin

loukkuvoiman määritys,” B. Sc. Thesis, Department of Physics, Biophysics

division, University of Oulu, 2009.

P. Puhakka, M. Kinnunen, M. Collins, and R. Myllylä, ”Stretching of red blood cells with a viscous drag

method,” Photonics and Laser Symphosium, Tampere, 2009.

Matti Kinnunen

[email protected]


Behaviour of an RBC in optical trap

‒ RBCs orient themselves in a similar

manner in single-beam optical traps, with

their maximum diameter in the direction

of the optical axis [Sato et al,Electron.

Lett. 1991]. RBCs orient themselves in

different optical tweezers in a way that

they enclose maximum intensity.

Matti Kinnunen

[email protected]


Red blood cell in optical tweezers. Stretching and rotation.


Optical tweezers calibration

‒ Optical tweezers (OT) can be calibrated

by recording high speed video of the

trapped particle

‒ The illumination is set for high speed

video recording and calibration video of

bead’s Brownian motion at various frame

rates and trapping powers are recorded

‒ The results were analyzed using CPC

program for OT calibration and compared

with hydrodynamic drag calibration

‒ The CPC program for OT calibration were

optimized for use with high speed video

camera

Matti Kinnunen

[email protected]


Calibration

‒ Trap can also be calibrated

by analyzing power spectrum

‒ Brownian motion can be

detected with high-speed

video

‒ Stiffness of trap can be found

from equation:

𝑓𝑐 =𝑘𝑡𝑟𝑎𝑝

2𝜋𝛾

𝑓𝑐 = 44 ± 2.5 𝐻𝑧

PM Hansen, IM Tolic-Nørrelykkeb, H Flyvbjergc, K Berg-Sørensen (2006)

tweezercalib 2.1: Faster version of MATLAB package for precise calibration of optical tweezers

Computer Physics Communications 175(8), pp. 572-573


OT calibration with high speed camera

Typical video (2.54um silica Bead 0.25 mW 1000fps)


Segmentation with MSER-method (maximally stable extremal regions)

Matas, J., Chum, O., Urban, M. & Pajdla, T. (2004)

Robust wide-baseline stereo from maximally stable extremal regions.

Image and Vision Computing 22, 761-767


Tweezer calib

𝑓𝑐 = 44 ± 2.5 𝐻𝑧

Modified from: PM Hansen, IM Tolic-Nørrelykkeb, H Flyvbjergc, K Berg-Sørensen (2006)

tweezercalib 2.1: Faster version of MATLAB package for precise calibration of optical tweezers

Computer Physics Communications 175(8), pp. 572-573


Drag force is based on Stoke’s law, where viscous drag is used.

fc is the characteristic frequency

ktrap is the force constant, and x the

measured amplitude of the displacement

The thermal fluctuations S(f) of a colloid in an optical trap can be

described by a Lorentzian profile

is the drag coefficient for a sphere with radius r moving in a viscous

medium with viscosity

When laser power increases, trap stiffness increases and characteristic

frequency moves to upper frequencies.

Otto et al. Rev. Sci. Instrum. 79, 023710 2008

University of Oulu

Effect of setup/software modification

Typical PSD before (there few constant frequency peaks)

Typical PSD after (there are almost no intense peaks)


0.25 mW, 2.54 µm silica bead (1000 fps)


QPD-calibration ‒ QPD

‒ COMPONENTS


28

http://www.jpk.com/detection.426.en.html

Lee et al., Journal of Biomedical Optics 21(3), 035001 (March 2016)


Light matter interaction Elastic light scattering experiments

facilitated with optical tweezers

29


Motivation

‒ Light scattering phenomenom is present when using optical

methods to study turbid materials and tissues

‒ Good theoretical models are needed

‒ It is important that models can be verified with measurements

‒ Near field effects?


Some existing theoretical models

He et al., J. Opt. Soc. Am. A/Vol. 21, No. 10/October 2004

Simulation and modeling papers:

[1] Tsinopoulos, S. V., and Polyzos, D., “Scattering of He-Ne laser light by an average-sized red blood cell,“ Appl. Opt. 38, 5499-5510 (1999).

[2] Karlsson, A., He, J., Swartling, J., and Andersson-Engels, S., “Numerical simulations of light scattering by red blood cells,” IEEE Trans. Biomed. Eng. 52, 13-18 (2005).

[3] Nilsson, A. M. K., Alsholm, P., Karlsson, A., and Andersson-Engels, S., "T-matrix computations of light scattering by red blood cells," Appl. Opt. 37, 2735-2748 (1998).

[4] He, J., Karlsson, A., Swartling, J., and Andersson-Engels, S., “Light scattering by multiple red blood cells,” J. Opt.Soc. Am. A 21, 1953-1961 (2004).

[5] Lugovtsov, A. E., Priezzhev, A. V., and Nikitin, S. Y., “Red blood cells in laser beam field: calculations of light scattering,” Proc. SPIE 7022, 70220Y (2008).


Scattering calculations form spheres

1,00E-07

1,00E-06

1,00E-05

1,00E-04

1,00E-03

1,00E-02

1,00E-01

1,00E+00

0 10 20 30 40 50

Sc

ale

d in

ten

sit

y

Scattering angle º

23.25 µm

10.0 µm

6.0 µm

3.1 µm


33

Fig. Basic components of a typical goniometric setup with a cylindrical cuvette. L—light

source, C—cuvette, and D—detector/detection optics.

Kinnunen and Karmenyan, Journal of Biomedical Optics, 2015.


34

Fig. Schematic of an optically trapped red blood cell (RBC) (a) and a combination of a

double-beam optical trap and goniometric setup (b).

Kinnunen and Karmenyan, Journal of Biomedical Optics, 2015.

Kinnunen et al., Journal of Biomedical Optics, 2014.


Optical tweezers setup

Figure. Optical tweezer setup with Gaussian and elliptical tweezers.


‒How to measure light

scattering from a single

particle or red blood

cell or several cells at

different orientations?


How the fix the position of RBC in optical trap?

‒ Two beam optical tweezers system

- Two Gaussian beams

– Elliptical and Gaussian beams

M.Sc. Thesis, Antti Kauppila, Physics Department, University of Oulu, Finland (2009)

Red blood cells in elliptical optical tweezers

M.Sc. Thesis, Antti Kauppila, Physics Department,

University of Oulu, Finland (2009)


Light scattering measurements

Figure. Red blood cells in elliptical tweezers during measurement.

Setup

- A He-Ne laser (05-LHP-151, Melles Griot), 5 mW

- Vertical polarization was used

- Cylindrical cuvette (shortened version of Helma 540.115)

- Amplified photomultiplier tube (PMT) (Thorlabs PMM02)

- A motorized rotation stage (Standa 8MR190-2-28)

No scattering is allowed

from the background

medium


Sample preparation

- Fresh red blood cells (RBCs) were collected with the finger prick

method

- RBCs were diluted in a filtered PBS solution

- The PBS solution was filtered three times using a 0.2 μm filter

(GELMAN Acrodisc 13 CR PTFE)

- 6.0 µm polystyrene spheres were diluted in a filtered distilled

water

- Background purity is a key issue


Measurements from single particles and RBCs

1.00E-03

1.00E-02

1.00E-01

1.00E+00

1.00E+01

0 10 20 30 40 50

Scattering Angle [°]

Sca

tterin

g In

tens

ity [a

.u.]

Measurement

Modeling

Collins et al. Proc SPIE, Vol. 7376, 2010.

Kinnunen et al. Biomed. Opt. Express 2, 1803-1814 (2011).

Kinnunen et al. Biomed. Opt. Express 2, 1803-1814

(2011).


Two point tweezers

Kinnunen et al. Opt. Lett. 36(18), 3554-3556 (2011).


Point and elliptical tweezer

Figure. Single RBC in point and elliptical optical tweezers (a), the same RBC illuminated with a He-Ne laser

(b), two cells in elliptical optical tweezers (c), and two RBCs illuminated with a He-Ne laser (d). Arrows show

direction of the incident laser light. The scale bar is 10 µm.

video video

Kauppila et al. Proc. SPIE 8097, 80970K (2011).

Composite-2011-01-04_15-00-14h TWO CELLS FACE ON SCATTERING.avi

Composite-2011-01-04_12-09-27h_TWO CELLS FACE ON.avi


1.00E-03

1.00E-02

1.00E-01

1.00E+00

1.00E+01

5 10 15 20 25

Scattering Angle [º]

Inte

nsity

[a.u

.]

3RBC

2RBC1

2RBC2

2RBC3

Figure. Three RBCs trapped using elliptical optical tweezers (a), near-field intensity image of the scattering pattern from three cells

(b) and measured light scattering signals from two and three RBCs (c). Arrow shows direction of the incident laser light. The scale

bar is 10 µm. Kauppila et al. Proc. SPIE 8097, 80970K (2011).


1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

1.00E+01

0 10 20 30 40 50

Scattering Angle [º]

Inte

nsity

[a.u

.]

two RBCs, rim-on

two RBCs, rim-on

one RBC, rim-on

one RBC, rim-on

Figure. Two RBCs in rim-on position (a), near-field intensity image of scattering light from two cells (b) and

measured light scattering signals (c). Arrow shows direction of the incident laser light. The scale bar is 10 µm.

video

video

Kauppila et al. Proc. SPIE 8097, 80970K (2011).

Composite-2010-12-31_15-03-01h TWO CELLS RIM ON.avi

Composite-2011-01-05_12-33-53h (2) TWO CELLS RIM ON SCATTERING.avi


Discussion ‒ He et al. performed simulations with the FDTD

method and concluded that, when changing the

lateral distance of the cells in face-on

orientation, the scattering probability

distributions remain almost unaffected.

‒ Results for two cells in rim-on orientation show

that increasing the number of RBCs in rim-on

illumination has a clear effect on scattering.

