Nonlinear Dynamics

, Volume 76, Issue 2, pp 1013–1030 | Cite as

Dynamics of microscopic objects in optical tweezers: experimental determination of underdamped regime and numerical simulation using multiscale analysis

  • Mahdi Haghshenas-Jaryani
  • Bryan Black
  • Sarvenaz Ghaffari
  • James Drake
  • Alan Bowling
  • Samarendra Mohanty
Original Paper

Abstract

This article presents new experimental observations and numerical simulations to investigate the dynamic behavior of micro–nano-sized objects under the influence of optical tweezers (OTs). OTs are scientific tools that can apply forces and moments to small particles using a focused laser beam. The motions of three polystyrene microspheres of different diameters, 1,950, 990, and 500 nm, are examined. The results show a transition from the overdamped motion of the largest bead to the underdamped motion of the smallest bead. The experiments are verified using a dynamic model of a microbead under the influence of Gaussian beam OTs that is modeled using ray-optics. The time required to numerically integrate the classic Newton–Euler model is quite long because a picosecond step size must be used. This run time can be reduced using a first-order model, and greatly reduced using a new multiscale model. The difference between these two models is the underdamped behavior predicted by the multiscale model. The experimentally observed underdamped behavior proves that the multiscale model predicts the actual physics of a nano-sized particle moving in a fluid environment characterized by a low Reynolds number.

Keywords

Multiscale modeling Ray-optics Dynamics Optical tweezers Low Reynolds number Fluid dynamics Brownian motion Method multiple scales 

