Abstract

We demonstrate how optical tweezers combined with a three-dimensional force detection system and high-speed camera are used to study the swimming force and behavior of trapped micro-organisms. By utilizing position sensitive detection, we measure the motility force of trapped particles, regardless of orientation. This has the advantage of not requiring complex beam shaping or microfluidic controls for aligning trapped particles in a particular orientation, leading to unambiguous measurements of the propulsive force at any time. Correlating the direct force measurements with position data from a high-speed camera enables us to determine changes in the particle’s behavior. We demonstrate our technique by measuring the swimming force and observing distinctions between swimming and tumbling modes of the Escherichia coli (E. coli) strain MC4100. Our method shows promise for application in future studies of trappable but otherwise arbitrary-shaped biological swimmers and other active matter.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. A. Ashkin, J. M. Dziedzic, J. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
    [Crossref]
  2. A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of single living cells using infra-red laser beams,” Ber. Bunsenges. Phys. Chem. 93, 254–260 (1989).
    [Crossref]
  3. F. Hörner, M. Woerdemann, S. Müller, B. Maier, and C. Denz, “Full 3D translational and rotational optical control of multiple rod-shaped bacteria,” J. Biophoton. 3, 468–475 (2010).
    [Crossref]
  4. I. C. D. Lenton, D. J. Armstrong, A. B. Stilgoe, and T. A. Nieminen, and H. Rubinsztein-Dunlop, “Orientation of swimming cells with annular beam optical tweezers,” Opt. Commun. 459, 124864 (2020).
    [Crossref]
  5. T. A. Bell, G. Gauthier, T. W. Neely, H. Rubinsztein-Dunlop, M. J. Davis, and M. A. Baker, “Phase and micromotion of Bose-Einstein condensates in a time-averaged ring trap,” Phys. Rev. A 98, 013604 (2018).
    [Crossref]
  6. G. Volpe, G. Volpe, and S. Gigan, “Brownian motion in a speckle light field: tunable anomalous diffusion and selective optical manipulation,” Sci. Rep. 4, 3936 (2014).
    [Crossref]
  7. A. A. Bui, A. V. Kashchuk, M. A. Balanant, T. A. Nieminen, H. Rubinsztein-Dunlop, and A. B. Stilgoe, “Calibration of force detection for arbitrarily shaped particles in optical tweezers,” Sci. Rep. 8, 10798 (2018).
    [Crossref]
  8. H. Rubinsztein-Dunlop, T. Asavei, A. B. Stilgoe, V. L. Loke, R. Vogel, T. A. Nieminen, and N. R. Heckenberg, “Design of optically driven microrotors,” in Optical Nano and Micro Actuator Technology (2012), pp. 277–306.
  9. A. V. Kashchuk, T. A. Nieminen, H. Rubinsztein-Dunlop, and A. B. Stilgoe, “High-speed transverse and axial optical force measurements using amplitude filter masks,” Opt. Express 27, 10034–10049 (2019).
    [Crossref]
  10. A. Farré and M. Montes-Usategui, “A force detection technique for single-beam optical traps based on direct measurement of light momentum changes,” Opt. Express 18, 11955–11968 (2010).
    [Crossref]
  11. C. J. Bustamante and S. B. Smith, and The Regents of the University of California, “A light-force sensor and method for measuring axial optical-trap forces from changes in light momentum along an optic axis,” (2004), https://patentscope.wipo.int/search/en/detail.jsf?docId=WO2005029139 .
  12. J. Hu, M. Yang, G. Gompper, and R. G. Winkler, “Modelling the mechanics and hydrodynamics of swimming E. coli,” Soft Matter 11, 7867–7876 (2015).
    [Crossref]
  13. T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6, 831–833 (2009).
    [Crossref]
  14. G. Reshes, S. Vanounou, I. Fishov, and M. Feingold, “Cell shape dynamics in Escherichia coli,” Biophys. J. 94, 251–264 (2008).
    [Crossref]
  15. K. Namba, I. Yamashita, and F. Vonderviszt, “Structure of the core and central channel of bacterial flagella,” Nature 342, 648–651 (1989).
    [Crossref]
  16. S. Chattopadhyay, R. Moldovan, C. Yeung, and X. Wu, “Swimming efficiency of bacterium Escherichia coli,” Proc. Natl. Acad. Sci. USA 103, 13712–13717 (2006).
    [Crossref]
  17. J. Saragosti, P. Silberzan, and A. Buguin, “Modeling E. coli tumbles by rotational diffusion. Implications for chemotaxis,” PLoS ONE 7, e35412 (2012).
    [Crossref]
  18. H. C. Berg, E. coli in Motion (Springer, 2008).
  19. N. C. Darnton and H. C. Berg, “Force-extension measurements on bacterial flagella: triggering polymorphic transformations,” Biophys. J. 92, 2230–2236 (2007).
    [Crossref]
  20. H. Zhang and K.-K. Liu, “Optical tweezers for single cells,” J. R. Soc. Interface 5, 671–690 (2008).
    [Crossref]
  21. A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
    [Crossref]
  22. R. C. Gauthier, M. Ashman, and C. P. Grover, “Experimental confirmation of the optical-trapping properties of cylindrical objects,” Appl. Opt. 38, 4861–4869 (1999).
    [Crossref]
  23. A. Keloth, O. Anderson, D. Risbridger, and L. Paterson, “Single cell isolation using optical tweezers,” Micromachines 9, 434–439 (2018).
    [Crossref]
  24. G. Carmon and M. Feingold, “Controlled alignment of bacterial cells with oscillating optical tweezers,” J. Nanophoton. 5, 051803 (2011).
    [Crossref]
  25. G. Thalhammer, L. Obmascher, and M. Ritsch-Marte, “Direct measurement of axial optical forces,” Opt. Express 23, 6112–6129 (2015).
    [Crossref]
  26. S. B. Smith, Y. Cui, and C. Bustamante, “7. Optical-trap force transducer that operates by direct measurement of light momentum,” in Methods in Enzymology (Elsevier, 2003), Vol. 361, pp. 134–162.
  27. A. Farré, F. Marsà, and M. Montes-Usategui, “Optimized back-focal-plane interferometry directly measures forces of optically trapped particles,” Opt. Express 20, 12270–12291 (2012).
    [Crossref]
  28. T. Altindal, S. Chattopadhyay, and X.-L. Wu, “Bacterial chemotaxis in an optical trap,” PLoS ONE 6, e18231 (2011).
    [Crossref]
  29. G. Volpe and G. Volpe, “Simulation of a Brownian particle in an optical trap,” Am. J. Phys. 81, 224–230 (2013).
    [Crossref]