‒ To increase the stability of the elliptical optical

tweezers, our measurements were made near

the bottom of the cuvette. Then again, to

decrease background reflections from the

bottom, it was necessary to conduct the

measurements as far above the bottom as

possible. This led to a compromise in the

signal-to-noise ratio.

‒ Measurement results supports the simulations


RBC interaction force measurements

47


UTILIZING OPTICAL TWEEZERS FOR MEASURING AGGREGATION FORCES AT A CELLULAR LEVEL

𝑓𝑐 = 44 ± 2.5 𝐻𝑧

P.M.Hansen et al., Computer Physics Communications 175(8),

2006

Figure. Trap can be calibrated by analyzing

power spectrum of Brownian motion.

𝑓𝑐 =𝑘𝑡𝑟𝑎𝑝

2𝜋𝛾

Figure. (a) – illustration of optical trapping, (b) – simplified schematic layout

Matti Kinnunen

[email protected]


Experimental details

• The blood was drawn from a single healthy

male donor to avoid individual and gender

differences in the measured parameters.

• Age separation of RBCs was performed by 1

hour-long centrifugation at 30,000g @ 30°C as

described and used by most authors studying

RBCs aggregation

• Experiments were performed in autologous

plasma and gamma-globulin (IgG) solutions (20

mg/ml) within 8 hours after drawing the blood.

• Aggregation strength of RBC doublets was

calculated from the measured drag velocity

required to separate two cells trapped in a

single laser tweezers.


Red blood cell aggregation and disaggregation in plasma and protein solutions

50



51

Fig. Schematic layout of the optical tweezers setup.



52

Fig. (1) Two noninteracting RBCs are trapped with OT and (2) a small interaction

area is formed, after which the OT are turned off. (3–5) RBCs start to spontaneously

overlap and form a compact doublet in the case of:

(a) plasma, or they do not spontaneously overlap in the case of:

(b) fibrinogen 2.5 mg∕ml þ albumin 35 mg∕ml solution. The cross marks show the

positions of the OT.



53

Fig. Schematic sequences of RBC disaggregating force measurement: (1) two noninteracting RBCs

are trapped with OT; (2) the pair aggregate is formed by attaching the RBCs with a known interaction

area; (3) the RBCs are held aggregated at low OT power during the known interaction time; (4) one of the

cells is pulled with a known force. Step 4 is repeated multiple times slowly while increasing the

disaggregating force until (5) the cells are separated and the minimum force required for doublet

disaggregation is found. The cross marks show the positions of the OT, and the arrows show the direction

of pulling.



54



55

Fig. (a) Dependence of maximum achievable displacement on the trapping force in

plasma (concentrations of fibrinogen 1.9 mg∕ml and albumin 45 mg∕ml) and in the solution

of fibrinogen (2.5 mg∕ml) with albumin (35 mg∕ml). (b) Set of frames (1–4) demonstrating

the measurement process. As the linear overlap distance (A) decreases, a

higher force (F) is required to further separate the RBCs. The cross marks show the

positions of the OT and the arrows show the direction of pulling.



56

Fig. Schematic description of force measurement. RBCs are trapped by two independent optical traps shown

as springs. The points of force application are shown only to designate the force direction, the actual force

being applied through a certain area. The trapping force of the unmoving trap (Ftrap1) was

always slightly stronger than that of the movable trap (Ftrap2 ). FA refers to the aggregating force. (A) The

cells are trapped and held from overlapping to each other with OT force greater than FA . (B) The cell escapes

from OT, as FA becomes slightly stronger or equal to the OT force. At this moment the FA is

considered to be matching Ftrap2 .

Lee et al., IEEE JSTQE, VOL. 22,

NO. 3, MAY/JUNE 2016

University of Oulu University of Oulu 57

Fig. (a) Set of frames demonstrating the steps of the measurement procedure.

The cross marks show the positions of OT and the arrow showthe direction

of pulling. The black arrow shows time course of the measurement and indicates

that force increases every step. (b) Dependence of maximum achievable linear

overlap distance on the pulling force in plasma.




58

Fig. (a) Set of frames demonstrating the steps of the measurement procedure.

The cross marks show the positions of OT and the arrow showthe direction

of pulling. The black arrows show time course of the measurement. (b) Disaggregation

force dependence on the “initial” interaction area of the RBCs. The

grey colour stands for small and the black for large “initial” interaction area.




Conclusions ‒ Optical tweezers is an appropriate tool for

manipulating particles and cells. It can be

used to keep the sample at place during

light scattering measurements as well as

to measure interaction forces between

different cells.

59


Acknowledgments ‒ K. Lee

‒ M. D. Khokhlova

‒ E. V. Lyubin

‒ A. V. Priezzhev

‒ I. Meglinski

‒ A. V. Danilina

‒ V. D. Ustinov

‒ S. Shin

‒ A. A. Fedyanin

‒ A. Karmenyan

‒ A. Kauppila

‒ R. Myllylä

‒ J. Heikkilä

‒ S. Huttunen

60

Financial support:

• Academy of Finland,

• Infotech Oulu, University of Oulu

• Faculty of Information Technology and

Electrical Engineering, University of OUlu

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