Measuring mechanical stress in living tissues

Abstract

Living tissues are active, multifunctional materials capable of generating, sensing, withstanding and responding to mechanical stress. These capabilities enable tissues to adopt complex shapes during development, to sustain those shapes during homeostasis and to restore them during healing and regeneration. Abnormal stress is associated with a broad range of pathological conditions, including developmental defects, inflammatory diseases, tumour growth and metastasis. A number of techniques are available to measure mechanical stress in living tissues at cellular and subcellular resolution. 2D techniques that map stress in cultured cell monolayers provide the highest resolution and accessibility, and include 2D traction force microscopy, micropillar arrays, monolayer stress microscopy and monolayer stretching between flexible cantilevers. Mapping stresses in tissues cultured in 3D can be achieved using 3D traction force microscopy and the microbulge test. Techniques for measuring stress in vivo include servo-null methods for measuring luminal pressure, deformable inclusions, Förster resonance energy transfer tension sensors, laser ablation and computational methods for force inference. Although these techniques are far from becoming everyday tools in biomedical laboratories, their rapid development is fostering key advances in our understanding of the role of mechanics in morphogenesis, homeostasis and disease.

Key points

  • Mechanical stresses generated by cells determine the fate, form and function of living tissues.

  • Several techniques have been developed to measure tissue stress at subcellular resolution.

  • State-of-the-art technologies now enable high-resolution mapping of time-varying stress fields in 2D and 3D cell cultures.

  • Measuring stresses in vivo remains an outstanding challenge that is currently addressed through the combination of image-based computational modelling and the insertion of soft inclusions in tissues of interest.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Techniques for measuring tractions and internal stresses in 2D tissues in vitro.
Fig. 2: Techniques for measuring tractions and internal stresses in 3D tissues in vitro.
Fig. 3: Techniques for measuring internal stresses in vivo.

References

  1. 1.

    Guillot, C. & Lecuit, T. Mechanics of epithelial tissue homeostasis and morphogenesis. Science 340, 1185–1189 (2013).

    ADS  Article  Google Scholar 

  2. 2.

    Barker, N. Adult intestinal stem cells: critical drivers of epithelial homeostasis and regeneration. Nat. Rev. Mol. Cell Biol. 15, 19–33 (2014).

    Article  Google Scholar 

  3. 3.

    Krndija, D. et al. Active cell migration is critical for steady-state epithelial turnover in the gut. Science 365, 705–710 (2019).

    ADS  Article  Google Scholar 

  4. 4.

    Brugués, A. et al. Forces driving epithelial wound healing. Nat. Phys. 10, 683–690 (2014).

    Article  Google Scholar 

  5. 5.

    Northey, J. J., Przybyla, L. & Weaver, V. M. Tissue force programs cell fate and tumor aggression. Cancer Discov. 7, 1224–1237 (2017).

    Article  Google Scholar 

  6. 6.

    Nia, H. T. et al. Solid stress and elastic energy as measures of tumour mechanopathology. Nat. Biomed. Eng. 1, 0004 (2016).

    Article  Google Scholar 

  7. 7.

    Hannezo, E. & Heisenberg, C.-P. Mechanochemical feedback loops in development and disease. Cell 178, 12–25 (2019).

    Article  Google Scholar 

  8. 8.

    Gudipaty, S. A. et al. Mechanical stretch triggers rapid epithelial cell division through Piezo1. Nature 543, 118–121 (2017).

    ADS  Article  Google Scholar 

  9. 9.

    Benham-Pyle, B. W., Sim, J. Y., Hart, K. C., Pruitt, B. L. & Nelson, W. J. Increasing β-catenin/Wnt3A activity levels drive mechanical strain-induced cell cycle progression through mitosis. eLife 5, e19799 (2016).

    Article  Google Scholar 

  10. 10.

    Uroz, M. et al. Regulation of cell cycle progression by cell–cell and cell–matrix forces. Nat. Cell Biol. 20, 646–654 (2018).

    Article  Google Scholar 

  11. 11.

    Crick, F. H. C. & Hughes, A. F. W. The physical properties of cytoplasm. Exp. Cell Res. 1, 37–80 (1950).

    Article  Google Scholar 

  12. 12.

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

    Article  Google Scholar 

  13. 13.

    Ashkin, A. Acceleration and trapping of particles by radiation pressure. Phys. Rev. Lett. 24, 156–159 (1970).

    ADS  Article  Google Scholar 

  14. 14.

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

    ADS  Article  Google Scholar 

  15. 15.

    Wu, J. Acoustical tweezers. J. Acoust. Soc. Am. 89, 2140–2143 (1991).

    ADS  Article  Google Scholar 

  16. 16.

    Binnig, G., Quate, C. F. & Gerber, C. Atomic force microscope. Phys. Rev. Lett. 56, 930–933 (1986).

    ADS  Article  Google Scholar 

  17. 17.

    Mitchison, J. M. & Swann, M. M. The mechanical properties of the cell surface: I. The cell elastimeter. J. Exp. Biol. 31, 443–460 (1954).

    Google Scholar 

  18. 18.

    Zamir, E. A., Srinivasan, V., Perucchio, R. & Taber, L. A. Mechanical asymmetry in the embryonic chick heart during looping. Ann. Biomed. Eng. 31, 1327–1336 (2003).

    Article  Google Scholar 

  19. 19.

    Foty, R. A., Forgacs, G., Pfleger, C. M. & Steinberg, M. S. Liquid properties of embryonic tissues: measurement of interfacial tensions. Phys. Rev. Lett. 72, 2298–2301 (1994).

    ADS  Article  Google Scholar 

  20. 20.

    Brillouin, L. Diffusion de la lumière et des rayons X par un corps transparent homogène. Ann. Phys. (Paris) 9, 88–122 (1922).

    ADS  Google Scholar 

  21. 21.

    Scarcelli, G. & Yun, S. H. Confocal Brillouin microscopy for three-dimensional mechanical imaging. Nat. Photonics 2, 39–43 (2008).

    ADS  Article  Google Scholar 

  22. 22.

    Moore, A. R. & Burt, A. S. On the locus and nature of the forces causing gastrulation in the embryos of Dendraster excentricus. J. Exp. Zool. 82, 159–171 (1939).

    Article  Google Scholar 

  23. 23.

    Rehfeldt, F. & Schmidt, C. F. Physical probing of cells. J. Phys. D. Appl. Phys. 50, 463001 (2017).

    ADS  Article  Google Scholar 

  24. 24.

    Basoli, F. et al. Biomechanical characterization at the cell scale: present and prospects. Front. Physiol. 9, 1449 (2018).

    Article  Google Scholar 

  25. 25.

    Zhang, H. & Liu, K.-K. Optical tweezers for single cells. J. R. Soc. Interface 5, 671–690 (2008).

    Article  Google Scholar 

  26. 26.

    Favre-Bulle, I. A., Stilgoe, A. B., Scott, E. K. & Rubinsztein-Dunlop, H. Optical trapping in vivo: theory, practice, and applications. Nanophotonics 8, 1023–1040 (2019).

    Article  Google Scholar 

  27. 27.

    Ozcelik, A. et al. Acoustic tweezers for the life sciences. Nat. Methods 15, 1021–1028 (2018).

    Article  Google Scholar 

  28. 28.

    Krieg, M. et al. Atomic force microscopy-based mechanobiology. Nat. Rev. Phys. 1, 41–57 (2019).

    Article  Google Scholar 

  29. 29.

    Hochmuth, R. M. Micropipette aspiration of living cells. J. Biomech. 33, 15–22 (2000).

    Article  Google Scholar 

  30. 30.

    González-Bermúdez, B., Guinea, G. V. & Plaza, G. R. Advances in micropipette aspiration: applications in cell biomechanics, models, and extended studies. Biophys. J. 116, 587–594 (2019).

    ADS  Article  Google Scholar 

  31. 31.

    Campàs, O. A toolbox to explore the mechanics of living embryonic tissues. Semin. Cell Dev. Biol. 55, 119–130 (2016).

    Article  Google Scholar 

  32. 32.

    Sugimura, K., Lenne, P.-F. & Graner, F. Measuring forces and stresses in situ in living tissues. Development 143, 186–196 (2016).

    Article  Google Scholar 

  33. 33.

    Roca-Cusachs, P., Conte, V. & Trepat, X. Quantifying forces in cell biology. Nat. Cell Biol. 19, 742–751 (2017).

    Article  Google Scholar 

  34. 34.

    Prevedel, R., Diz-Muñoz, A., Ruocco, G. & Antonacci, G. Brillouin microscopy: an emerging tool for mechanobiology. Nat. Methods 16, 969–977 (2019).

    Article  Google Scholar 

  35. 35.

    Pérez-González, C. et al. Active wetting of epithelial tissues. Nat. Phys. 15, 79–88 (2019).

    Article  Google Scholar 

  36. 36.

    Bergert, M. et al. Confocal reference free traction force microscopy. Nat. Commun. 7, 12814 (2016).

    ADS  Article  Google Scholar 

  37. 37.

    Latorre, E. et al. Active superelasticity in three-dimensional epithelia of controlled shape. Nature 563, 203–208 (2018). This paper reports the first use of the microbulge test to measure the internal stress of a curved epithelium.

    ADS  Article  Google Scholar 

  38. 38.

    Ban, E. et al. Mechanisms of plastic deformation in collagen networks induced by cellular forces. Biophys. J. 114, 450–461 (2018).

    ADS  Article  Google Scholar 

  39. 39.

    Girardo, S. et al. Standardized microgel beads as elastic cell mechanical probes. J. Mater. Chem. B 6, 6245–6261 (2018).

    Article  Google Scholar 

  40. 40.

    Saw, T. B. et al. Topological defects in epithelia govern cell death and extrusion. Nature 544, 212–216 (2017).

    ADS  Article  Google Scholar 

  41. 41.

    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). Description of the general concept underlying MSM, applied here to the inference of internal stress in a single cell.

    Article  Google Scholar 

  42. 42.

    Harris, A. K., Wild, P. & Stopak, D. Silicone rubber substrata: a new wrinkle in the study of cell locomotion. Science 208, 177–179 (1980). First qualitative implementation of TFM, based on the observation that cells are able to wrinkle thin polymer substrates.

    ADS  Article  Google Scholar 

  43. 43.

    Lee, J., Leonard, M., Oliver, T., Ishihara, A. & Jacobson, K. Traction forces generated by locomoting keratocytes. J. Cell Biol. 127, 1957–1964 (1994).

    Article  Google Scholar 

  44. 44.

    Oliver, T., Dembo, M. & Jacobson, K. Traction forces in locomoting cells. Cell Motil. Cytoskeleton 31, 225–240 (1995).

    Article  Google Scholar 

  45. 45.

    Dembo, M., Oliver, T., Ishihara, A. & Jacobson, K. Imaging the traction stresses exerted by locomoting cells with the elastic substratum method. Biophys. J. 70, 2008–2022 (1996).

    ADS  Article  Google Scholar 

  46. 46.

    Dembo, M. & Wang, Y.-L. Stresses at the cell-to-substrate interface during locomotion of fibroblasts. Biophys. J. 76, 2307–2316 (1999). This study reports the first quantitative implementation of 2D TFM.

    ADS  Article  Google Scholar 

  47. 47.

    Schwarz, U. S. & Soiné, J. R. D. Traction force microscopy on soft elastic substrates: A guide to recent computational advances. Biochim. Biophys. Acta 1853, 3095–3104 (2015).

    Article  Google Scholar 

  48. 48.

    Style, R. W. et al. Traction force microscopy in physics and biology. Soft Matter 10, 4047–4055 (2014).

    ADS  Article  Google Scholar 

  49. 49.

    Polio, S. R., Rothenberg, K. E., StamenoviĆ, D. & Smith, M. L. A micropatterning and image processing approach to simplify measurement of cellular traction forces. Acta Biomater. 8, 82–88 (2012).

    Article  Google Scholar 

  50. 50.

    Butler, J. P., ToliĆ-Nørrelykke, I. M., Fabry, B. & Fredberg, J. J. Traction fields, moments, and strain energy that cells exert on their surroundings. Am. J. Physiol. Cell Physiol. 282, C595–C605 (2002). This paper formulates Fourier 2D TFM, resulting in the speeding up of traction calculations by orders of magnitude.

    Article  Google Scholar 

  51. 51.

    del Álamo, J. C. et al. Spatio-temporal analysis of eukaryotic cell motility by improved force cytometry. Proc. Natl Acad. Sci. USA 104, 13343–13348 (2007).

    ADS  Article  Google Scholar 

  52. 52.

    Schwarz, U. S. et al. Calculation of forces at focal adhesions from elastic substrate data: the effect of localized force and the need for regularization. Biophys. J. 83, 1380–1394 (2002).

    ADS  Article  Google Scholar 

  53. 53.

    Sabass, B., Gardel, M. L., Waterman, C. M. & Schwarz, U. S. High resolution traction force microscopy based on experimental and computational advances. Biophys. J. 94, 207–220 (2008).

    Article  Google Scholar 

  54. 54.

    Huang, Y. et al. Traction force microscopy with optimized regularization and automated Bayesian parameter selection for comparing cells. Sci. Rep. 9, 539 (2019).

    ADS  Article  Google Scholar 

  55. 55.

    Yang, Z., Lin, J.-S., Chen, J. & Wang, J. H.-C. Determining substrate displacement and cell traction fields — a new approach. J. Theor. Biol. 242, 607–616 (2006).

    MathSciNet  Article  Google Scholar 

  56. 56.

    Griffin, B. P., Largaespada, C. J., Rinaldi, N. A. & Lemmon, C. A. A novel method for quantifying traction forces on hexagonal micropatterned protein features on deformable poly-dimethyl siloxane sheets. MethodsX 6, 1343–1352 (2019).

    Article  Google Scholar 

  57. 57.

    Burton, K. & Taylor, D. L. Traction forces of cytokinesis measured with optically modified elastic substrata. Nature 385, 450–454 (1997).

    ADS  Article  Google Scholar 

  58. 58.

    Elosegui-Artola, A. et al. Mechanical regulation of a molecular clutch defines force transmission and transduction in response to matrix rigidity. Nat. Cell Biol. 18, 540–548 (2016).

    Article  Google Scholar 

  59. 59.

    Balaban, N. Q. et al. Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates. Nat. Cell Biol. 3, 466–472 (2001).

    Article  Google Scholar 

  60. 60.

    Trepat, X. et al. Physical forces during collective cell migration. Nat. Phys. 5, 426–430 (2009).

    Article  Google Scholar 

  61. 61.

    Serra-Picamal, X. et al. Mechanical waves during tissue expansion. Nat. Phys. 8, 628–634 (2012).

    Article  Google Scholar 

  62. 62.

    Sunyer, R. et al. Collective cell durotaxis emerges from long-range intercellular force transmission. Science 353, 1157–1161 (2016).

    ADS  Article  Google Scholar 

  63. 63.

    Kim, J. H. et al. Propulsion and navigation within the advancing monolayer sheet. Nat. Mater. 12, 856–863 (2013).

    ADS  Article  Google Scholar 

  64. 64.

    Park, J.-A. et al. Unjamming and cell shape in the asthmatic airway epithelium. Nat. Mater. 14, 1040–1048 (2015).

    ADS  Article  Google Scholar 

  65. 65.

    Uroz, M. et al. Traction forces at the cytokinetic ring regulate cell division and polyploidy in the migrating zebrafish epicardium. Nat. Mater. 18, 1015–1023 (2019).

    ADS  Article  Google Scholar 

  66. 66.

    Jerison, E. R., Xu, Y., Wilen, L. A. & Dufresne, E. R. Deformation of an elastic substrate by a three-phase contact line. Phys. Rev. Lett. 106, 186103 (2011).

    ADS  Article  Google Scholar 

  67. 67.

    Xu, Y. et al. Imaging in-plane and normal stresses near an interface crack using traction force microscopy. Proc. Natl Acad. Sci. USA 107, 14964–14967 (2010).

    ADS  Article  Google Scholar 

  68. 68.

    Casares, L. et al. Hydraulic fracture during epithelial stretching. Nat. Mater. 14, 343–351 (2015).

    ADS  Article  Google Scholar 

  69. 69.

    Oria, R. et al. Force loading explains spatial sensing of ligands by cells. Nature 552, 219–224 (2017).

    ADS  Article  Google Scholar 

  70. 70.

    Nguyen, D. T. et al. Surface pressure and shear stress fields within a frictional contact on rubber. J. Adhes. 87, 235–250 (2011).

    Article  Google Scholar 

  71. 71.

    Chateauminois, A. & Fretigny, C. Local friction at a sliding interface between an elastomer and a rigid spherical probe. Eur. Phys. J. E Soft Matter 27, 221–227 (2008).

    Article  Google Scholar 

  72. 72.

    del Álamo, J. C. et al. Three-dimensional quantification of cellular traction forces and mechanosensing of thin substrata by Fourier traction force microscopy. PLoS ONE 8, e69850 (2013). This paper formulates Fourier 2.5D TFM.

    ADS  Article  Google Scholar 

  73. 73.

    Álvarez-González, B. et al. Cytoskeletal mechanics regulating amoeboid cell locomotion. Appl. Mech. Rev. 66, 050804 (2014).

    ADS  Article  Google Scholar 

  74. 74.

    Tan, J. L. et al. Cells lying on a bed of microneedles: an approach to isolate mechanical force. Proc. Natl Acad. Sci. USA 100, 1484–1489 (2003). This paper pioneered the use of micropillar arrays for force quantification.

    ADS  Article  Google Scholar 

  75. 75.

    Saez, A., Ghibaudo, M., Buguin, A., Silberzan, P. & Ladoux, B. Rigidity-driven growth and migration of epithelial cells on microstructured anisotropic substrates. Proc. Natl Acad. Sci. USA 104, 8281–8286 (2007).

    ADS  Article  Google Scholar 

  76. 76.

    Legant, W. R. et al. Microfabricated tissue gauges to measure and manipulate forces from 3D microtissues. Proc. Natl Acad. Sci. USA 106, 10097–10102 (2009).

    ADS  Article  Google Scholar 

  77. 77.

    Boudou, T. et al. A microfabricated platform to measure and manipulate the mechanics of engineered cardiac microtissues. Tissue Eng. Part A 18, 910–919 (2012).

    Article  Google Scholar 

  78. 78.

    du Roure, O. et al. Force mapping in epithelial cell migration. Proc. Natl Acad. Sci. USA 102, 2390–2395 (2005).

    ADS  Article  Google Scholar 

  79. 79.

    Rabodzey, A., Alcaide, P., Luscinskas, F. W. & Ladoux, B. Mechanical forces induced by the transendothelial migration of human neutrophils. Biophys. J. 95, 1428–1438 (2008).

    Article  Google Scholar 

  80. 80.

    Reffay, M. et al. Interplay of RhoA and mechanical forces in collective cell migration driven by leader cells. Nat. Cell Biol. 16, 217–223 (2014).

    Article  Google Scholar 

  81. 81.

    Saez, A. et al. Traction forces exerted by epithelial cell sheets. J. Phys. Condens. Matter 22, 194119 (2010).

    ADS  Article  Google Scholar 

  82. 82.

    Yang, B. et al. Stopping transformed cancer cell growth by rigidity sensing. Nat. Mater. 19, 239–250 (2020).

    ADS  Article  Google Scholar 

  83. 83.

    Schoen, I., Hu, W., Klotzsch, E. & Vogel, V. Probing cellular traction forces by micropillar arrays: contribution of substrate warping to pillar deflection. Nano Lett. 10, 1823–1830 (2010).

    ADS  Article  Google Scholar 

  84. 84.

    Liu, Z. et al. Mechanical tugging force regulates the size of cell–cell junctions. Proc. Natl Acad. Sci. USA 107, 9944–9949 (2010).

    ADS  Article  Google Scholar 

  85. 85.

    Bastounis, E., Álvarez-González, B., del Álamo, J. C., Lasheras, J. C. & Firtel, R. A. Cooperative cell motility during tandem locomotion of amoeboid cells. Mol. Biol. Cell 27, 1262–1271 (2016).

    Article  Google Scholar 

  86. 86.

    Maruthamuthu, V., Sabass, B., Schwarz, U. S. & Gardel, M. L. Cell–ECM traction force modulates endogenous tension at cell–cell contacts. Proc. Natl Acad. Sci. USA 108, 4708–4713 (2011).

    ADS  Article  Google Scholar 

  87. 87.

    Ng, M. R., Besser, A., Brugge, J. S. & Danuser, G. Mapping the dynamics of force transduction at cell–cell junctions of epithelial clusters. eLife 3, e03282 (2014).

    Article  Google Scholar 

  88. 88.

    Tambe, D. T. et al. Monolayer stress microscopy: limitations, artifacts, and accuracy of recovered intercellular stresses. PLoS ONE 8, e55172 (2013).

    ADS  Article  Google Scholar 

  89. 89.

    Tambe, D. T. et al. Collective cell guidance by cooperative intercellular forces. Nat. Mater. 10, 469–475 (2011). This paper marks the rigorous mathematical formulation of MSM to compute all components of the stress tensor in a cell monolayer.

    ADS  Article  Google Scholar 

  90. 90.

    Moussus, M. et al. Intracellular stresses in patterned cell assemblies. Soft Matter 10, 2414–2423 (2014).

    ADS  Article  Google Scholar 

  91. 91.

    Nier, V. et al. Inference of internal stress in a cell monolayer. Biophys. J. 110, 1625–1635 (2016).

    ADS  Article  Google Scholar 

  92. 92.

    Serrano, R. et al. Three-dimensional monolayer stress microscopy. Biophys. J. 117, 111–128 (2019).

    ADS  Article  Google Scholar 

  93. 93.

    Timoshenko, S. & Woinowsky-Krieger, S. Theory of Plates and Shells 2nd edn (McGraw-Hill, 1959).

  94. 94.

    Vishwakarma, M. et al. Mechanical interactions among followers determine the emergence of leaders in migrating epithelial cell collectives. Nat. Commun. 9, 3469 (2018).

    ADS  Article  Google Scholar 

  95. 95.

    Harris, A. R. et al. Characterizing the mechanics of cultured cell monolayers. Proc. Natl Acad. Sci. USA 109, 16449–16454 (2012). This paper shows the first implementation of the suspended-monolayer technique.

    ADS  Article  Google Scholar 

  96. 96.

    Khalilgharibi, N. et al. Stress relaxation in epithelial monolayers is controlled by the actomyosin cortex. Nat. Phys. 15, 839–847 (2019).

    Article  Google Scholar 

  97. 97.

    Harris, A. R. et al. Generating suspended cell monolayers for mechanobiological studies. Nat. Protoc. 8, 2516–2530 (2013).

    Article  Google Scholar 

  98. 98.

    Merzouki, A., Malaspinas, O. & Chopard, B. The mechanical properties of a cell-based numerical model of epithelium. Soft Matter 12, 4745–4754 (2016).

    ADS  Article  Google Scholar 

  99. 99.

    Wyatt, T. P. J. et al. Emergence of homeostatic epithelial packing and stress dissipation through divisions oriented along the long cell axis. Proc. Natl Acad. Sci. USA 112, 5726–5731 (2015).

    ADS  Article  Google Scholar 

  100. 100.

    Xu, G.-K., Liu, Y. & Zheng, Z. Oriented cell division affects the global stress and cell packing geometry of a monolayer under stretch. J. Biomech. 49, 401–407 (2016).

    Article  Google Scholar 

  101. 101.

    Wyatt, T. P. J. et al. Actomyosin controls planarity and folding of epithelia in response to compression. Nat. Mater. 19, 109–117 (2020).

    Article  ADS  Google Scholar 

  102. 102.

    Fouchard, J. et al. Curling of epithelial monolayers reveals coupling between active bending and tissue tension. Proc. Natl Acad. Sci. USA 117, 9377–9383 (2020).

    Article  Google Scholar 

  103. 103.

    Bloom, R. J., George, J. P., Celedon, A., Sun, S. X. & Wirtz, D. Mapping local matrix remodeling induced by a migrating tumor cell using three-dimensional multiple-particle tracking. Biophys. J. 95, 4077–4088 (2008).

    ADS  Article  Google Scholar 

  104. 104.

    Hur, S. S., Zhao, Y., Li, Y.-S., Botvinick, E. & Chien, S. Live cells exert 3-dimensional traction forces on their substrata. Cell Mol. Bioeng. 2, 425–436 (2009).

    Article  Google Scholar 

  105. 105.

    Álvarez-González, B. et al. Three-dimensional balance of cortical tension and axial contractility enables fast amoeboid migration. Biophys. J. 108, 821–832 (2015).

    ADS  Article  Google Scholar 

  106. 106.

    Maskarinec, S. A., Franck, C., Tirrell, D. A. & Ravichandran, G. Quantifying cellular traction forces in three dimensions. Proc. Natl Acad. Sci. USA 106, 22108–22113 (2009).

    ADS  Article  Google Scholar 

  107. 107.

    Toyjanova, J. et al. High resolution, large deformation 3D traction force microscopy. PLoS ONE 9, e90976 (2014).

    ADS  Article  Google Scholar 

  108. 108.

    Delanoë-Ayari, H., Rieu, J. P. & Sano, M. 4D traction force microscopy reveals asymmetric cortical forces in migrating Dictyostelium cells. Phys. Rev. Lett. 105, 248103 (2010).

    ADS  Article  Google Scholar 

  109. 109.

    Aung, A. et al. 3D traction stresses activate protease-dependent invasion of cancer cells. Biophys. J. 107, 2528–2537 (2014).

    ADS  Article  Google Scholar 

  110. 110.

    Yeh, Y.-T. et al. Three-dimensional forces exerted by leukocytes and vascular endothelial cells dynamically facilitate diapedesis. Proc. Natl Acad. Sci. USA 115, 133–138 (2018).

    Article  Google Scholar 

  111. 111.

    Álvarez-González, B. et al. Two-layer elastographic 3-D traction force microscopy. Sci. Rep. 7, 39315 (2017).

    ADS  Article  Google Scholar 

  112. 112.

    Gordon, V. D. et al. Measuring the mechanical stress induced by an expanding multicellular tumor system: a case study. Exp. Cell Res. 289, 58–66 (2003). This paper reports a pioneering implementation of 3D TFM.

    Article  Google Scholar 

  113. 113.

    Zhou, J., Pal, S., Maiti, S. & Davidson, L. A. Force production and mechanical accommodation during convergent extension. Development 142, 692–701 (2015).

    Article  Google Scholar 

  114. 114.

    Legant, W. R. et al. Measurement of mechanical tractions exerted by cells in three-dimensional matrices. Nat. Methods 7, 969–971 (2010).

    Article  Google Scholar 

  115. 115.

    Steinwachs, J. et al. Three-dimensional force microscopy of cells in biopolymer networks. Nat. Methods 13, 171–176 (2016).

    Article  Google Scholar 

  116. 116.

    Mark, C. et al. Collective forces of tumor spheroids in three-dimensional biopolymer networks. eLife 9, e51912 (2020).

    Article  Google Scholar 

  117. 117.

    Alessandri, K. et al. Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro. Proc. Natl Acad. Sci. USA 110, 14843–14848 (2013).

    ADS  Article  Google Scholar 

  118. 118.

    Leonavicius, K. et al. Mechanics of mouse blastocyst hatching revealed by a hydrogel-based microdeformation assay. Proc. Natl Acad. Sci. USA 115, 10375–10380 (2018).

    Article  Google Scholar 

  119. 119.

    Leighton, J., Brada, Z., Estes, L. W. & Justh, G. Secretory activity and oncogenicity of a cell line (MDCK) derived from canine kidney. Science 163, 472–473 (1969).

    ADS  Article  Google Scholar 

  120. 120.

    Rabito, C. A., Tchao, R., Valentich, J. & Leighton, J. Effect of cell–substratum interaction on hemicyst formation by MDCK cells. In Vitro 16, 461–468 (1980).

    Article  Google Scholar 

  121. 121.

    Tanner, C., Frambach, D. A. & Misfeldt, D. S. Transepithelial transport in cell culture. A theoretical and experimental analysis of the biophysical properties of domes. Biophys. J. 43, 183–190 (1983). This paper reports the first application of a servo-null device to an in vitro-grown tissue.

    Article  Google Scholar 

  122. 122.

    de Laplace, P.- S. Supplément au dixième livre du Traité de Mécanique Céleste: Sur L’Action Capillaire Vol. 4 (Chez J. B. M. Duprat, 1805).

  123. 123.

    Lamb, H. Statics: Including Hydrostatics and the Elements of the Theory of Elasticity 3rd edn (Cambridge Univ. Press, 1960).

  124. 124.

    Hildebrand, S. et al. The E-cadherin/AmotL2 complex organizes actin filaments required for epithelial hexagonal packing and blastocyst hatching. Sci. Rep. 7, 9540 (2017).

    ADS  Article  Google Scholar 

  125. 125.

    Deglincerti, A. et al. Self-organization of the in vitro attached human embryo. Nature 533, 251–254 (2016).

    ADS  Article  Google Scholar 

  126. 126.

    Navis, A. & Bagnat, M. Developing pressures: fluid forces driving morphogenesis. Curr. Opin. Genet. Dev. 32, 24–30 (2015).

    Article  Google Scholar 

  127. 127.

    Hales, S. Statical Essays, Containing Haemastaticks, or, An Account of Some Hydraulick and Hydrostatical Experiments Made on the Blood and Blood Vessels of Animals (W. Innys and R. Manby, 1733).

  128. 128.

    Wiederhielm, C. A., Woodbury, J. W., Kirk, S. & Rushmer, R. F. Pulsatile pressures in the microcirculation of frog’s mesentery. Am. J. Physiol. 207, 173–176 (1964). Implementation of servo-null systems and their application to measure pulsatile pressure in a capillary.

    Article  Google Scholar 

  129. 129.

    Petrie, R. J. & Koo, H. Direct measurement of intracellular pressure. Curr. Protoc. Cell Biol. 63, 12.9.1–12.9.9 (2014).

    Article  Google Scholar 

  130. 130.

    Falchuk, K. H. & Berliner, R. W. Hydrostatic pressures in peritubular capillaries and tubules in the rat kidney. Am. J. Physiol. 220, 1422–1426 (1971).

    Article  Google Scholar 

  131. 131.

    Kelly, S. M. & Macklem, P. T. Direct measurement of intracellular pressure. Am. J. Physiol. 260, C652–C657 (1991).

    Article  Google Scholar 

  132. 132.

    Petrie, R. J., Koo, H. & Yamada, K. M. Generation of compartmentalized pressure by a nuclear piston governs cell motility in a 3D matrix. Science 345, 1062–1065 (2014).

    ADS  Article  Google Scholar 

  133. 133.

    Myers, R. R., Rydevik, B. L., Heckman, H. M. & Powell, H. C. Proximodistal gradient in endoneurial fluid pressure. Exp. Neurol. 102, 368–370 (1988).

    Article  Google Scholar 

  134. 134.

    Wit, H. P., Thalen, E. O. & Albers, F. W. J. Dynamics of inner ear pressure release, measured with a double-barreled micropipette in the guinea pig. Hearing Res. 132, 131–139 (1999).

    Article  Google Scholar 

  135. 135.

    Avila, M. Y., Carré, D. A., Stone, R. A. & Civan, M. M. Reliable measurement of mouse intraocular pressure by a servo-null micropipette system. Investig. Ophthalmol. Vis. Sci. 42, 1841–1846 (2001).

    Google Scholar 

  136. 136.

    Hu, N., Yost, H. J. & Clark, E. B. Cardiac morphology and blood pressure in the adult zebrafish. Anat. Rec. 264, 1–12 (2001).

    Article  Google Scholar 

  137. 137.

    Hu, N., Sedmera, D., Yost, H. J. & Clark, E. B. Structure and function of the developing zebrafish heart. Anat. Rec. 260, 148–157 (2000).

    Article  Google Scholar 

  138. 138.

    Stekelenburg-de Vos, S. et al. Systolic and diastolic ventricular function assessed by pressure-volume loops in the stage 21 venous clipped chick embryo. Pediatr. Res. 57, 16–21 (2005).

    Article  Google Scholar 

  139. 139.

    Desmond, M. E., Levitan, M. L. & Haas, A. R. Internal luminal pressure during early chick embryonic brain growth: descriptive and empirical observations. Anat. Rec. 285, 737–747 (2005).

    Article  Google Scholar 

  140. 140.

    Chan, C. J. et al. Hydraulic control of mammalian embryo size and cell fate. Nature 571, 112–116 (2019).

    ADS  Article  Google Scholar 

  141. 141.

    Mosaliganti, K. R. et al. Size control of the inner ear via hydraulic feedback. eLife 8, e39596 (2019).

    Article  Google Scholar 

  142. 142.

    Lorenz, J. N. Micropuncture of the kidney: a primer on techniques. Compr. Physiol. 2, 621–637 (2012).

    Google Scholar 

  143. 143.

    Campàs, O. et al. Quantifying cell-generated mechanical forces within living embryonic tissues. Nat. Methods 11, 183–189 (2014). This paper reports the first use of exogenous inclusions as cell-force transducers.

    Article  Google Scholar 

  144. 144.

    Vorselen, D. et al. Microparticle traction force microscopy reveals subcellular force exertion patterns in immune cell–target interactions. Nat. Commun. 11, 20 (2020).

    ADS  Article  Google Scholar 

  145. 145.

    Serwane, F. et al. In vivo quantification of spatially varying mechanical properties in developing tissues. Nat. Methods 14, 181–186 (2017).

    Article  Google Scholar 

  146. 146.

    Ingremeau, F. et al. Optical sensing of mechanical pressure based on diffusion measurement in polyacrylamide cell-like barometers. Soft Matter 13, 4210–4213 (2017).

    Article  Google Scholar 

  147. 147.

    Dolega, M. E. et al. Cell-like pressure sensors reveal increase of mechanical stress towards the core of multicellular spheroids under compression. Nat. Commun. 8, 14056 (2017).

    ADS  Article  Google Scholar 

  148. 148.

    Mohagheghian, E. et al. Quantifying compressive forces between living cell layers and within tissues using elastic round microgels. Nat. Commun. 9, 1878 (2018).

    ADS  Article  Google Scholar 

  149. 149.

    Bar-Kochba, E., Toyjanova, J., Andrews, E., Kim, K.-S. & Franck, C. A fast iterative digital volume correlation algorithm for large deformations. Exp. Mech. 55, 261–274 (2015).

    Article  Google Scholar 

  150. 150.

    Shen, J., Sun, L.-D. & Yan, C.-H. Luminescent rare earth nanomaterials for bioprobe applications. Dalton Trans. 42, 5687–5697 (2008).

    Article  Google Scholar 

  151. 151.

    Mehlenbacher, R. D., Kolbl, R., Lay, A. & Dionne, J. A. Nanomaterials for in vivo imaging of mechanical forces and electrical fields. Nat. Rev. Mater. 3, 17080 (2018).

    ADS  Article  Google Scholar 

  152. 152.

    Wisser, M. D. et al. Strain-induced modification of optical selection rules in lanthanide-based upconverting nanoparticles. Nano Lett. 15, 1891–1897 (2015).

    ADS  Article  Google Scholar 

  153. 153.

    Lay, A. et al. Upconverting nanoparticles as optical sensors of nano- to micro-Newton forces. Nano Lett. 17, 4172–4177 (2017).

    ADS  Article  Google Scholar 

  154. 154.

    Humar, M. & Yun, S. H. Intracellular microlasers. Nat. Photonics 9, 572–576 (2015).

    ADS  Article  Google Scholar 

  155. 155.

    Schubert, M. et al. Monitoring contractility in single cardiomyocytes and whole hearts with bio-integrated microlasers. Prepr. bioRxiv https://doi.org/10.1101/605444 (2019).

    Article  Google Scholar 

  156. 156.

    Lucio, A. A. et al. Spatiotemporal variation of endogenous cell-generated stresses within 3D multicellular spheroids. Sci. Rep. 7, 12022 (2017).

    ADS  Article  Google Scholar 

  157. 157.

    Träber, N. et al. Polyacrylamide bead sensors for in vivo quantification of cell-scale stress in zebrafish development. Sci. Rep. 9, 17031 (2019).

    ADS  Article  Google Scholar 

  158. 158.

    Gayrard, C. & Borghi, N. FRET-based molecular tension microscopy. Methods 94, 33–42 (2016).

    Article  Google Scholar 

  159. 159.

    Yasunaga, A., Murad, Y. & Li, I. T. S. Quantifying molecular tension-classifications, interpretations and limitations of force sensors. Phys. Biol. 17, 011001 (2019).

    ADS  Article  Google Scholar 

  160. 160.

    Meng, F., Suchyna, T. M. & Sachs, F. A fluorescence energy transfer-based mechanical stress sensor for specific proteins in situ. FEBS J. 275, 3072–3087 (2008).

    Article  Google Scholar 

  161. 161.

    Grashoff, C. et al. Measuring mechanical tension across vinculin reveals regulation of focal adhesion dynamics. Nature 466, 263–266 (2010).

    ADS  Article  Google Scholar 

  162. 162.

    Meng, F. & Sachs, F. Visualizing dynamic cytoplasmic forces with a compliance-matched FRET sensor. J. Cell Sci. 124, 261–269 (2011).

    Article  Google Scholar 

  163. 163.

    Förster, T. Zwischenmolekulare Energiewanderung und Fluoreszenz. Ann. Phys. (Leipz.) 437, 55–75 (1948).

    ADS  MATH  Article  Google Scholar 

  164. 164.

    Conway, D. E. et al. Fluid shear stress on endothelial cells modulates mechanical tension across VE-cadherin and PECAM-1. Curr. Biol. 23, 1024–1030 (2013).

    Article  Google Scholar 

  165. 165.

    Cai, D. et al. Mechanical feedback through E-cadherin promotes direction sensing during collective cell migration. Cell 157, 1146–1159 (2014).

    Article  Google Scholar 

  166. 166.

    Price, A. J. et al. Mechanical loading of desmosomes depends on the magnitude and orientation of external stress. Nat. Commun. 9, 5284 (2018).

    ADS  Article  Google Scholar 

  167. 167.

    Borghi, N. et al. E-cadherin is under constitutive actomyosin-generated tension that is increased at cell–cell contacts upon externally applied stretch. Proc. Natl Acad. Sci. USA 109, 12568–12573 (2012).

    ADS  Article  Google Scholar 

  168. 168.

    Narayanan, V. et al. Osmotic gradients in epithelial acini increase mechanical tension across E-cadherin, drive morphogenesis, and maintain homeostasis. Curr. Biol. 30, 624–633 (2020).

    Article  Google Scholar 

  169. 169.

    Eder, D., Basler, K. & Aegerter, C. M. Challenging FRET-based E-cadherin force measurements in Drosophila. Sci. Rep. 7, 13692 (2017).

    ADS  Article  Google Scholar 

  170. 170.

    Stabley, D. R., Jurchenko, C., Marshall, S. S. & Salaita, K. S. Visualizing mechanical tension across membrane receptors with a fluorescent sensor. Nat. Methods 9, 64–67 (2012).

    Article  Google Scholar 

  171. 171.

    Colombelli, J. & Solon, J. Force communication in multicellular tissues addressed by laser nanosurgery. Cell Tissue Res. 352, 133–147 (2013).

    Article  Google Scholar 

  172. 172.

    Zulueta-Coarasa, T. & Fernandez-Gonzalez, R. in Integrative Mechanobiology: Micro- and Nano- Techniques in Cell Mechanobiology Ch. 8 (eds Sun, Y., Kim, D.-H. & Simmons, C. A.) 128–147 (Cambridge Univ. Press, 2015).

  173. 173.

    Bonnet, I. et al. Mechanical state, material properties and continuous description of an epithelial tissue. J. R. Soc. Interface 9, 2614–2623 (2012).

    Article  Google Scholar 

  174. 174.

    Etournay, R. et al. Interplay of cell dynamics and epithelial tension during morphogenesis of the Drosophila pupal wing. eLife 4, e07090 (2015).

    Article  Google Scholar 

  175. 175.

    Hutson, M. S. et al. Forces for morphogenesis investigated with laser microsurgery and quantitative modeling. Science 300, 145–149 (2003).

    ADS  Article  Google Scholar 

  176. 176.

    Ma, X., Lynch, H. E., Scully, P. C. & Hutson, M. S. Probing embryonic tissue mechanics with laser hole drilling. Phys. Biol. 6, 036004 (2009).

    ADS  Article  Google Scholar 

  177. 177.

    Hutson, M. S. et al. Combining laser microsurgery and finite element modeling to assess cell-level epithelial mechanics. Biophys. J. 97, 3075–3085 (2009).

    ADS  Article  Google Scholar 

  178. 178.

    Kiehart, D. P., Galbraith, C. G., Edwards, K. A., Rickoll, W. L. & Montague, R. A. Multiple forces contribute to cell sheet morphogenesis for dorsal closure in Drosophila. J. Cell Biol. 149, 471–490 (2000). This paper is a pioneering work in the implementation of laser ablation as a tissue-stress-inference method.

    Article  Google Scholar 

  179. 179.

    Solon, J., Kaya-Çopur, A., Colombelli, J. & Brunner, D. Pulsed forces timed by a ratchet-like mechanism drive directed tissue movement during dorsal closure. Cell 137, 1331–1342 (2009).

    Article  Google Scholar 

  180. 180.

    Hunter, G. L., Crawford, J. M., Genkins, J. Z. & Kiehart, D. P. Ion channels contribute to the regulation of cell sheet forces during Drosophila dorsal closure. Development 141, 325–334 (2014).

    Article  Google Scholar 

  181. 181.

    Fernandez-Gonzalez, R. & Zallen, J. A. Wounded cells drive rapid epidermal repair in the early Drosophila embryo. Mol. Biol. Cell 24, 3227–3237 (2013).

    Article  Google Scholar 

  182. 182.

    Campinho, P. et al. Tension-oriented cell divisions limit anisotropic tissue tension in epithelial spreading during zebrafish epiboly. Nat. Cell Biol. 15, 1405–1414 (2013).

    Article  Google Scholar 

  183. 183.

    Maître, J.-L. et al. Asymmetric division of contractile domains couples cell positioning and fate specification. Nature 536, 344–348 (2016).

    ADS  Article  Google Scholar 

  184. 184.

    Maître, J.-L., Niwayama, R., Turlier, H., Nédélec, F. & Hiiragi, T. Pulsatile cell-autonomous contractility drives compaction in the mouse embryo. Nat. Cell Biol. 17, 849–855 (2015).

    Article  Google Scholar 

  185. 185.

    Yang, X. et al. Correlating cell shape and cellular stress in motile confluent tissues. Proc. Natl Acad. Sci. USA 114, 12663–12668 (2017).

    Article  Google Scholar 

  186. 186.

    Alt, S., Ganguly, P. & Salbreux, G. Vertex models: from cell mechanics to tissue morphogenesis. Philos. Trans. R. Soc. B Biol. Sci. 372, 20150520 (2017).

    Article  Google Scholar 

  187. 187.

    Cranston, P. G., Veldhuis, J. H., Narasimhan, S. & Brodland, G. W. Cinemechanometry (CMM): A method to determine the forces that drive morphogenetic movements from time-lapse images. Ann. Biomed. Eng. 38, 2937–2947 (2010).

    Article  Google Scholar 

  188. 188.

    Ishihara, S. et al. Comparative study of non-invasive force and stress inference methods in tissue. Eur. Phys. J. E Soft Matter 36, 9859 (2013).

    Article  Google Scholar 

  189. 189.

    Ishihara, S. & Sugimura, K. Bayesian inference of force dynamics during morphogenesis. J. Theor. Biol. 313, 201–211 (2012).

    MATH  Article  Google Scholar 

  190. 190.

    Stein, M. B. & Gordon, R. Epithelia as bubble rafts: a new method for analysis of cell shape and intercellular adhesion in embryonic and other epithelia. J. Theor. Biol. 97, 625–639 (1982). One of the earliest implementations of a force-inference method applied to a cellular tissue.

    Article  Google Scholar 

  191. 191.

    Hayashi, T. & Carthew, R. W. Surface mechanics mediate pattern formation in the developing retina. Nature 431, 647–652 (2004).

    ADS  Article  Google Scholar 

  192. 192.

    Chiou, K. K., Hufnagel, L. & Shraiman, B. I. Mechanical stress inference for two dimensional cell arrays. PLoS Comput. Biol. 8, e1002512 (2012).

    ADS  Article  Google Scholar 

  193. 193.

    Brodland, G. W. et al. CellFIT: a cellular force-inference toolkit using curvilinear cell boundaries. PLoS ONE 9, e99116 (2014).

    ADS  Article  Google Scholar 

  194. 194.

    Kong, W. et al. Experimental validation of force inference in epithelia from cell to tissue scale. Sci. Rep. 9, 14647 (2019).

    ADS  Article  Google Scholar 

  195. 195.

    Veldhuis, J. H., Mashburn, D., Hutson, M. S. & Brodland, G. W. Practical aspects of the cellular force inference toolkit (CellFIT). Methods Cell Biol. 125, 331–351 (2015).

    Article  Google Scholar 

  196. 196.

    Veldhuis, J. H. et al. Inferring cellular forces from image stacks. Philos. Trans. R. Soc. B Biol. Sci. 372, 20160261 (2017).

    Article  Google Scholar 

  197. 197.

    Chen, H. H. & Brodland, G. W. Cell-level finite element studies of viscous cells in planar aggregates. J. Biomech. Eng. 122, 394–401 (2000).

    Article  Google Scholar 

  198. 198.

    Brodland, G. W., Viens, D. & Veldhuis, J. H. A new cell-based FE model for the mechanics of embryonic epithelia. Comput. Methods Biomech. Biomed. Eng. 10, 121–128 (2007).

    Article  Google Scholar 

  199. 199.

    Brodland, G. W. et al. Video force microscopy reveals the mechanics of ventral furrow invagination in Drosophila. Proc. Natl Acad. Sci. USA 107, 22111–22116 (2010).

    ADS  Article  Google Scholar 

  200. 200.

    Sugimura, K. & Ishihara, S. The mechanical anisotropy in a tissue promotes ordering in hexagonal cell packing. Development 140, 4091–4101 (2013).

    Article  Google Scholar 

  201. 201.

    Xu, M., Wu, Y., Shroff, H., Wu, M. & Mani, M. A scheme for 3-dimensional morphological reconstruction and force inference in the early C. elegans embryo. PLoS ONE 13, e0199151 (2018).

    Article  Google Scholar 

  202. 202.

    Nestor-Bergmann, A. et al. Decoupling the roles of cell shape and mechanical stress in orienting and cueing epithelial mitosis. Cell Rep. 26, 2088–2100.e4 (2019).

    Article  Google Scholar 

  203. 203.

    Krens, S. F. G. et al. Interstitial fluid osmolarity modulates the action of differential tissue surface tension in progenitor cell segregation during gastrulation. Development 144, 1798–1806 (2017).

    Article  Google Scholar 

  204. 204.

    Notbohm, J., Kim, J. H., Asthagiri, A. R. & Ravichandran, G. Three-dimensional analysis of the effect of epidermal growth factor on cell-cell adhesion in epithelial cell clusters. Biophys. J. 102, 1323–1330 (2012).

    ADS  Article  Google Scholar 

  205. 205.

    Mongera, A. et al. A fluid-to-solid jamming transition underlies vertebrate body axis elongation. Nature 561, 401–405 (2018).

    ADS  Article  Google Scholar 

  206. 206.

    Farhadifar, R., Röper, J.-C., Aigouy, B., Eaton, S. & Jülicher, F. The influence of cell mechanics, cell–cell interactions, and proliferation on epithelial packing. Curr. Biol. 17, 2095–2104 (2007).

    Article  Google Scholar 

  207. 207.

    Barresi, M. J. F. & Gilbert, S. F. Developmental Biology 12th edn (Oxford Univ. Press, 2019).

Download references

Acknowledgements

The authors apologize to the many colleagues whose work could not be cited owing to space constraints. The authors thank N. Grummel, D. Böhringer and B. Fabry for providing Fig. 2d, and A. Marin-Llauradó and T. Golde for critical reading of the manuscript. The authors are funded by the Spanish Ministry of Science, Innovation and Universities MICINN/FEDER (PGC2018-099645-B-I00 to X.T., DPI2015-71789-R to M.A.), the Generalitat de Catalunya (2017-FI-B1-00068 grant to E.L., SGR-2017-01602 grant to X.T. and 2014-SGR-1471 grant to M.A.), the CERCA Programme and ICREA Academia award (to M.A.), the European Research Council (grant CoG-616480 to X.T. and grant CoG-681434 to M.A.), the European Union’s Horizon 2020 research and innovation programme (under the Marie Skłodowska-Curie grant agreement no. 797621 to M.G.-G.), Obra Social “la Caixa” and Fundació la Marató de TV3 (project 201903-30-31-32 to X.T.). The IBEC is the recipient of a Severo Ochoa Award of Excellence from the Spanish Ministry of Economy and Competitiveness (MINECO).

Author information

Affiliations

Authors

Contributions

The authors contributed equally to all aspects of the article.

Corresponding authors

Correspondence to Manuel Gómez-González or Marino Arroyo or Xavier Trepat.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information

Nature Reviews Physics thanks U. Schwartz and C.J. Chan for their contribution to the peer review of this work.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Gómez-González, M., Latorre, E., Arroyo, M. et al. Measuring mechanical stress in living tissues. Nat Rev Phys 2, 300–317 (2020). https://doi.org/10.1038/s42254-020-0184-6

Download citation