2020 (1)

I. C. D. Lenton, D. J. Armstrong, A. B. Stilgoe, and T. A. Nieminen, and H. Rubinsztein-Dunlop, “Orientation of swimming cells with annular beam optical tweezers,” Opt. Commun. 459, 124864 (2020).
[Crossref]

I. C. D. Lenton, D. J. Armstrong, A. B. Stilgoe, and T. A. Nieminen, and H. Rubinsztein-Dunlop, “Orientation of swimming cells with annular beam optical tweezers,” Opt. Commun. 459, 124864 (2020).
[Crossref]

2019 (1)

2018 (3)

A. A. Bui, A. V. Kashchuk, M. A. Balanant, T. A. Nieminen, H. Rubinsztein-Dunlop, and A. B. Stilgoe, “Calibration of force detection for arbitrarily shaped particles in optical tweezers,” Sci. Rep. 8, 10798 (2018).
[Crossref]

T. A. Bell, G. Gauthier, T. W. Neely, H. Rubinsztein-Dunlop, M. J. Davis, and M. A. Baker, “Phase and micromotion of Bose-Einstein condensates in a time-averaged ring trap,” Phys. Rev. A 98, 013604 (2018).
[Crossref]

A. Keloth, O. Anderson, D. Risbridger, and L. Paterson, “Single cell isolation using optical tweezers,” Micromachines 9, 434–439 (2018).
[Crossref]

2015 (2)

G. Thalhammer, L. Obmascher, and M. Ritsch-Marte, “Direct measurement of axial optical forces,” Opt. Express 23, 6112–6129 (2015).
[Crossref]

J. Hu, M. Yang, G. Gompper, and R. G. Winkler, “Modelling the mechanics and hydrodynamics of swimming E. coli,” Soft Matter 11, 7867–7876 (2015).
[Crossref]

2014 (1)

G. Volpe, G. Volpe, and S. Gigan, “Brownian motion in a speckle light field: tunable anomalous diffusion and selective optical manipulation,” Sci. Rep. 4, 3936 (2014).
[Crossref]

2013 (1)

G. Volpe and G. Volpe, “Simulation of a Brownian particle in an optical trap,” Am. J. Phys. 81, 224–230 (2013).
[Crossref]

2012 (2)

A. Farré, F. Marsà, and M. Montes-Usategui, “Optimized back-focal-plane interferometry directly measures forces of optically trapped particles,” Opt. Express 20, 12270–12291 (2012).
[Crossref]

J. Saragosti, P. Silberzan, and A. Buguin, “Modeling E. coli tumbles by rotational diffusion. Implications for chemotaxis,” PLoS ONE 7, e35412 (2012).
[Crossref]

2011 (2)

T. Altindal, S. Chattopadhyay, and X.-L. Wu, “Bacterial chemotaxis in an optical trap,” PLoS ONE 6, e18231 (2011).
[Crossref]

G. Carmon and M. Feingold, “Controlled alignment of bacterial cells with oscillating optical tweezers,” J. Nanophoton. 5, 051803 (2011).
[Crossref]

2010 (2)

F. Hörner, M. Woerdemann, S. Müller, B. Maier, and C. Denz, “Full 3D translational and rotational optical control of multiple rod-shaped bacteria,” J. Biophoton. 3, 468–475 (2010).
[Crossref]

