Skip to main content
SpringerLink
Log in

Microscopic artificial swimmers

  • Letter
  • Published:

From Nature

View current issue Submit your manuscript

Abstract

Microorganisms such as bacteria and many eukaryotic cells propel themselves with hair-like structures known as flagella, which can exhibit a variety of structures and movement patterns1. For example, bacterial flagella are helically shaped2 and driven at their bases by a reversible rotary engine3, which rotates the attached flagellum to give a motion similar to that of a corkscrew. In contrast, eukaryotic cells use flagella that resemble elastic rods4 and exhibit a beating motion: internally generated stresses give rise to a series of bends that propagate towards the tip5,6,7. In contrast to this variety of swimming strategies encountered in nature, a controlled swimming motion of artificial micrometre-sized structures has not yet been realized. Here we show that a linear chain of colloidal magnetic particles linked by DNA and attached to a red blood cell can act as a flexible artificial flagellum. The filament aligns with an external uniform magnetic field and is readily actuated by oscillating a transverse field. We find that the actuation induces a beating pattern that propels the structure, and that the external fields can be adjusted to control the velocity and the direction of motion.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1: Schematic representation of a flexible magnetic filament.
Figure 2: Beating pattern of the motion of a magnetic flexible filament attached to a red blood cell.
Figure 3: Sequence of deformation of the end of a free filament.
Figure 4: Scaled velocity as a function of Sp.

Similar content being viewed by others

References

  1. Bray, D. Cell Movements: from Molecules to Motility 6–12 (Garland Publ., New York, 1992)

    Google Scholar 

  2. Berg, H. C. & Anderson, R. A. Bacteria swim by rotating their flagellar filaments. Nature 245, 380–384 (1973)

    Article  ADS  CAS  PubMed  Google Scholar 

  3. Schuster, S. C. & Khan, S. The bacterial flagellar motor. Annu. Rev. Biophys. Biomol. Struct. 23, 509–539 (1994)

    Article  CAS  PubMed  Google Scholar 

  4. Gibbons, I. R. Cilia and flagella of eukaryotes. J. Cell Biol. 91, S107–S124 (1981)

    Article  Google Scholar 

  5. Satir, P. Studies on cilia. 3. Further studies on cilium tip and a sliding filament model of ciliary motility. J. Cell Biol. 39, 77–94 (1968)

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  6. Taylor, G. I. Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. Ser. A 209, 447–461 (1951)

    Article  ADS  MathSciNet  Google Scholar 

  7. Gray, J. & Hancock, G. J. The propulsion of sea-urchin spermatozoa. J. Exp. Biol. 32, 802–814 (1955)

    Google Scholar 

  8. Purcell, E. M. Life at low Reynolds number. Am. J. Phys. 45, 3–11 (1977)

    Article  ADS  Google Scholar 

  9. Becker, L. E., Koehler, S. A. & Stone, H. A. On self-propulsion of micro-machines at low Reynolds number: Purcell's three-link swimmer. J. Fluid Mech. 490, 15–35 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  10. Najafi, A. & Golestanian, R. Simple swimmer at low Reynolds number: Three linked spheres. Phys. Rev. E. 69, 062901–062904 (2004)

    Article  ADS  Google Scholar 

  11. Cox, R. G. Motion of long slender bodies in a viscous fluid. Part I. General theory. J. Fluid Mech. 45, 791–810 (1971)

    Article  Google Scholar 

  12. Brennen, C. Locomotion of flagellates with mastigonemes. J. Mechanochem. Cell Motil. 3, 207–217 (1976)

    CAS  PubMed  Google Scholar 

  13. Avron, J. E., Gat, O. & Kenneth, O. Optimal swimming at low Reynolds numbers. Phys. Rev. Lett. 93, 186001–186004 (2004)

    Article  ADS  CAS  PubMed  Google Scholar 

  14. Lagomarsino, M. C., Capuani, F. & Lowe, C. P. A simulation study of the dynamics of a driven filament in an Aristotelian fluid. J. Theor. Biol. 224, 215–224 (2003)

    Article  MathSciNet  CAS  PubMed  Google Scholar 

  15. Wiggins, C. H. & Goldstein, R. E. Flexive and propulsive dynamics of elastica at low Reynolds number. Phys. Rev. Lett. 80, 3879–3882 (1998)

    Article  ADS  CAS  Google Scholar 

  16. Lowe, C. P. Dynamics of filaments: modelling the dynamics of driven microfilaments. Phil. Trans. R. Soc. Lond. B 358, 1543–1550 (2003)

