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Mechanical plasticity of cells


Under mechanical loading, most living cells show a viscoelastic deformation that follows a power law in time1. After removal of the mechanical load, the cell shape recovers only incompletely to its original undeformed configuration. Here, we show that incomplete shape recovery is due to an additive plastic deformation that displays the same power-law dynamics as the fully reversible viscoelastic deformation response. Moreover, the plastic deformation is a constant fraction of the total cell deformation and originates from bond ruptures within the cytoskeleton. A simple extension of the prevailing viscoelastic power-law response theory with a plastic element correctly predicts the cell behaviour under cyclic loading. Our findings show that plastic energy dissipation during cell deformation is tightly linked to elastic cytoskeletal stresses, which suggests the existence of an adaptive mechanism that protects the cell against mechanical damage.

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Figure 1: Cell shape recovery after force application is incomplete.
Figure 2: Superposition of viscoelastic and plastic power-law responses.
Figure 3: Timescale invariance and force dependency.
Figure 4: Deformation map of the actin network.
Figure 5: Dependence of plasticity on actin fibre orientation and stability.


  1. Fabry, B. et al. Scaling the microrheology of living cells. Phys. Rev. Lett. 87, 148102 (2001).

    CAS  Article  Google Scholar 

  2. Wolf, K. et al. Physical limits of cell migration: control by ECM space and nuclear deformation and tuning by proteolysis and traction force. J. Cell Biol. 201, 1069–1084 (2013).

    CAS  Article  Google Scholar 

  3. Wang, N. et al. Cell prestress. I. Stiffness and prestress are closely associated in adherent contractile cells. Am. J. Physiol. Cell Physiol. 282, C606–C616 (2002).

    CAS  Article  Google Scholar 

  4. Kollmannsberger, P. & Fabry, B. Linear and nonlinear rheology of living cells. Annu. Rev. Mater. Res. 41, 75–97 (2011).

    CAS  Google Scholar 

  5. Bursac, P. et al. Cytoskeletal remodelling and slow dynamics in the living cell. Nature Mater. 4, 557–561 (2005).

    CAS  Article  Google Scholar 

  6. Trepat, X., Lenormand, G. & Fredberg, J. J. Universality in cell mechanics. Soft Matter 4, 1750–1759 (2008).

    CAS  Article  Google Scholar 

  7. Bouchaud, J. Weak ergodicity breaking and aging in disordered systems. J. Phys. I 2, 1705–1713 (1992).

    Google Scholar 

  8. Sollich, P., Lequeux, F., Hébraud, P. & Cates, M. E. Rheology of soft glassy materials. Phys. Rev. Lett. 78, 2020–2023 (1997).

    CAS  Article  Google Scholar 

  9. Mak, M. & Erickson, D. A serial micropipette microfluidic device with applications to cancer cell repeated deformation studies. Integr. Biol. 5, 1374–1384 (2013).

    CAS  Article  Google Scholar 

  10. Bausch, A. R., Ziemann, F., Boulbitch, A. A., Jacobson, K. & Sackmann, E. Local measurements of viscoelastic parameters of adherent cell surfaces by magnetic bead microrheometry. Biophys. J. 75, 2038–2049 (1998).

    CAS  Article  Google Scholar 

  11. Bausch, A. R., Moller, W. & Sackmann, E. Measurement of local viscoelasticity and forces in living cells by magnetic tweezers. Biophys. J. 76, 573–579 (1999).

    CAS  Article  Google Scholar 

  12. Butler, J. P. & Kelly, S. M. A model for cytoplasmic rheology consistent with magnetic twisting cytometry. Biorheology 35, 193–209 (1998).

    CAS  Article  Google Scholar 

  13. Tschumperlin, D. J. & Margulies, S. S. Equibiaxial deformation-induced injury of alveolar epithelial cells in vitro. Am. J. Physiol. 275, L1173–L1183 (1998).

    CAS  Google Scholar 

  14. Fredberg, J. J. Airway obstruction in asthma: does the response to a deep inspiration matter? Respir. Res. 2, 273–275 (2001).