A. Farré and M. Montes-Usategui, “A force detection technique for single-beam optical traps based on direct measurement of light momentum changes,” Opt. Express 18, 11955–11968 (2010).
[Crossref]

2009 (1)

T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6, 831–833 (2009).
[Crossref]

2008 (2)

G. Reshes, S. Vanounou, I. Fishov, and M. Feingold, “Cell shape dynamics in Escherichia coli,” Biophys. J. 94, 251–264 (2008).
[Crossref]

H. Zhang and K.-K. Liu, “Optical tweezers for single cells,” J. R. Soc. Interface 5, 671–690 (2008).
[Crossref]

2007 (1)

N. C. Darnton and H. C. Berg, “Force-extension measurements on bacterial flagella: triggering polymorphic transformations,” Biophys. J. 92, 2230–2236 (2007).
[Crossref]

2006 (1)

S. Chattopadhyay, R. Moldovan, C. Yeung, and X. Wu, “Swimming efficiency of bacterium Escherichia coli,” Proc. Natl. Acad. Sci. USA 103, 13712–13717 (2006).
[Crossref]

1999 (1)

1989 (2)

K. Namba, I. Yamashita, and F. Vonderviszt, “Structure of the core and central channel of bacterial flagella,” Nature 342, 648–651 (1989).
[Crossref]

A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of single living cells using infra-red laser beams,” Ber. Bunsenges. Phys. Chem. 93, 254–260 (1989).
[Crossref]

1987 (1)

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
[Crossref]

1986 (1)

Altindal, T.

T. Altindal, S. Chattopadhyay, and X.-L. Wu, “Bacterial chemotaxis in an optical trap,” PLoS ONE 6, e18231 (2011).
[Crossref]

Anderson, O.

A. Keloth, O. Anderson, D. Risbridger, and L. Paterson, “Single cell isolation using optical tweezers,” Micromachines 9, 434–439 (2018).
[Crossref]

Armstrong, D. J.

I. C. D. Lenton, D. J. Armstrong, A. B. Stilgoe, and T. A. Nieminen, and H. Rubinsztein-Dunlop, “Orientation of swimming cells with annular beam optical tweezers,” Opt. Commun. 459, 124864 (2020).
[Crossref]

Asavei, T.

H. Rubinsztein-Dunlop, T. Asavei, A. B. Stilgoe, V. L. Loke, R. Vogel, T. A. Nieminen, and N. R. Heckenberg, “Design of optically driven microrotors,” in Optical Nano and Micro Actuator Technology (2012), pp. 277–306.

Ashkin, A.

A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of single living cells using infra-red laser beams,” Ber. Bunsenges. Phys. Chem. 93, 254–260 (1989).
[Crossref]

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
[Crossref]

A. Ashkin, J. M. Dziedzic, J. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
[Crossref]

Ashman, M.

Baker, M. A.

T. A. Bell, G. Gauthier, T. W. Neely, H. Rubinsztein-Dunlop, M. J. Davis, and M. A. Baker, “Phase and micromotion of Bose-Einstein condensates in a time-averaged ring trap,” Phys. Rev. A 98, 013604 (2018).
[Crossref]

Balanant, M. A.

A. A. Bui, A. V. Kashchuk, M. A. Balanant, T. A. Nieminen, H. Rubinsztein-Dunlop, and A. B. Stilgoe, “Calibration of force detection for arbitrarily shaped particles in optical tweezers,” Sci. Rep. 8, 10798 (2018).
[Crossref]

Bell, T. A.

T. A. Bell, G. Gauthier, T. W. Neely, H. Rubinsztein-Dunlop, M. J. Davis, and M. A. Baker, “Phase and micromotion of Bose-Einstein condensates in a time-averaged ring trap,” Phys. Rev. A 98, 013604 (2018).
[Crossref]

Berg, H. C.

N. C. Darnton and H. C. Berg, “Force-extension measurements on bacterial flagella: triggering polymorphic transformations,” Biophys. J. 92, 2230–2236 (2007).
[Crossref]

H. C. Berg, E. coli in Motion (Springer, 2008).

Bjorkholm, J.

Buguin, A.

J. Saragosti, P. Silberzan, and A. Buguin, “Modeling E. coli tumbles by rotational diffusion. Implications for chemotaxis,” PLoS ONE 7, e35412 (2012).
[Crossref]

Bui, A. A.

A. A. Bui, A. V. Kashchuk, M. A. Balanant, T. A. Nieminen, H. Rubinsztein-Dunlop, and A. B. Stilgoe, “Calibration of force detection for arbitrarily shaped particles in optical tweezers,” Sci. Rep. 8, 10798 (2018).
[Crossref]

Bustamante, C.

S. B. Smith, Y. Cui, and C. Bustamante, “7. Optical-trap force transducer that operates by direct measurement of light momentum,” in Methods in Enzymology (Elsevier, 2003), Vol. 361, pp. 134–162.

Bustamante, C. J.

