Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Directing cell motions on micropatterned ratchets

Nature Physics volume 5, pages 606–612 (2009)Cite this article

Abstract

Cell motility is a process deriving from the synchronized dynamics of the cytoskeleton. In several important physiological processes—notably, cancer metastasis—the randomly moving cells can acquire a directional motility phenotype and bias their motions in response to environmental cues. Despite intense research, however, the current understanding of directional cell migration is incomplete and there is a growing need to develop systems that would enable the study and control of this process. This article demonstrates that random motions of motile cells can be rectified by asymmetric (‘ratchet’) microgeometries. Interactions between the cells and the imposed geometrical cues guide cell polarization and give rise to directional motility. Depending on the ratchet design, cells of different types can move either in the same or in opposite directions on the same imposed pattern. In the latter case, it is possible to partially sort mixed cell populations into different collecting reservoirs.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Fabrication of substrates for cell locomotion and motility characteristics of cells on various micropatterns.
Figure 2: Directional cell migration on connected-triangle ratchets.
Figure 3: Mechanism of directional cell migration on micropatterned ratchets.
Figure 4: Probabilities of directional migration, ratcheting efficiency and the scaling properties of the reservoir bias, b2.
Figure 5: Cells on bi-directional ‘lines-with-spikes’ ratchets.

Similar content being viewed by others

References

  1. Lee, S. H. & Grier, D. G. One-dimensional optical thermal ratchets. J. Phys. Condens. Matter 17, S3685–S3695 (2005).

    Article  Google Scholar 

  2. Lee, C. S., Janko, B., Derenyi, I. & Barabasi, A. L. Reducing vortex density in superconductors using the ‘ratchet effect’. Nature 400, 337–340 (1999).

    Article  ADS  Google Scholar 

  3. Lorke, A. et al. Far-infrared and transport properties of antidot arrays with broken symmetry. Physica B 251, 312–316 (1998).

    Article  ADS  Google Scholar 

  4. Rousselet, J., Salome, L., Ajdari, A. & Prost, J. Directional motion of Brownian particles induced by a periodic asymmetric potential. Nature 370, 446–448 (1994).

    Article  ADS  Google Scholar 

  5. Engel, A., Muller, H. W., Reimann, P. & Jung, A. Ferrofluids as thermal ratchets. Phys. Rev. Lett. 91, 060602 (2003).

    Article  ADS  Google Scholar 

  6. Linke, H. et al. Experimental tunneling ratchets. Science 286, 2314–2317 (1999).

    Article  Google Scholar 

  7. van Oudenaarden, A. & Boxer, S. G. Brownian ratchets: Molecular separations in lipid bilayers supported on patterned arrays. Science 285, 1046–1048 (1999).

    Article  Google Scholar 

  8. Villegas, J. E. et al. A superconducting reversible rectifier that controls the motion of magnetic flux quanta. Science 302, 1188–1191 (2003).

    Article  ADS  Google Scholar 

  9. Hiratsuka, Y., Tada, T., Oiwa, K., Kanayama, T. & Uyeda, T. Q. P. Controlling the direction of kinesin-driven microtubule movements along microlithographic tracks. Biophys. J. 81, 1555–1561 (2001).

    Article  Google Scholar 

  10. Matthias, S. & Muller, F. Asymmetric pores in a silicon membrane acting as massively parallel Brownian ratchets. Nature 424, 53–57 (2003).

    Article  ADS  Google Scholar 

  11. Reimann, P. Brownian motors: Noisy transport far from equilibrium. Phys. Rep.-Rev. Sec. Phys. Lett. 361, 57–265 (2002).

    MathSciNet  MATH  Google Scholar 

  12. Astumian, R. D. & Hanggi, P. Brownian motors. Phys. Today 55, 33–39 (2002).

    Article  Google Scholar 

  13. Feynman, R. P., Leighton, R. B. & Sands, M. L. The Feynman Lectures on Physics Vol. 1 (Pearson/Addison-Wesley, 2006).

    MATH  Google Scholar 

  14. Peskin, C. S., Odell, G. M. & Oster, G. F. Cellular motions and thermal fluctuations—the Brownian ratchet. Biophys. J. 65, 316–324 (1993).

    Article  ADS  Google Scholar 

  15. Silva, C. C. D., de Vondel, J. V., Morelle, M. & Moshchalkov, V. V. Controlled multiple reversals of a ratchet effect. Nature 440, 651–654 (2006).

    Article  ADS  Google Scholar 

  16. Kelly, T. R., De Silva, H. & Silva, R. A. Unidirectional rotary motion in a molecular system. Nature 401, 150–152 (1999).

    Article  ADS  Google Scholar 

  17. Simon, S. M., Peskin, C. S. & Oster, G. F. What drives the translocation of proteins. Proc. Natl Acad. Sci. USA 89, 3770–3774 (1992).