    Article  Google Scholar 

  17. Goubault, C. et al. Flexible magnetic filaments as micromechanical sensors. Phys. Rev. Lett. 91, 260802–260805 (2003)

    Article  ADS  CAS  PubMed  Google Scholar 

  18. Koenig, A. et al. Magnetic force probe for nanoscale biomolecules. Phys. Rev. Lett. (in the press)

  19. Strick, T. R., Allemand, J. F., Bensimon, D., Bensimon, A. & Croquette, V. The elasticity of a single supercoiled DNA molecule. Science 271, 1835–1837 (1996)

    Article  ADS  CAS  PubMed  Google Scholar 

  20. Zahn, K., Lenke, R. & Maret, G. Friction coefficient of rod-like chains of spheres at very-low Reynolds-numbers.1. Experiment. J. Phys. II 4, 555–560 (1994)

    CAS  Google Scholar 

  21. Meunier, A. Friction coefficient of rod-like chains of spheres at very-low Reynolds-numbers.2. Numerical simulations. J. Phys. II 4, 561–566 (1994)

    CAS  Google Scholar 

  22. Terray, A., Oakey, J. & Marr, D. W. M. Microfluidic control using colloidal devices. Science 296, 1841–1844 (2002)

    Article  ADS  CAS  PubMed  Google Scholar 

  23. Darnton, N., Turner, L., Breuer, K. & Berg, H. C. Moving fluid with bacterial carpets. Biophys. J. 86, 1863–1870 (2004)

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  24. Camalet, S., Julicher, F. & Prost, J. Self-organized beating and swimming of internally driven filaments. Phys. Rev. Lett. 82, 1590–1593 (1999)

    Article  ADS  CAS  Google Scholar 

  25. Ishijima, S. & Hiramoto, Y. Flexural rigidity of echinoderm sperm flagella. Cell Struct. Funct. 19, 349–362 (1994)

    Article  CAS  PubMed  Google Scholar 

  26. Wiggins, C. H., Riveline, D., Ott, A. & Goldstein, R. E. Trapping and wiggling: Elastohydrodynamics of driven microfilaments. Biophys. J. 74, 1043–1060 (1998)

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

Download references

Acknowledgements

We thank the Imphy Company for providing us with free Mumetal. We also thank A. Ajdari, J. Prost, J.-B. Salmon and D. Weitz for discussions, and C. Gosse, A. Koenig, F. Montel and C. Goubault for help in material preparation.

Author information

Authors and Affiliations

  1. Laboratoire Colloïdes et Matériaux Divisés, ESPCI, UMR CNRS 7612 UPMC, ParisTech, 10 rue Vauquelin, 75005, Paris, France

    Rémi Dreyfus, Jean Baudry & Jérôme Bibette

  2. Division of Engineering and Applied Sciences, Harvard University, Massachusetts, 02138, Cambridge, USA

    Marcus L. Roper & Howard A. Stone

  3. Laboratoire Physique et Mécanique des Milieux Hétérogènes, ESPCI, UMR CNRS 7636, ParisTech, 10 rue Vauquelin, 75005, Paris, France

    Marc Fermigier

Authors
  1. Rémi Dreyfus
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jean Baudry
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marcus L. Roper
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Marc Fermigier
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Howard A. Stone
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Jérôme Bibette
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rémi Dreyfus.

Ethics declarations

Competing interests

Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests.

Supplementary information

Supplementary Methods

This document describes the physics of the motion of the magnetic filament attached to a red blood cell. (DOC 84 kb)

Supplementary Video 1

This movie shows the dynamics of a filament tethered to a red blood cell on a single period of magnetic field (f=10Hz, Bx=9mT, By=14.5mT). The frame rate is 440 frames/s. One can clearly see how the filament bends to follow the direction of the magnetic field. (MOV 311 kb)

Supplementary Video 2

This movie shows the dynamics of the same filament on 25 periods of magnetic field (f=10Hz, Bx=9mT, B>y=14.5mT). The frame rate is 40 frames/s. The filament is moving towards the direction of the free extremity at a velocity corresponding to the red cell size per second. (MOV 770 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dreyfus, R., Baudry, J., Roper, M. et al. Microscopic artificial swimmers. Nature 437, 862–865 (2005). https://doi.org/10.1038/nature04090

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature04090

  • Springer Nature Limited

This article is cited by

Search

Navigation