C. J. Bustamante and S. B. Smith, and The Regents of the University of California, “A light-force sensor and method for measuring axial optical-trap forces from changes in light momentum along an optic axis,” (2004), https://patentscope.wipo.int/search/en/detail.jsf?docId=WO2005029139 .

Carmon, G.

G. Carmon and M. Feingold, “Controlled alignment of bacterial cells with oscillating optical tweezers,” J. Nanophoton. 5, 051803 (2011).
[Crossref]

Chattopadhyay, S.

T. Altindal, S. Chattopadhyay, and X.-L. Wu, “Bacterial chemotaxis in an optical trap,” PLoS ONE 6, e18231 (2011).
[Crossref]

S. Chattopadhyay, R. Moldovan, C. Yeung, and X. Wu, “Swimming efficiency of bacterium Escherichia coli,” Proc. Natl. Acad. Sci. USA 103, 13712–13717 (2006).
[Crossref]

Chemla, Y. R.

T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6, 831–833 (2009).
[Crossref]

Chu, S.

Chubiz, L. M.

T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6, 831–833 (2009).
[Crossref]

Cui, Y.

S. B. Smith, Y. Cui, and C. Bustamante, “7. Optical-trap force transducer that operates by direct measurement of light momentum,” in Methods in Enzymology (Elsevier, 2003), Vol. 361, pp. 134–162.

Darnton, N. C.

N. C. Darnton and H. C. Berg, “Force-extension measurements on bacterial flagella: triggering polymorphic transformations,” Biophys. J. 92, 2230–2236 (2007).
[Crossref]

Davis, M. J.

T. A. Bell, G. Gauthier, T. W. Neely, H. Rubinsztein-Dunlop, M. J. Davis, and M. A. Baker, “Phase and micromotion of Bose-Einstein condensates in a time-averaged ring trap,” Phys. Rev. A 98, 013604 (2018).
[Crossref]

Denz, C.

F. Hörner, M. Woerdemann, S. Müller, B. Maier, and C. Denz, “Full 3D translational and rotational optical control of multiple rod-shaped bacteria,” J. Biophoton. 3, 468–475 (2010).
[Crossref]

Dziedzic, J.

A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of single living cells using infra-red laser beams,” Ber. Bunsenges. Phys. Chem. 93, 254–260 (1989).
[Crossref]

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
[Crossref]

A. Ashkin, J. M. Dziedzic, J. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288–290 (1986).
[Crossref]

Farré, A.

Feingold, M.

G. Carmon and M. Feingold, “Controlled alignment of bacterial cells with oscillating optical tweezers,” J. Nanophoton. 5, 051803 (2011).
[Crossref]

G. Reshes, S. Vanounou, I. Fishov, and M. Feingold, “Cell shape dynamics in Escherichia coli,” Biophys. J. 94, 251–264 (2008).
[Crossref]

Fishov, I.

G. Reshes, S. Vanounou, I. Fishov, and M. Feingold, “Cell shape dynamics in Escherichia coli,” Biophys. J. 94, 251–264 (2008).
[Crossref]

Gauthier, G.

T. A. Bell, G. Gauthier, T. W. Neely, H. Rubinsztein-Dunlop, M. J. Davis, and M. A. Baker, “Phase and micromotion of Bose-Einstein condensates in a time-averaged ring trap,” Phys. Rev. A 98, 013604 (2018).
[Crossref]

Gauthier, R. C.

Gigan, S.

G. Volpe, G. Volpe, and S. Gigan, “Brownian motion in a speckle light field: tunable anomalous diffusion and selective optical manipulation,” Sci. Rep. 4, 3936 (2014).
[Crossref]

Golding, I.

T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6, 831–833 (2009).
[Crossref]

Gompper, G.

J. Hu, M. Yang, G. Gompper, and R. G. Winkler, “Modelling the mechanics and hydrodynamics of swimming E. coli,” Soft Matter 11, 7867–7876 (2015).
[Crossref]

Grover, C. P.

Heckenberg, N. R.

H. Rubinsztein-Dunlop, T. Asavei, A. B. Stilgoe, V. L. Loke, R. Vogel, T. A. Nieminen, and N. R. Heckenberg, “Design of optically driven microrotors,” in Optical Nano and Micro Actuator Technology (2012), pp. 277–306.

Hörner, F.

F. Hörner, M. Woerdemann, S. Müller, B. Maier, and C. Denz, “Full 3D translational and rotational optical control of multiple rod-shaped bacteria,” J. Biophoton. 3, 468–475 (2010).
[Crossref]

Hu, J.

J. Hu, M. Yang, G. Gompper, and R. G. Winkler, “Modelling the mechanics and hydrodynamics of swimming E. coli,” Soft Matter 11, 7867–7876 (2015).
[Crossref]

Kashchuk, A. V.

A. V. Kashchuk, T. A. Nieminen, H. Rubinsztein-Dunlop, and A. B. Stilgoe, “High-speed transverse and axial optical force measurements using amplitude filter masks,” Opt. Express 27, 10034–10049 (2019).
[Crossref]

A. A. Bui, A. V. Kashchuk, M. A. Balanant, T. A. Nieminen, H. Rubinsztein-Dunlop, and A. B. Stilgoe, “Calibration of force detection for arbitrarily shaped particles in optical tweezers,” Sci. Rep. 8, 10798 (2018).
[Crossref]

Keloth, A.

A. Keloth, O. Anderson, D. Risbridger, and L. Paterson, “Single cell isolation using optical tweezers,” Micromachines 9, 434–439 (2018).
[Crossref]

Lenton, I. C. D.

I. C. D. Lenton, D. J. Armstrong, A. B. Stilgoe, and T. A. Nieminen, and H. Rubinsztein-Dunlop, “Orientation of swimming cells with annular beam optical tweezers,” Opt. Commun. 459, 124864 (2020).
[Crossref]

Liu, K.-K.

H. Zhang and K.-K. Liu, “Optical tweezers for single cells,” J. R. Soc. Interface 5, 671–690 (2008).
[Crossref]

Loke, V. L.

H. Rubinsztein-Dunlop, T. Asavei, A. B. Stilgoe, V. L. Loke, R. Vogel, T. A. Nieminen, and N. R. Heckenberg, “Design of optically driven microrotors,” in Optical Nano and Micro Actuator Technology (2012), pp. 277–306.

Maier, B.

F. Hörner, M. Woerdemann, S. Müller, B. Maier, and C. Denz, “Full 3D translational and rotational optical control of multiple rod-shaped bacteria,” J. Biophoton. 3, 468–475 (2010).
[Crossref]

Marsà, F.

Mears, P. J.

T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6, 831–833 (2009).
[Crossref]

Min, T. L.

T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6, 831–833 (2009).
[Crossref]

Moldovan, R.

S. Chattopadhyay, R. Moldovan, C. Yeung, and X. Wu, “Swimming efficiency of bacterium Escherichia coli,” Proc. Natl. Acad. Sci. USA 103, 13712–13717 (2006).
[Crossref]

Montes-Usategui, M.

Müller, S.

F. Hörner, M. Woerdemann, S. Müller, B. Maier, and C. Denz, “Full 3D translational and rotational optical control of multiple rod-shaped bacteria,” J. Biophoton. 3, 468–475 (2010).
[Crossref]

Namba, K.

K. Namba, I. Yamashita, and F. Vonderviszt, “Structure of the core and central channel of bacterial flagella,” Nature 342, 648–651 (1989).
[Crossref]

Neely, T. W.

T. A. Bell, G. Gauthier, T. W. Neely, H. Rubinsztein-Dunlop, M. J. Davis, and M. A. Baker, “Phase and micromotion of Bose-Einstein condensates in a time-averaged ring trap,” Phys. Rev. A 98, 013604 (2018).
[Crossref]

Nieminen, T. A.

I. C. D. Lenton, D. J. Armstrong, A. B. Stilgoe, and T. A. Nieminen, and H. Rubinsztein-Dunlop, “Orientation of swimming cells with annular beam optical tweezers,” Opt. Commun. 459, 124864 (2020).
[Crossref]

A. V. Kashchuk, T. A. Nieminen, H. Rubinsztein-Dunlop, and A. B. Stilgoe, “High-speed transverse and axial optical force measurements using amplitude filter masks,” Opt. Express 27, 10034–10049 (2019).
[Crossref]

A. A. Bui, A. V. Kashchuk, M. A. Balanant, T. A. Nieminen, H. Rubinsztein-Dunlop, and A. B. Stilgoe, “Calibration of force detection for arbitrarily shaped particles in optical tweezers,” Sci. Rep. 8, 10798 (2018).
[Crossref]

H. Rubinsztein-Dunlop, T. Asavei, A. B. Stilgoe, V. L. Loke, R. Vogel, T. A. Nieminen, and N. R. Heckenberg, “Design of optically driven microrotors,” in Optical Nano and Micro Actuator Technology (2012), pp. 277–306.

Obmascher, L.

Paterson, L.

A. Keloth, O. Anderson, D. Risbridger, and L. Paterson, “Single cell isolation using optical tweezers,” Micromachines 9, 434–439 (2018).
[Crossref]

Rao, C. V.

T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6, 831–833 (2009).
[Crossref]

Reshes, G.

G. Reshes, S. Vanounou, I. Fishov, and M. Feingold, “Cell shape dynamics in Escherichia coli,” Biophys. J. 94, 251–264 (2008).
[Crossref]

Risbridger, D.

A. Keloth, O. Anderson, D. Risbridger, and L. Paterson, “Single cell isolation using optical tweezers,” Micromachines 9, 434–439 (2018).
[Crossref]

Ritsch-Marte, M.

Rubinsztein-Dunlop, H.

I. C. D. Lenton, D. J. Armstrong, A. B. Stilgoe, and T. A. Nieminen, and H. Rubinsztein-Dunlop, “Orientation of swimming cells with annular beam optical tweezers,” Opt. Commun. 459, 124864 (2020).
[Crossref]

A. V. Kashchuk, T. A. Nieminen, H. Rubinsztein-Dunlop, and A. B. Stilgoe, “High-speed transverse and axial optical force measurements using amplitude filter masks,” Opt. Express 27, 10034–10049 (2019).
[Crossref]

A. A. Bui, A. V. Kashchuk, M. A. Balanant, T. A. Nieminen, H. Rubinsztein-Dunlop, and A. B. Stilgoe, “Calibration of force detection for arbitrarily shaped particles in optical tweezers,” Sci. Rep. 8, 10798 (2018).
[Crossref]

T. A. Bell, G. Gauthier, T. W. Neely, H. Rubinsztein-Dunlop, M. J. Davis, and M. A. Baker, “Phase and micromotion of Bose-Einstein condensates in a time-averaged ring trap,” Phys. Rev. A 98, 013604 (2018).
[Crossref]

H. Rubinsztein-Dunlop, T. Asavei, A. B. Stilgoe, V. L. Loke, R. Vogel, T. A. Nieminen, and N. R. Heckenberg, “Design of optically driven microrotors,” in Optical Nano and Micro Actuator Technology (2012), pp. 277–306.

Saragosti, J.

J. Saragosti, P. Silberzan, and A. Buguin, “Modeling E. coli tumbles by rotational diffusion. Implications for chemotaxis,” PLoS ONE 7, e35412 (2012).
[Crossref]

Silberzan, P.

J. Saragosti, P. Silberzan, and A. Buguin, “Modeling E. coli tumbles by rotational diffusion. Implications for chemotaxis,” PLoS ONE 7, e35412 (2012).
[Crossref]

Smith, S. B.

C. J. Bustamante and S. B. Smith, and The Regents of the University of California, “A light-force sensor and method for measuring axial optical-trap forces from changes in light momentum along an optic axis,” (2004), https://patentscope.wipo.int/search/en/detail.jsf?docId=WO2005029139 .

S. B. Smith, Y. Cui, and C. Bustamante, “7. Optical-trap force transducer that operates by direct measurement of light momentum,” in Methods in Enzymology (Elsevier, 2003), Vol. 361, pp. 134–162.

Stilgoe, A. B.

I. C. D. Lenton, D. J. Armstrong, A. B. Stilgoe, and T. A. Nieminen, and H. Rubinsztein-Dunlop, “Orientation of swimming cells with annular beam optical tweezers,” Opt. Commun. 459, 124864 (2020).
[Crossref]

A. V. Kashchuk, T. A. Nieminen, H. Rubinsztein-Dunlop, and A. B. Stilgoe, “High-speed transverse and axial optical force measurements using amplitude filter masks,” Opt. Express 27, 10034–10049 (2019).
[Crossref]

A. A. Bui, A. V. Kashchuk, M. A. Balanant, T. A. Nieminen, H. Rubinsztein-Dunlop, and A. B. Stilgoe, “Calibration of force detection for arbitrarily shaped particles in optical tweezers,” Sci. Rep. 8, 10798 (2018).
[Crossref]

H. Rubinsztein-Dunlop, T. Asavei, A. B. Stilgoe, V. L. Loke, R. Vogel, T. A. Nieminen, and N. R. Heckenberg, “Design of optically driven microrotors,” in Optical Nano and Micro Actuator Technology (2012), pp. 277–306.

Thalhammer, G.

Vanounou, S.

G. Reshes, S. Vanounou, I. Fishov, and M. Feingold, “Cell shape dynamics in Escherichia coli,” Biophys. J. 94, 251–264 (2008).
[Crossref]

Vogel, R.

H. Rubinsztein-Dunlop, T. Asavei, A. B. Stilgoe, V. L. Loke, R. Vogel, T. A. Nieminen, and N. R. Heckenberg, “Design of optically driven microrotors,” in Optical Nano and Micro Actuator Technology (2012), pp. 277–306.

Volpe, G.

G. Volpe, G. Volpe, and S. Gigan, “Brownian motion in a speckle light field: tunable anomalous diffusion and selective optical manipulation,” Sci. Rep. 4, 3936 (2014).
[Crossref]

G. Volpe, G. Volpe, and S. Gigan, “Brownian motion in a speckle light field: tunable anomalous diffusion and selective optical manipulation,” Sci. Rep. 4, 3936 (2014).
[Crossref]

G. Volpe and G. Volpe, “Simulation of a Brownian particle in an optical trap,” Am. J. Phys. 81, 224–230 (2013).
[Crossref]

G. Volpe and G. Volpe, “Simulation of a Brownian particle in an optical trap,” Am. J. Phys. 81, 224–230 (2013).
[Crossref]

Vonderviszt, F.

K. Namba, I. Yamashita, and F. Vonderviszt, “Structure of the core and central channel of bacterial flagella,” Nature 342, 648–651 (1989).
[Crossref]

Winkler, R. G.

J. Hu, M. Yang, G. Gompper, and R. G. Winkler, “Modelling the mechanics and hydrodynamics of swimming E. coli,” Soft Matter 11, 7867–7876 (2015).
[Crossref]

Woerdemann, M.

