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Minimal model for spontaneous cell polarization and edge activity in oscillating, rotating and migrating cells

Nature Physics volume 12, pages 367–373 (2016)Cite this article

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Abstract

How cells break symmetry and organize activity at their edges to move directionally is a fundamental question in cell biology. Physical models of cell motility commonly incorporate gradients of regulatory proteins and/or feedback from the motion itself to describe the polarization of this edge activity. These approaches, however, fail to explain cell behaviour before the onset of polarization. We use polarizing and moving fish epidermal cells as a model system to bridge the gap between cell behaviours before and after polarization. Our analysis suggests a novel and simple principle of self-organizing cell activity, in which local cell-edge dynamics depends on the distance from the cell centre, but not on the orientation with respect to the front–back axis. We validate this principle with a stochastic model that faithfully reproduces a range of cell-migration behaviours. Our findings indicate that spontaneous polarization, persistent motion and cell shape are emergent properties of the local cell-edge dynamics controlled by the distance from the cell centre.

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Figure 1: Edge dynamics and distribution of switches between protrusion and retraction in migrating cells.
Figure 2: Protrusion–retraction switches depend on the distance from the cell centre, but not on the orientation.
Figure 3: Distribution of switches between protrusion and retraction and shape properties during polarization.
Figure 4: Effect of blebbistatin, hypo-osmotic treatment, and nocodazole on cell width and behaviour in body-blocking experiments.
Figure 5: Computer model simulations of cell-edge dynamics.

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Change history

  • 02 March 2016

    In the version of this Article originally published, in the Methods section 'Mapping protrusion–retraction switches', a minus sign was mistakenly omitted from a sentence, which should have read: 'Consequently, switches from protrusion PR(n) (retraction RP(n)) to retraction (protrusion) were determined as intersections of protruding (retracting) regions between frames n and n − 1 with the retracting (protruding) regions between frames n and n + 1 (Fig. 1c).' This has been corrected in all versions of the Article.

References

  1. Ridley, A. J. et al. Cell migration: integrating signals from front to back. Science 302, 1704–1709 (2003).

    Article  ADS  Google Scholar 

  2. Danuser, G., Allard, J. & Mogilner, A. Mathematical modeling of eukaryotic cell migration: insights beyond experiments. Annu. Rev. Cell Dev. Biol. 29, 501–528 (2013).

    Article  Google Scholar 

  3. Mogilner, A. & Keren, K. The shape of motile cells. Curr. Biol. 19, R762–R771 (2009).

    Article  Google Scholar 

  4. Wedlich-Soldner, R. & Li, R. Spontaneous cell polarization: undermining determinism. Nature Cell Biol. 5, 267–270 (2003).

    Article  Google Scholar 

  5. Devreotes, P. & Janetopoulos, C. Eukaryotic chemotaxis: distinctions between directional sensing and polarization. J. Biol. Chem. 278, 20445–20448 (2003).

    Article  Google Scholar 

  6. Verkhovsky, A. B., Svitkina, T. M. & Borisy, G. G. Self-polarization and directional motility of cytoplasm. Curr. Biol. 9, 11–20 (1999).

    Article  Google Scholar 

  7. Tkachenko, E. et al. Protein kinase A governs a RhoA-RhoGDI protrusion-retraction pacemaker in migrating cells. Nature Cell Biol. 13, 660–667 (2011).

    Article  Google Scholar 

  8. Burnette, D. T. et al. A role for actin arcs in the leading-edge advance of migrating cells. Nature Cell Biol. 13, 371–381 (2011).

    Article  Google Scholar 

  9. Ryan, G. L., Petroccia, H. M., Watanabe, N. & Vavylonis, D. Excitable actin dynamics in lamellipodial protrusion and retraction. Biophys. J. 102, 1493–1502 (2012).

    Article  ADS  Google Scholar 

  10. Giannone, G. et al. Lamellipodial actin mechanically links myosin activity with adhesion-site formation. Cell 128, 561–575 (2007).

    Article  Google Scholar 

  11. Ji, L., Lim, J. & Danuser, G. Fluctuations of intracellular forces during cell protrusion. Nature Cell Biol. 10, 1393–1400 (2008).

    Article  Google Scholar 

  12. Lakayo, C. I. et al. Emergence of large-scale cell morphology and movement from local actin filament growth dynamics. PLoS Biol. 5, e233 (2007).