    Article  ADS  Google Scholar 

  18. Alt, W. Biased random-walk models for chemotaxis and related diffusion approximations. J. Math. Biol. 9, 147–177 (1980).

    Article  MathSciNet  Google Scholar 

  19. Dunn, G. A. & Brown, A. F. A unified approach to analyzing cell motility. J. Cell Sci. Suppl 8, 81–102 (1987).

    Article  Google Scholar 

  20. Theriot, J. A. & Mitchison, T. J. Actin microfilament dynamics in locomoting cells. Nature 352, 126–131 (1991).

    Article  ADS  Google Scholar 

  21. Ponti, A., Machacek, M., Gupton, S. L., Waterman-Storer, C. M. & Danuser, G. Two distinct actin networks drive the protrusion of migrating cells. Science 305, 1782–1786 (2004).

    Article  ADS  Google Scholar 

  22. Thery, M. et al. Anisotropy of cell adhesive microenvironment governs cell internal organization and orientation of polarity. Proc. Natl Acad. Sci. USA 103, 19771–19776 (2006).

    Article  ADS  Google Scholar 

  23. Thery, M., Pepin, A., Dressaire, E., Chen, Y. & Bornens, M. Cell distribution of stress fibres in response to the geometry of the adhesive environment. Cell Motil. Cytoskeleton 63, 341–355 (2006).

    Article  Google Scholar 

  24. Jiang, X. Y. et al. A general method for patterning gradients of biomolecules on surfaces using microfluidic networks. Anal. Chem. 77, 2338–2347 (2005).

    Article  Google Scholar 

  25. Dertinger, S. K. W., Jiang, X. Y., Li, Z. Y., Murthy, V. N. & Whitesides, G. M. Gradients of substrate-bound laminin orient axonal specification of neurons. Proc. Natl Acad. Sci. USA 99, 12542–12547 (2002).

    Article  ADS  Google Scholar 

  26. Brandley, B. K. & Schnaar, R. L. Tumor-cell haptotaxis on covalently immobilized linear and exponential gradients of a cell-adhesion peptide. Dev. Biol. 135, 74–86 (1989).

    Article  Google Scholar 

  27. Smith, J. T. et al. Measurement of cell migration on surface-bound fibronectin gradients. Langmuir 20, 8279–8286 (2004).

    Article  Google Scholar 

  28. Plummer, S. T., Wang, Q., Bohn, P. W., Stockton, R. & Schwartz, M. A. Electrochemically derived gradients of the extracellular matrix protein fibronectin on gold. Langmuir 19, 7528–7536 (2003).

    Article  Google Scholar 

  29. Campbell, C. J., Smoukov, S. K., Bishop, K. J. M., Baker, E. & Grzybowski, B. A. Direct printing of 3d and curvilinear micrometer-sized architectures into solid substrates with sub-micrometer resolution. Adv. Mater. 18, 2004–2008 (2006).

    Article  Google Scholar 

  30. Kandere-Grzybowska, K., Campbell, C., Komarova, Y., Grzybowski, B. A. & Borisy, G. G. Molecular dynamics imaging in micropatterned living cells. Nature Meth. 2, 739–741 (2005).

    Article  Google Scholar 

  31. Maroudas, N. G. Polymer exclusion, cell adhesion and membrane-fusion. Nature 254, 695–696 (1975).

    Article  ADS  Google Scholar 

  32. Prime, K. L. & Whitesides, G. M. Self-assembled organic monolayers—model systems for studying adsorption of proteins at surfaces. Science 252, 1164–1167 (1991).

    Article  ADS  Google Scholar 

  33. Singhvi, R. et al. Engineering cell-shape and function. Science 264, 696–698 (1994).

    Article  ADS  Google Scholar 

  34. Kandere-Grzybowska, K. et al. Cell motility on micropatterned treadmills and tracks. Soft Matter 3, 672–679 (2007).

    Article  ADS  Google Scholar 

  35. Jiang, X. Y., Bruzewicz, D. A., Wong, A. P., Piel, M. & Whitesides, G. M. Directing cell migration with asymmetric micropatterns. Proc. Natl Acad. Sci. USA 102, 975–978 (2005).

    Article  ADS  Google Scholar 

  36. Groisman, A. & Quake, S. R. A microfluidic rectifier: Anisotropic flow resistance at low reynolds numbers. Phys. Rev. Lett. 92, 094501 (2004).

    Article  ADS  Google Scholar 

  37. Grazi, E., Cintio, O. & Trombetta, G. On the mechanics of the actin filament: The linear relationship between stiffness and yield strength allows estimation of the yield strength of thin filament in vivo. J. Muscle Res. Cell Motil. 25, 103–105 (2004).