F. Hörner, M. Woerdemann, S. Müller, B. Maier, and C. Denz, “Full 3D translational and rotational optical control of multiple rod-shaped bacteria,” J. Biophoton. 3, 468–475 (2010).
[Crossref]

Wu, X.

S. Chattopadhyay, R. Moldovan, C. Yeung, and X. Wu, “Swimming efficiency of bacterium Escherichia coli,” Proc. Natl. Acad. Sci. USA 103, 13712–13717 (2006).
[Crossref]

Wu, X.-L.

T. Altindal, S. Chattopadhyay, and X.-L. Wu, “Bacterial chemotaxis in an optical trap,” PLoS ONE 6, e18231 (2011).
[Crossref]

Yamane, T.

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
[Crossref]

Yamashita, I.

K. Namba, I. Yamashita, and F. Vonderviszt, “Structure of the core and central channel of bacterial flagella,” Nature 342, 648–651 (1989).
[Crossref]

Yang, M.

J. Hu, M. Yang, G. Gompper, and R. G. Winkler, “Modelling the mechanics and hydrodynamics of swimming E. coli,” Soft Matter 11, 7867–7876 (2015).
[Crossref]

Yeung, C.

S. Chattopadhyay, R. Moldovan, C. Yeung, and X. Wu, “Swimming efficiency of bacterium Escherichia coli,” Proc. Natl. Acad. Sci. USA 103, 13712–13717 (2006).
[Crossref]

Zhang, H.

H. Zhang and K.-K. Liu, “Optical tweezers for single cells,” J. R. Soc. Interface 5, 671–690 (2008).
[Crossref]

Am. J. Phys. (1)

G. Volpe and G. Volpe, “Simulation of a Brownian particle in an optical trap,” Am. J. Phys. 81, 224–230 (2013).
[Crossref]

Appl. Opt. (1)

Ber. Bunsenges. Phys. Chem. (1)

A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of single living cells using infra-red laser beams,” Ber. Bunsenges. Phys. Chem. 93, 254–260 (1989).
[Crossref]

Biophys. J. (2)

N. C. Darnton and H. C. Berg, “Force-extension measurements on bacterial flagella: triggering polymorphic transformations,” Biophys. J. 92, 2230–2236 (2007).
[Crossref]

G. Reshes, S. Vanounou, I. Fishov, and M. Feingold, “Cell shape dynamics in Escherichia coli,” Biophys. J. 94, 251–264 (2008).
[Crossref]

J. Biophoton. (1)

F. Hörner, M. Woerdemann, S. Müller, B. Maier, and C. Denz, “Full 3D translational and rotational optical control of multiple rod-shaped bacteria,” J. Biophoton. 3, 468–475 (2010).
[Crossref]

J. Nanophoton. (1)

G. Carmon and M. Feingold, “Controlled alignment of bacterial cells with oscillating optical tweezers,” J. Nanophoton. 5, 051803 (2011).
[Crossref]

J. R. Soc. Interface (1)

H. Zhang and K.-K. Liu, “Optical tweezers for single cells,” J. R. Soc. Interface 5, 671–690 (2008).
[Crossref]

Micromachines (1)

A. Keloth, O. Anderson, D. Risbridger, and L. Paterson, “Single cell isolation using optical tweezers,” Micromachines 9, 434–439 (2018).
[Crossref]

Nat. Methods (1)

T. L. Min, P. J. Mears, L. M. Chubiz, C. V. Rao, I. Golding, and Y. R. Chemla, “High-resolution, long-term characterization of bacterial motility using optical tweezers,” Nat. Methods 6, 831–833 (2009).
[Crossref]

Nature (2)

A. Ashkin, J. M. Dziedzic, and T. Yamane, “Optical trapping and manipulation of single cells using infrared laser beams,” Nature 330, 769–771 (1987).
[Crossref]

K. Namba, I. Yamashita, and F. Vonderviszt, “Structure of the core and central channel of bacterial flagella,” Nature 342, 648–651 (1989).
[Crossref]

Opt. Commun. (1)

I. C. D. Lenton, D. J. Armstrong, A. B. Stilgoe, and T. A. Nieminen, and H. Rubinsztein-Dunlop, “Orientation of swimming cells with annular beam optical tweezers,” Opt. Commun. 459, 124864 (2020).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. A (1)

T. A. Bell, G. Gauthier, T. W. Neely, H. Rubinsztein-Dunlop, M. J. Davis, and M. A. Baker, “Phase and micromotion of Bose-Einstein condensates in a time-averaged ring trap,” Phys. Rev. A 98, 013604 (2018).
[Crossref]

PLoS ONE (2)

J. Saragosti, P. Silberzan, and A. Buguin, “Modeling E. coli tumbles by rotational diffusion. Implications for chemotaxis,” PLoS ONE 7, e35412 (2012).
[Crossref]

T. Altindal, S. Chattopadhyay, and X.-L. Wu, “Bacterial chemotaxis in an optical trap,” PLoS ONE 6, e18231 (2011).
[Crossref]

Proc. Natl. Acad. Sci. USA (1)

S. Chattopadhyay, R. Moldovan, C. Yeung, and X. Wu, “Swimming efficiency of bacterium Escherichia coli,” Proc. Natl. Acad. Sci. USA 103, 13712–13717 (2006).
[Crossref]

Sci. Rep. (2)

G. Volpe, G. Volpe, and S. Gigan, “Brownian motion in a speckle light field: tunable anomalous diffusion and selective optical manipulation,” Sci. Rep. 4, 3936 (2014).
[Crossref]

A. A. Bui, A. V. Kashchuk, M. A. Balanant, T. A. Nieminen, H. Rubinsztein-Dunlop, and A. B. Stilgoe, “Calibration of force detection for arbitrarily shaped particles in optical tweezers,” Sci. Rep. 8, 10798 (2018).
[Crossref]

Soft Matter (1)

J. Hu, M. Yang, G. Gompper, and R. G. Winkler, “Modelling the mechanics and hydrodynamics of swimming E. coli,” Soft Matter 11, 7867–7876 (2015).
[Crossref]

Other (4)

C. J. Bustamante and S. B. Smith, and The Regents of the University of California, “A light-force sensor and method for measuring axial optical-trap forces from changes in light momentum along an optic axis,” (2004), https://patentscope.wipo.int/search/en/detail.jsf?docId=WO2005029139 .

H. Rubinsztein-Dunlop, T. Asavei, A. B. Stilgoe, V. L. Loke, R. Vogel, T. A. Nieminen, and N. R. Heckenberg, “Design of optically driven microrotors,” in Optical Nano and Micro Actuator Technology (2012), pp. 277–306.

H. C. Berg, E. coli in Motion (Springer, 2008).

S. B. Smith, Y. Cui, and C. Bustamante, “7. Optical-trap force transducer that operates by direct measurement of light momentum,” in Methods in Enzymology (Elsevier, 2003), Vol. 361, pp. 134–162.

Supplementary Material (2)

NameDescription
» Supplement 1       Revised supplemental .TEX files. Figures used within supplemental file are included within the .zip folder
» Visualization 1       Updated video showing a simulated optically trapped E.coli

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Figures (4)

Fig. 1.
Fig. 1. Layout of optical tweezers setup used for trapping and force detection. A 1064 nm laser is passed through an high numerical aperture (1.2 NA) objective to create a diffraction-limited optical trap. Light transmitted through the sample is collected by a condenser and passed to a 3D force detection system. Radial forces are measured with a position sensitive detector, and axial forces are found through position sensitive mask detection, as discussed in Section 2.C.
Fig. 2.
Fig. 2. (a) E. coli propel themselves with the use of a rotating helical flagella ($\omega$); this rotation then causes a subsequent counter-rotation of the cell body ($\Omega$). (b) Power spectra for a nonmotile cell (red) and a motile (blue) E. coli. The two prominent peaks in the power spectrum correspond to the cell’s body and flagellum rotation, respectively. (c) Time series data used to generate the (red) power spectrum in (b).
Fig. 3.
Fig. 3. E. coli held in an optical trap. Simulation of how measured forces change when an optically trapped E. coli starts swimming, a still image from Visualization 1. (a) shows an E. coli held in a Gaussian optical trap. (b) Particle position relative to the trap center. (c) Average and instantaneous cell velocity, which could be measured with a sufficiently fast detector. (d) shows how the optical force (${F_o}$) and the drag force (${F_d}$) change as a result of the E. coli swimming force (${F_s}$). The drag force depends on the particle velocity relative to the surrounding fluid. For simplicity, the simulation only shows cell motion along the axial direction.
Fig. 4.
Fig. 4. Force distributions in three dimensions for an optically trapped motile E. coli. (a) and (b) show the distribution of forces in the focal plane, resembling behavior of a nonmotile Brownian particle. These distributions reveal little information about the dynamics or behavior of the cell. (c) shows the axial force distribution, where distinct modes are observed, corresponding to periods of swimming and tumbling of the cell. (d) 3D representation of force contributions for an optically trapped motile E. coli using measurements presented in (a)–(c).

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

F V ( x , y ) = ( F x F y ) = 1 c m ( I ( x , y ) x / R d x d y I ( x , y ) y / R d x d y ) F V 0 ( x , y ) .
exp ( k N / m ( x , y ) 2 2 k B T ) = exp ( k N / m F V 2 2 k V / m 2 k B T ) ,
exp ( C r a d 2 F V 2 2 k N / m k B T ) .
σ v = k N / m k B T C r a d 2 .
C r a d = k B T σ c a m σ v .
M = k a x i a l 1 C A C A 2 ( x 2 + y 2 ) .
F N(z) = C r a d k r a d k a x i a l ( F V ( z ) F V 0 ( z ) ) .
F O p t i c a l = F S w i m F B M F D r a g ,

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