    Article  Google Scholar 

  13. Lin, B. et al. Synthetic spatially graded Rac activation drives cell polarization and movement. Proc. Natl Acad. Sci. USA 109, E3668–E3677 (2012).

    Article  Google Scholar 

  14. Keren, K. et al. Mechanism of shape determination in motile cells. Nature 453, 475–480 (2008).

    Article  ADS  Google Scholar 

  15. Onsum, M. D. & Rao, C. V. Calling heads from tails: the role of mathematical modeling in understanding cell polarization. Curr. Opin. Cell Biol. 21, 74–81 (2009).

    Article  Google Scholar 

  16. Holmes, W. R. & Edelstein-Keshet, L. A comparison of computational models for eukaryotic cell shape and motility. PLoS Comput. Biol. 8, e1002793 (2012).

    Article  ADS  Google Scholar 

  17. Marée, A. F., Jilkine, A., Dawes, A., Grieneisen, V. A. & Edelstein-Keshet, L. Polarization and movement of keratocytes: a multiscale modelling approach. Bull. Math. Biol. 68, 1169–1211 (2006).

    Article  Google Scholar 

  18. Mori, Y., Jilkine, A. & Edelstein-Keshet, L. Wave-pinning and cell polarity from a bistable reaction-diffusion system. Biophys. J. 94, 3684–3697 (2008).

    Article  ADS  Google Scholar 

  19. Satulovsky, J., Lui, R. & Wang, Y. L. Exploring the control circuit of cell migration by mathematical modeling. Biophys. J. 94, 3671–3683 (2008).

    Article  ADS  Google Scholar 

  20. Doubrovinski, K. & Kruse, K. Cell motility resulting from spontaneous polymerization waves. Phys. Rev. Lett. 107, 258103 (2011).

    Article  ADS  Google Scholar 

  21. Nishimura, S. I., Ueda, M. & Sasai, M. Cortical factor feedback model for cellular locomotion and cytofission. PLoS Comput. Biol. 5, e1000310 (2009).

    Article  ADS  Google Scholar 

  22. Ziebert, F., Swaminathan, S. & Aranson, I. S. Model for self-polarization and motility of keratocyte fragments. J. R. Soc. Interface 9, 1084–1092 (2012).

    Article  Google Scholar 

  23. Du, X., Doubrovinski, K. & Osterfield, M. Self-organized cell motility from motor-filament interactions. Biophys. J. 102, 1738–1745 (2012).

    Article  ADS  Google Scholar 

  24. Maiuri, P. et al. Actin flows mediate a universal coupling between cell speed and cell persistence. Cell 161, 374–386 (2015).

    Article  Google Scholar 

  25. Barnhart, E., Kun-Chun, L., Allen, G. M., Theriot, J. A. & Mogilner, A. Balance between cell-substrate adhesion and myosin contraction determines the frequency of motility initiation in fish keratocytes. Proc. Natl Acad. Sci. USA 112, E5045–E5050 (2015).

    Article  ADS  Google Scholar 

  26. Lee, J., Ishihara, A., Theriot, J. A. & Jacobson, K. Principles of locomotion for simple-shaped cells. Nature 362, 167–171 (1993).

    Article  ADS  Google Scholar 

  27. Barnhart, E. L., Lee, K. C., Keren, K., Mogilner, A. & Theriot, J. A. An adhesion-dependent switch between mechanisms that determine motile cell shape. PLoS Biol. 9, e1001059 (2011).

    Article  Google Scholar 

  28. Wilson, C. A. et al. Myosin II contributes to cell-scale actin network treadmilling through network disassembly. Nature 465, 373–377 (2010).

    Article  ADS  Google Scholar 

  29. Grimm, H. P., Verkhovsky, A. B., Mogilner, A. & Meister, J.-J. Analysis of actin dynamics at the leading edge of crawling cells: implications for the shape of keratocyte lamellipodia. Eur. Biophys. J. 32, 563–577 (2003).

    Article  Google Scholar 

  30. Wolgemuth, C. W., Stajic, J. & Mogilner, A. Redundant mechanisms for stable cell locomotion revealed by minimal models. Biophys. J. 101, 545–553 (2011).

    Article  ADS  Google Scholar 

  31. Lou, S. S., Diz-Munoz, A., Weiner, O. D., Fletcher, D. A. & Theriot, J. A. Myosin light chain kinase regulates cell polarization independently of membrane tension or Rho kinase. J. Cell Biol. 209, 275–288 (2015).

    Article  Google Scholar 

  32. Ambühl, M. E., Brepsant, C., Meister, J.-J., Verkhovsky, A. B. & Sbalzarini, I. F. High-resolution cell outline segmentation and tracking from phase-contrast microscopy images. J. Microsc. 245, 161–170 (2012).

    Article  Google Scholar 

  33. Schaub, S., Bohnet, S., Laurent, V. M., Meister, J.-J. & Verkhovsky, A. B. Comparative maps of motion and assembly of filamentous actin and myosin II in migrating cells. Mol. Biol. Cell 18, 3723–3732 (2007).

    Article  Google Scholar 

  34. Gabella, C. et al. Contact angle at the leading edge controls cell protrusion rate. Curr. Biol. 24, 1126–1132 (2013).

    Article  Google Scholar 

  35. Martin, S. G. Microtubule-dependent cell morphogenesis in the fission yeast. Trends Cell Biol. 19, 447–454 (2009).

    Article  Google Scholar 

  36. Picone, R. et al. A polarised population of dynamic microtubules mediates homeostatic length control in animal cells. PLoS Biol. 8, e1000542 (2010).

    Article  Google Scholar 

  37. Fouchard, J. et al. Three-dimensional cell body shape dictates the onset of traction force generation and growth of focal adhesions. Proc. Natl Acad. Sci. USA 111, 13075–13080 (2014).

    Article  ADS  Google Scholar 

  38. Schweizer, J. et al. Geometry sensing by self-organized protein patterns. Proc. Natl Acad. Sci. USA 109, 15283–15288 (2012).

    Article  ADS  Google Scholar 

  39. Pollard, T. D. Regulation of actin filament assembly by Arp2/3 complex and formins. Annu. Rev. Biophys. Biomol. Struct. 36, 451–477 (2007).

    Article  Google Scholar 

  40. Wein, R. et al. CGAL User and Reference Manual 4.7 edn (CGAL Editorial Board, 2015).

    Google Scholar 

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Acknowledgements

We would like to thank F. Nédélec and M. Balland for useful discussions, S. Bohnet for the first observation of cell rotation, and H. Troyon for experimental assistance. This work is supported by Swiss National Science Foundation Grant 31003A-135661. M.E.A. was funded by a PhD fellowship from the Swiss National Competence Center for Biomedical Imaging, to A.B.V. and I.F.S.

Author information

Author notes

  1. Franck Raynaud, Mark E. Ambühl & Alexander B. Verkhovsky

    Present address: Present addresses: Computational Biology and Cancer Genomics, Department of Computational Biology, University of Lausanne, 1015 Lausanne, Switzerland (F.R.); SICHH, Swiss Integrative Center for Human Health, 1700 Fribourg, Switzerland (M.E.A.); Laboratory of Physics of Living Matter, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland (A.B.V.).,

Authors and Affiliations

  1. Laboratory of Cell Biophysics, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

    Franck Raynaud, Mark E. Ambühl, Chiara Gabella, Alicia Bornert, Jean-Jacques Meister & Alexander B. Verkhovsky

  2. MOSAIC Group, Chair of Scientific Computing for Systems Biology, Faculty of Computer Science, TU Dresden, D-01069 Dresden, Germany

    Ivo F. Sbalzarini

  3. MOSAIC Group, Center for Systems Biology Dresden, Max Planck Institute of Molecular Cell Biology and Genetics, D-01307 Dresden, Germany

    Ivo F. Sbalzarini

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Contributions

F.R. and A.B.V. designed the study. M.E.A., C.G., A.B. and A.B.V. performed the experiments. F.R. and M.E.A. analysed the data. F.R. developed the numerical model. F.R., I.F.S. and A.B.V. wrote the paper. All authors have discussed the results and the interpretation. F.R. and M.E.A. have contributed equally to the study.

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Correspondence to Franck Raynaud.

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The authors declare no competing financial interests.

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Raynaud, F., Ambühl, M., Gabella, C. et al. Minimal model for spontaneous cell polarization and edge activity in oscillating, rotating and migrating cells. Nature Phys 12, 367–373 (2016). https://doi.org/10.1038/nphys3615

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