    CAS  Article  Google Scholar 

  15. Summers, C. et al. Pulmonary retention of primed neutrophils: a novel protective host response, which is impaired in the acute respiratory distress syndrome. Thorax 69, 623–629 (2014).

    Article  Google Scholar 

  16. Trepat, X. et al. Universal physical responses to stretch in the living cell. Nature 447, 592–595 (2007).

    CAS  Article  Google Scholar 

  17. Smith, B. A., Tolloczko, B., Martin, J. G. & Grutter, P. Probing the viscoelastic behavior of cultured airway smooth muscle cells with atomic force microscopy: stiffening induced by contractile agonist. Biophys. J. 88, 2994–3007 (2005).

    CAS  Article  Google Scholar 

  18. Balland, M. et al. Power laws in microrheology experiments on living cells: comparative analysis and modeling. Phys. Rev. E 74, 021911 (2006).

    Article  Google Scholar 

  19. Maloney, J. M. et al. Mesenchymal stem cell mechanics from the attached to the suspended state. Biophys. J. 99, 2479–2487 (2010).

    CAS  Article  Google Scholar 

  20. Fabry, B. et al. Time course and heterogeneity of contractile responses in cultured human airway smooth muscle cells. J. Appl. Physiol. 91, 986–994 (2001).

    CAS  Article  Google Scholar 

  21. Hildebrandt, J. Comparison of mathematical models for cat lung and viscoelastic balloon derived by Laplace transform methods from pressure-volume data. Bull. Math. Biophys. 31, 651–667 (1969).

    CAS  Article  Google Scholar 

  22. Bausch, A. R., Hellerer, U., Essler, M., Aepfelbacher, M. & Sackmann, E. Rapid stiffening of integrin receptor-actin linkages in endothelial cells stimulated with thrombin: a magnetic bead microrheology study. Biophys. J. 80, 2649–2657 (2001).

    CAS  Article  Google Scholar 

  23. Fernandez, P. & Ott, A. Single cell mechanics: stress stiffening and kinematic hardening. Phys. Rev. Lett. 100, 238102 (2008).

    Article  Google Scholar 

  24. Desprat, N., Richert, A., Simeon, J. & Asnacios, A. Creep function of a single living cell. Biophys. J. 88, 2224–2233 (2005).

    CAS  Article  Google Scholar 

  25. Hu, S. et al. Intracellular stress tomography reveals stress focusing and structural anisotropy in cytoskeleton of living cells. Am. J. Physiol. Cell Physiol. 285, C1082–C1090 (2003).

    CAS  Article  Google Scholar 

  26. Munster, S. et al. Strain history dependence of the nonlinear stress response of fibrin and collagen networks. Proc. Natl Acad. Sci. USA 110, 12197–12202 (2013).

    CAS  Article  Google Scholar 

  27. Pelham, R. J. Jr & Wang, Y. Cell locomotion and focal adhesions are regulated by substrate flexibility. Proc. Natl Acad. Sci. USA 94, 13661–13665 (1997).

    CAS  Article  Google Scholar 

  28. del Alamo, J. C., Norwich, G. N., Li, Y. S., Lasheras, J. C. & Chien, S. Anisotropic rheology and directional mechanotransduction in vascular endothelial cells. Proc. Natl Acad. Sci. USA 105, 15411–15416 (2008).

    CAS  Article  Google Scholar 

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This work was funded by the Deutsche Forschungsgemeinschaft (DFG) and the European Research Council Starting Grant MINATRAN 211166. We thank A. Mainka for help with cell culture and K. Kroy and M. Gralka for valuable discussions.

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Authors and Affiliations



N.B., M.K., M.S. and A.L. performed experiments, N.B. and W.S. designed the rotation stage, N.B., K.E.A. and B.F. developed the model, N.B., R.G. and B.F. analysed the data, and N.B., R.G., K.E.A. and B.F. wrote the manuscript.

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Correspondence to Navid Bonakdar.

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The authors declare no competing financial interests.

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Bonakdar, N., Gerum, R., Kuhn, M. et al. Mechanical plasticity of cells. Nature Mater 15, 1090–1094 (2016).

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