Abstract

Time-sharing optical tweezers is a versatile technique to realize multiple traps for manipulating biological cells and macromolecules. It has been based on an intuitive hypothesis that the trapped viscoelastic object does not “sense” blinking of the optical beam. We present a quantitative analysis using mechanical modeling and numerical simulation, showing that the local stress and strain are jumping all the time and at all locations with the jumping amplitude independent of the recovery time of the viscoelastic material and the jumping frequency. Effects of the stress and strain jumping on the object deformation and the internal energy dissipation are analyzed.

© 2014 Optical Society of America

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References

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  1. F. M. Fazal, S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5(6), 318–321 (2011).
    [CrossRef] [PubMed]
  2. M. Dao, C. T. Lim, S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11–12), 2259–2280 (2003).
    [CrossRef]
  3. M. T. Wei, A. Zaorski, H. C. Yalcin, J. Wang, S. N. Ghadiali, A. Chiou, H. D. Ou-Yang, “A comparative study of living cell micromechanical properties by oscillatory optical tweezers,” Opt. Express 16(12), 8594–8603 (2008).
    [CrossRef] [PubMed]
  4. Y. Z. Yoon, J. Kotar, A. T. Brown, P. Cicuta, “Red blood cell dynamics: from spontaneous fluctuations to non-linear response,” Soft Matter 7(5), 2042–2051 (2011).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. Y. Q. Chen, C. W. Chen, Y. L. Ni, Y. S. Huang, O. Lin, S. Chien, L. A. Sung, and A. Chiou, “Effect of N-ethylmaleimide, chymotrypsin, and H2O2 on the viscoelasticity of human erythrocytes: Experimental measurement and theoretical analysis,” J. Biophotonics, published online (2013), http://onlinelibrary.wiley.com/doi/10.1002/jbio.201300081/abstract .
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    [CrossRef] [PubMed]
  12. T. Sawetzki, C. D. Eggleton, S. A. Desai, D. W. M. Marr, “Viscoelasticity as a Biomarker for High-Throughput Flow Cytometry,” Biophys. J. 105(10), 2281–2288 (2013).
    [CrossRef] [PubMed]
  13. Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissue, 2nd ed. (Springer, 1993), Chap. 2.
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    [CrossRef]
  15. R. Tran-Son-Tay, S. P. Sutera, P. R. Rao, “Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion,” Biophys. J. 46(1), 65–72 (1984).
    [CrossRef] [PubMed]
  16. S. Chien, K. L. Sung, R. Skalak, S. Usami, A. Tözeren, “Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane,” Biophys. J. 24(2), 463–487 (1978).
    [CrossRef] [PubMed]
  17. L. Yu, Y. Sheng, A. Chiou, “Three-dimensional light-scattering and deformation of individual biconcave human blood cells in optical tweezers,” Opt. Express 21(10), 12174–12184 (2013).
    [CrossRef] [PubMed]

2013

T. Sawetzki, C. D. Eggleton, S. A. Desai, D. W. M. Marr, “Viscoelasticity as a Biomarker for High-Throughput Flow Cytometry,” Biophys. J. 105(10), 2281–2288 (2013).
[CrossRef] [PubMed]

L. Yu, Y. Sheng, A. Chiou, “Three-dimensional light-scattering and deformation of individual biconcave human blood cells in optical tweezers,” Opt. Express 21(10), 12174–12184 (2013).
[CrossRef] [PubMed]

2012

E. V. Lyubin, M. D. Khokhlova, M. N. Skryabina, A. A. Fedyanin, “Cellular viscoelasticity probed by active rheology in optical tweezers,” J. Biomed. Opt. 17(10), 101510 (2012).
[CrossRef] [PubMed]

2011

F. M. Fazal, S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5(6), 318–321 (2011).
[CrossRef] [PubMed]

Y. Z. Yoon, J. Kotar, A. T. Brown, P. Cicuta, “Red blood cell dynamics: from spontaneous fluctuations to non-linear response,” Soft Matter 7(5), 2042–2051 (2011).
[CrossRef]

2010

2008

2007

2004

B. L. McClain, I. J. Finkelstein, M. D. Fayer, “vibrational echo experiments on red blood cells: comparison of the dynamics of cytoplasmic and aqueous hemoglobin,” Chem. Phys. Lett. 392(4-6), 324–329 (2004).
[CrossRef]

2003

M. Dao, C. T. Lim, S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11–12), 2259–2280 (2003).
[CrossRef]

1996

K. Visscher, S. P. Gross, S. M. Block, “Construction of Multiple-Beam Optical Traps with Nanometer-Resolution Position Sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[CrossRef]

1984

R. Tran-Son-Tay, S. P. Sutera, P. R. Rao, “Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion,” Biophys. J. 46(1), 65–72 (1984).
[CrossRef] [PubMed]

1978

S. Chien, K. L. Sung, R. Skalak, S. Usami, A. Tözeren, “Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane,” Biophys. J. 24(2), 463–487 (1978).
[CrossRef] [PubMed]

Bai, J. J.

Bareil, P. B.

Bareil, P. P.

Block, S. M.

F. M. Fazal, S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5(6), 318–321 (2011).
[CrossRef] [PubMed]

K. Visscher, S. P. Gross, S. M. Block, “Construction of Multiple-Beam Optical Traps with Nanometer-Resolution Position Sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[CrossRef]

Brown, A. T.

Y. Z. Yoon, J. Kotar, A. T. Brown, P. Cicuta, “Red blood cell dynamics: from spontaneous fluctuations to non-linear response,” Soft Matter 7(5), 2042–2051 (2011).
[CrossRef]

Chen, Y. Q.

Chien, S.

S. Chien, K. L. Sung, R. Skalak, S. Usami, A. Tözeren, “Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane,” Biophys. J. 24(2), 463–487 (1978).
[CrossRef] [PubMed]

Chiou, A.

Cicuta, P.

Y. Z. Yoon, J. Kotar, A. T. Brown, P. Cicuta, “Red blood cell dynamics: from spontaneous fluctuations to non-linear response,” Soft Matter 7(5), 2042–2051 (2011).
[CrossRef]

Dao, M.

M. Dao, C. T. Lim, S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11–12), 2259–2280 (2003).
[CrossRef]

Desai, S. A.

T. Sawetzki, C. D. Eggleton, S. A. Desai, D. W. M. Marr, “Viscoelasticity as a Biomarker for High-Throughput Flow Cytometry,” Biophys. J. 105(10), 2281–2288 (2013).
[CrossRef] [PubMed]

Duval, P. L.

Eggleton, C. D.

T. Sawetzki, C. D. Eggleton, S. A. Desai, D. W. M. Marr, “Viscoelasticity as a Biomarker for High-Throughput Flow Cytometry,” Biophys. J. 105(10), 2281–2288 (2013).
[CrossRef] [PubMed]

Fayer, M. D.

B. L. McClain, I. J. Finkelstein, M. D. Fayer, “vibrational echo experiments on red blood cells: comparison of the dynamics of cytoplasmic and aqueous hemoglobin,” Chem. Phys. Lett. 392(4-6), 324–329 (2004).
[CrossRef]

Fazal, F. M.

F. M. Fazal, S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5(6), 318–321 (2011).
[CrossRef] [PubMed]

Fedyanin, A. A.

E. V. Lyubin, M. D. Khokhlova, M. N. Skryabina, A. A. Fedyanin, “Cellular viscoelasticity probed by active rheology in optical tweezers,” J. Biomed. Opt. 17(10), 101510 (2012).
[CrossRef] [PubMed]

Finkelstein, I. J.

B. L. McClain, I. J. Finkelstein, M. D. Fayer, “vibrational echo experiments on red blood cells: comparison of the dynamics of cytoplasmic and aqueous hemoglobin,” Chem. Phys. Lett. 392(4-6), 324–329 (2004).
[CrossRef]

Ghadiali, S. N.

Gross, S. P.

K. Visscher, S. P. Gross, S. M. Block, “Construction of Multiple-Beam Optical Traps with Nanometer-Resolution Position Sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[CrossRef]

Khokhlova, M. D.

E. V. Lyubin, M. D. Khokhlova, M. N. Skryabina, A. A. Fedyanin, “Cellular viscoelasticity probed by active rheology in optical tweezers,” J. Biomed. Opt. 17(10), 101510 (2012).
[CrossRef] [PubMed]

Kotar, J.

Y. Z. Yoon, J. Kotar, A. T. Brown, P. Cicuta, “Red blood cell dynamics: from spontaneous fluctuations to non-linear response,” Soft Matter 7(5), 2042–2051 (2011).
[CrossRef]

Liao, G. B.

Lim, C. T.

M. Dao, C. T. Lim, S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11–12), 2259–2280 (2003).
[CrossRef]

Lyubin, E. V.

E. V. Lyubin, M. D. Khokhlova, M. N. Skryabina, A. A. Fedyanin, “Cellular viscoelasticity probed by active rheology in optical tweezers,” J. Biomed. Opt. 17(10), 101510 (2012).
[CrossRef] [PubMed]

Marr, D. W. M.

T. Sawetzki, C. D. Eggleton, S. A. Desai, D. W. M. Marr, “Viscoelasticity as a Biomarker for High-Throughput Flow Cytometry,” Biophys. J. 105(10), 2281–2288 (2013).
[CrossRef] [PubMed]

McClain, B. L.

B. L. McClain, I. J. Finkelstein, M. D. Fayer, “vibrational echo experiments on red blood cells: comparison of the dynamics of cytoplasmic and aqueous hemoglobin,” Chem. Phys. Lett. 392(4-6), 324–329 (2004).
[CrossRef]

Ou-Yang, H. D.

Pesce, G.

Rancourt-Grenier, S.

Rao, P. R.

R. Tran-Son-Tay, S. P. Sutera, P. R. Rao, “Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion,” Biophys. J. 46(1), 65–72 (1984).
[CrossRef] [PubMed]

Rusciano, G.

Sasso, A.

Sawetzki, T.

T. Sawetzki, C. D. Eggleton, S. A. Desai, D. W. M. Marr, “Viscoelasticity as a Biomarker for High-Throughput Flow Cytometry,” Biophys. J. 105(10), 2281–2288 (2013).
[CrossRef] [PubMed]

Sheng, Y.

Skalak, R.

S. Chien, K. L. Sung, R. Skalak, S. Usami, A. Tözeren, “Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane,” Biophys. J. 24(2), 463–487 (1978).
[CrossRef] [PubMed]

Skryabina, M. N.

E. V. Lyubin, M. D. Khokhlova, M. N. Skryabina, A. A. Fedyanin, “Cellular viscoelasticity probed by active rheology in optical tweezers,” J. Biomed. Opt. 17(10), 101510 (2012).
[CrossRef] [PubMed]

Sung, K. L.

S. Chien, K. L. Sung, R. Skalak, S. Usami, A. Tözeren, “Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane,” Biophys. J. 24(2), 463–487 (1978).
[CrossRef] [PubMed]

Suresh, S.

M. Dao, C. T. Lim, S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11–12), 2259–2280 (2003).
[CrossRef]

Sutera, S. P.

R. Tran-Son-Tay, S. P. Sutera, P. R. Rao, “Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion,” Biophys. J. 46(1), 65–72 (1984).
[CrossRef] [PubMed]

Tözeren, A.

S. Chien, K. L. Sung, R. Skalak, S. Usami, A. Tözeren, “Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane,” Biophys. J. 24(2), 463–487 (1978).
[CrossRef] [PubMed]

Tran-Son-Tay, R.

R. Tran-Son-Tay, S. P. Sutera, P. R. Rao, “Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion,” Biophys. J. 46(1), 65–72 (1984).
[CrossRef] [PubMed]

Usami, S.

S. Chien, K. L. Sung, R. Skalak, S. Usami, A. Tözeren, “Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane,” Biophys. J. 24(2), 463–487 (1978).
[CrossRef] [PubMed]

Visscher, K.

K. Visscher, S. P. Gross, S. M. Block, “Construction of Multiple-Beam Optical Traps with Nanometer-Resolution Position Sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[CrossRef]

Wang, J.

Wei, M. T.

Yalcin, H. C.

Yoon, Y. Z.

Y. Z. Yoon, J. Kotar, A. T. Brown, P. Cicuta, “Red blood cell dynamics: from spontaneous fluctuations to non-linear response,” Soft Matter 7(5), 2042–2051 (2011).
[CrossRef]

Yu, L.

Zaorski, A.

Biophys. J.

T. Sawetzki, C. D. Eggleton, S. A. Desai, D. W. M. Marr, “Viscoelasticity as a Biomarker for High-Throughput Flow Cytometry,” Biophys. J. 105(10), 2281–2288 (2013).
[CrossRef] [PubMed]

R. Tran-Son-Tay, S. P. Sutera, P. R. Rao, “Determination of red blood cell membrane viscosity from rheoscopic observations of tank-treading motion,” Biophys. J. 46(1), 65–72 (1984).
[CrossRef] [PubMed]

S. Chien, K. L. Sung, R. Skalak, S. Usami, A. Tözeren, “Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane,” Biophys. J. 24(2), 463–487 (1978).
[CrossRef] [PubMed]

Chem. Phys. Lett.

B. L. McClain, I. J. Finkelstein, M. D. Fayer, “vibrational echo experiments on red blood cells: comparison of the dynamics of cytoplasmic and aqueous hemoglobin,” Chem. Phys. Lett. 392(4-6), 324–329 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

K. Visscher, S. P. Gross, S. M. Block, “Construction of Multiple-Beam Optical Traps with Nanometer-Resolution Position Sensing,” IEEE J. Sel. Top. Quantum Electron. 2(4), 1066–1076 (1996).
[CrossRef]

J. Biomed. Opt.

E. V. Lyubin, M. D. Khokhlova, M. N. Skryabina, A. A. Fedyanin, “Cellular viscoelasticity probed by active rheology in optical tweezers,” J. Biomed. Opt. 17(10), 101510 (2012).
[CrossRef] [PubMed]

J. Mech. Phys. Solids

M. Dao, C. T. Lim, S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11–12), 2259–2280 (2003).
[CrossRef]

Nat. Photonics

F. M. Fazal, S. M. Block, “Optical tweezers study life under tension,” Nat. Photonics 5(6), 318–321 (2011).
[CrossRef] [PubMed]

Opt. Express

Soft Matter

Y. Z. Yoon, J. Kotar, A. T. Brown, P. Cicuta, “Red blood cell dynamics: from spontaneous fluctuations to non-linear response,” Soft Matter 7(5), 2042–2051 (2011).
[CrossRef]

Other

Y. Q. Chen, C. W. Chen, Y. L. Ni, Y. S. Huang, O. Lin, S. Chien, L. A. Sung, and A. Chiou, “Effect of N-ethylmaleimide, chymotrypsin, and H2O2 on the viscoelasticity of human erythrocytes: Experimental measurement and theoretical analysis,” J. Biophotonics, published online (2013), http://onlinelibrary.wiley.com/doi/10.1002/jbio.201300081/abstract .

Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissue, 2nd ed. (Springer, 1993), Chap. 2.

Supplementary Material (2)

» Media 1: MP4 (1819 KB)     
» Media 2: MP4 (1504 KB)     

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Figures (7)

Fig. 1
Fig. 1

Linear distribution of stress in a 1D viscoelastic rod at time t = 0.5 ms after a constant stress σ0 = 1 Pa in + x-direction is applied at the right end of the rod, computed by finite element method.

Fig. 2
Fig. 2

Scheme of SLS model.

Fig. 3
Fig. 3

Local stress and strain in a 1D rod with an external load jumping at 1 KHz. (a) Recovery time τσ = 2.1 ms at x = 6 μm where σa = 0.75 Pa and σb = 0.25 Pa; (b) τσ = 1.1 s at point x = 8 μm where σa = 1.0 Pa and σb = 0 Pa.

Fig. 4
Fig. 4

Elongation of the entire rod with recovery time τσ = 2.1 ms when the stress load was jumping at 1 KHz and stopped at t = 15 ms.

Fig. 5
Fig. 5

Hysteresis loop of stress-strain at the rod end x = 8 μm in a time range from 12 to 15 ms when the rod elongation is saturated. Recovery time τσ = 2.1 ms. Stress jumping frequency 1 KHz

Fig. 6
Fig. 6

One frame of excerpt at t = 0.4 ms in the videos sequence of one cycle of the external load jumping at frequency: 1 KHz. Viscoelastic recovery time τσ = 0.1 s. (a) Color: the first principal stress; Red arrows: amplitudes and directions the acceleration vectors (Media 1); (b) Color: normalized first principal strains (Media 2)

Fig. 7
Fig. 7

Normalized principal stress distribution and deformation in the cross section of the RBC in the steady dual-trap. Red arrows: principal stresses, Color and shape: deformation.

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