References

  1. 1.
    Ashkin, A.: Forces of a single-beam gradient laser trap on a dielectric sphere in the ray-optics regime. Biophys. J. 61, 569–582 (1992)CrossRefGoogle Scholar
  2. 2.
    Ashkin, A., Dziedzic, J., Bjorkholm, J., Chu, S.: Observation of a single-beam gradient force optical trap for dielectric particles. Opt. Lett. 11(5), 288–290 (1986)CrossRefGoogle Scholar
  3. 3.
    Born, M., Wolf, E.: Principles of Optics, 7th edn. Cambridge University Press, Cambridge (1999)CrossRefGoogle Scholar
  4. 4.
    Bowling, A., Palmer, A.F.: The small mass assumption applied to the multibody dynamics of motor proteins. J. Biomech. 42(9), 1218–1223 (2009). doi:10.1016/j.jbiomech.2009.03.017. http://www.jbiomech.com/issues
  5. 5.
    Bowling, A., Palmer, A.F., Wilhelm, L.: Contact and impact in the multibody dynamics of motor protein locomotion. Langmuir 25(22), 12974–12981 (2009). http://pubs.acs.org/toc/langd5/0/0 Google Scholar
  6. 6.
    Cao, Y., Stilgoe, A.B., Chen, L., Nieminen, T.A., Rubinsztein-Dunlop, H.: Equilibrium orientations and positions of non-spherical particles in optical traps. Opt. Express 20(12), 12987–12996 (2012). doi:10.1364/OE.20.012987. http://www.opticsexpress.org/abstract.cfm?URI=oe-20-12-12987
  7. 7.
    Deng, Y., Bechhoefer, J., Forde, N.R.: Brownian motion in a modulated optical trap. J. Opt. A 9, S256–S263 (2007)CrossRefGoogle Scholar
  8. 8.
    DiLeonardo, R.: The trap forces applet (2011). http://glass.phys.uniroma1.it/dileonardo/. Accessed 19 Dec 2013
  9. 9.
    Fazal, F.M., Block, S.M.: Optical tweezers study life under tension. Nat. Photon. 5(6), 318–321 (2011). doi:10.1002/cyto.990120603. http://dx.doi.org/10.1038/nphoton.2011.100
  10. 10.
    Finer, J., Simmons, R., Spudich, J.: Single myosin molecule mechanics: piconewton forces and nanometre steps. Nature 368(6467), 113–119 (1994)CrossRefGoogle Scholar
  11. 11.
    Gauthier, R.C., Frangioudakis, A.: Theoretical investigation of the optical trapping properties of a micro-optic cubic glass structure. Appl. Opt. 39(18), 3060–3070 (2000). doi:10.1364/AO.39.003060. http://ao.osa.org/abstract.cfm?URI=ao-39-18-3060
  12. 12.
    Haghshenas-Jaryani, M., Bowling, A.: Multiscale dynamic modeling of processive motor proteins. In: Proceedings of the IEEE International Conference Robotics and Biomimetics (ROBIO), pp. 1403–1408 (2011)Google Scholar
  13. 13.
    Haghshenas-Jaryani, M., Bowling, A.: Multiscale dynamic modeling flexibility in myosin V. In: Proceedings of the ASME International Design Engineering Technical Conferences (IDETC) and Computers and Information in Engineering Conference (CIE) (2013)Google Scholar
  14. 14.
    Harada, Y., Ohara, O., Takatsuki, A., Itoh, H., Shimamoto, N., Kinosita, K.: Direct observation of DNA rotation during transcription by Escherichia coli RNA polymerase. Nature 409(6816), 113–115 (2001)CrossRefGoogle Scholar
  15. 15.
    Hayashi, K., Takano, M.: Violation of the fluctuation–dissipation theorem in a protein system. Biophys. J. 93(3), 895–901 (2007)CrossRefGoogle Scholar
  16. 16.
    Jamali, Y., Lohrasebi, A., Rafii-Tabar, H.: Computational modelling of the stochastic dynamics of kinesin biomolecular motors. Phys. A 381, 239–254 (2007)CrossRefGoogle Scholar
  17. 17.
    Josep Mas, A.F., Cuadros, J., Juvells, I., Carnicer, A.: Understanding optical trapping phenomenon: a simulation for undergraduates. IEEE Trans. Educ. 54, 133–140 (2011)Google Scholar
  18. 18.
    Kasas, S., Thomson, N., Smith, B., Hansma, H., Zhu, X., Guthold, M., Bustamante, C., Kool, E., Kashlev, M., Hansma, P.: Escherichia coli RNA polymerase activity observed using atomic force microscopy. Biochemistry 36(3), 461–468 (1997)CrossRefGoogle Scholar
  19. 19.
    Kim, J.H., Mulholland, G.W., Kukuck, S.R., Pui, D.Y.H.: Slip correction measurements of certified PSL nanoparticles using a nanometer differential mobility analyzer (nano-DMA) for Knudsen number from 0.5 to 83. J. Res. Natl Inst. Stand. Technol. 110(1), 31–54 (2005)CrossRefGoogle Scholar
  20. 20.
    Lei, U., Yang, C.Y., Wu, K.C.: Viscous torque on a sphere under arbitrary rotation. Appl. Phys. Lett. 89(18), 181908 (2006). doi:10.1063/1.2372704. http://link.aip.org/link/?APL/89/181908/1 Google Scholar
  21. 21.
    Mansfield, S., Kino, G.: Solid immersion microscope. Appl. Phys. Lett. 57, 2615–2616 (1990)CrossRefGoogle Scholar
  22. 22.
    Mohanty, K.S., Liberale, C., Mohanty, S., Degiorgio, V.: In depth fiber optic trapping of low-index microscopic objects. Appl. Phys. Lett. 92(15), 151113 (2008)CrossRefGoogle Scholar
  23. 23.
    Mohanty, S.K.: Optically-actuated translational and rotational motion at the microscale for microfluidic manipulation and characterization. Lab Chip 12, 3624–3636 (2012)CrossRefGoogle Scholar
  24. 24.
    Mohanty, S.K., Mohanty, K.S., Berns, M.W.: Manipulation of mammalian cells using a single-fiber optical microbeam. J. Biomed. Opt. 13(5), 054049 (2008)CrossRefGoogle Scholar
  25. 25.
    Mohanty, S.K., Uppal, A., Gupta, P.K.: Optofluidic stretching of RBCs using single optical tweezers. J. Biophoton. 1(6), 522 (2008)CrossRefGoogle Scholar
  26. 26.
    Nayfeh, A.H.: Perturbation Methods. Wiley, New York (1973)MATHGoogle Scholar
  27. 27.
    Padgett, M., Di Leonardo, R.: Holographic optical tweezers and their relevance to lab on chip devices. Lab Chip 11, 1196–1205 (2011). doi:10.1039/C0LC00526F. http://dx.doi.org/10.1039/C0LC00526F
  28. 28.
    PHET: The physics education technology project: optical tweezers and application (2011). http://phet.colorado.edu/en/simulation/optical-tweezers. Accessed 19 Dec 2013
  29. 29.
    Purcell, E.M.: Life at low Reynolds number. Am. J. Phys. 45(1), 3–11 (1977)CrossRefMathSciNetGoogle Scholar
  30. 30.
    Roosen, G.: Optical levitation of spheres. Can. J. Phys. 57, 1260–1279 (1979)CrossRefGoogle Scholar
  31. 31.
    Roosen, G., Imbert, C.: Optical levitation by means of 2 horizontal laser beams: theoretical and experimental study. Phys. Lett. 59A, 6–8 (1976)CrossRefGoogle Scholar
  32. 32.
    Svoboda, K., Schmidt, C., Schnapp, B., Block, S.: Direct observation of kinesin stepping by optical trapping interferometry. Nature 365(6448), 721–727 (1993)CrossRefGoogle Scholar
  33. 33.
    Ungut, A., Grehan, G., Gouesbet, G.: Comparisons between geometrical optics and Lorenz–Mie theory. Appl. Opt. 20(17), 2911–2918 (1981). doi:10.1364/AO.20.002911. http://ao.osa.org/abstract.cfm?URI=ao-20-17-2911 Google Scholar
  34. 34.
    Xing, Q., Mao, F., Chai, L., Wang, Q.: Numerical modeling and theoretical analysis of femtosecond laser tweezers. Opt. Laser Technol. 36(8), 635–639 (2004). doi:10.1016/j.optlastec.2004.01.016.
  35. 35.
    Yasuda, R., Noji, H., Kinosita Jr, K., Yoshida, M.: F1-ATPase is a highly efficient molecular motor that rotates with discrete 120-degree steps. Cell 93(7), 1117–1124 (1998)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Mahdi Haghshenas-Jaryani
    • 1
  • Bryan Black
    • 3
  • Sarvenaz Ghaffari
    • 1
  • James Drake
    • 2
  • Alan Bowling
    • 1
  • Samarendra Mohanty
    • 3
  1. 1.Department of Mechanical and Aerospace EngineeringThe University of Texas at ArlingtonArlingtonUSA
  2. 2.Department of BioengineeringThe University of Texas at ArlingtonArlingtonUSA
  3. 3.Department of PhysicsThe University of Texas at ArlingtonArlingtonUSA

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