    Article  Google Scholar 

  38. Brown, C. M. et al. Probing the integrin-actin linkage using high-resolution protein velocity mapping. J. Cell Sci. 119, 5204–5214 (2006).

    Article  Google Scholar 

  39. Thatcher, A. R. Studies in the history of probability and statistics vi. A note on the early solutions of the problem of the duration of play. Biometrika 44, 515–518 (1957).

    MathSciNet  MATH  Google Scholar 

  40. Kumar, A., Galaev, I. Y. & Mattiasson, B. (eds) Cell Separation: Fundamentals, Analytical and Preparative Methods Vol. 106 (Springer, 2007).

  41. Steinberg, M. S. & Takeichi, M. Experimental specification of cell sorting, tissue spreading, and specific spatial patterning by quantitative differences in cadherin expression. Proc. Natl Acad. Sci. USA 91, 206–209 (1994).

    Article  ADS  Google Scholar 

  42. Xu, Q. L., Mellitzer, G., Robinson, V. & Wilkinson, D. G. In vivo cell sorting in complementary segmental domains mediated by eph receptors and ephrins. Nature 399, 267–271 (1999).

    Article  ADS  Google Scholar 

  43. Keren, D. F., McCoy, J. P. & Carey, J. L. Flow Cytometry in Clinical Diagnosis 3rd edn (American Society Clinical Pathology, 2001).

    Google Scholar 

  44. Jennings, C. D. & Foon, K. A. Recent advances in flow cytometry: Application to the diagnosis of hematologic malignancy. Blood 90, 2863–2892 (1997).

    Google Scholar 

  45. Steinberg, M. S. Reconstruction of tissues by dissociated cells. Science 141, 401–408 (1963).

    Article  ADS  Google Scholar 

  46. Townes, P. L. & Holtfreter, J. Directed movements and selective adhesion of embryonic amphibian cells. J. Exp. Zool. 128, 53–120 (1955).

    Article  Google Scholar 

  47. Discher, D. E., Janmey, P. & Wang, Y. L. Tissue cells feel and respond to the stiffness of their substrate. Science 310, 1139–1143 (2005).

    Article  ADS  Google Scholar 

  48. Wyckoff, J. B., Segall, J. E. & Condeelis, J. S. The collection of the motile population of cells from a living tumor. Cancer Res. 60, 5401–5404 (2000).

    Google Scholar 

  49. Gail, M. H. & Boone, C. W. Locomotion of mouse fibroblasts in tissue culture. Biophys. J. 10, 980–993 (1970).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the NCI Northwestern CCNE (NIH 1U54CA119341-01), the Pew Scholars Program in the Biomedical Sciences (to B.A.G.) and the Sloan Fellowship (to B.A.G.). G.M. was supported by a Gates Fellowship. C.J.C. was supported by a Northwestern University Presidential Fellowship. K.J.M.B. was supported by an NSF Graduate Research Fellowship. K.K.-G. was supported by a Fellowship from a Department of Defense Breast Cancer Research Program (W81XW4-05-1-0312).

Author information

Authors and Affiliations

  1. Department of Chemical and Biological Engineering and Department of Chemistry, Northwestern University, 2145 Sheridan Rd, Illinois 60208, USA

    Goher Mahmud, Christopher J. Campbell, Kyle J. M. Bishop, Yulia A. Komarova, Oleg Chaga, Siowling Soh, Sabil Huda, Kristiana Kandere-Grzybowska & Bartosz A. Grzybowski

Authors
  1. Goher Mahmud
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christopher J. Campbell
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kyle J. M. Bishop
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yulia A. Komarova
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Oleg Chaga
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Siowling Soh
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Sabil Huda
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Kristiana Kandere-Grzybowska
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Bartosz A. Grzybowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

G.M. C.J.C, Y.A.K. and K.K.-G. carried out most experiments and data analysis; Y.A.K., K.K.-G., O.C. and S.H. carried out high-resolution in-cell imaging; K.J.M.B. and S.S. developed the theoretical model; K.K.-G. and B.A.G. conceived the experiments and wrote the paper.

Corresponding authors

Correspondence to Kristiana Kandere-Grzybowska or Bartosz A. Grzybowski.

Supplementary information

Supplementary Information

Supplementary Information (PDF 721 kb)

Supplementary Information

Supplementary Movie 1 (MOV 226 kb)

Supplementary Information

Supplementary Movie 2 (MOV 573 kb)

Supplementary Information

Supplementary Movie 3 (MOV 409 kb)

Supplementary Information

Supplementary Movie 4 (MOV 347 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mahmud, G., Campbell, C., Bishop, K. et al. Directing cell motions on micropatterned ratchets. Nature Phys 5, 606–612 (2009). https://doi.org/10.1038/nphys1306

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys1306

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing