Abstract
Cortical stiffness is an important cellular property that changes during migration, adhesion and growth. Previous atomic force microscopy (AFM) indentation measurements of cells cultured on deformable substrates have suggested that cells adapt their stiffness to that of their surroundings. Here we show that the force applied by AFM to a cell results in a significant deformation of the underlying substrate if this substrate is softer than the cell. This ‘soft substrate effect’ leads to an underestimation of a cell’s elastic modulus when analysing data using a standard Hertz model, as confirmed by finite element modelling and AFM measurements of calibrated polyacrylamide beads, microglial cells and fibroblasts. To account for this substrate deformation, we developed a ‘composite cell–substrate model’. Correcting for the substrate indentation revealed that cortical cell stiffness is largely independent of substrate mechanics, which has major implications for our interpretation of many physiological and pathological processes.
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Data availability
The data underlying this study are available from the authors upon reasonable request. The AFM force–distance curves raw data can be found at https://doi.org/10.6084/m9.figshare.10732415.
Code availability
Codes used for processing of AFM and confocal laser scanning microscopy raw data can be found at https://github.com/FranzeLab/AFM-data-analysis-and-processing/tree/master/Cell%20stiffness. Comsol models can be found at https://doi.org/10.6084/m9.figshare.10731869.
References
Koser, D. E. et al. Mechanosensing is critical for axon growth in the developing brain. Nat. Neurosci. 19, 1592–1598 (2016).
Barriga, E. H., Franze, K., Charras, G. & Mayor, R. Tissue stiffening coordinates morphogenesis by triggering collective cell migration in vivo. Nature 554, 523–527 (2018).
Haase, K. & Pelling, A. E. Investigating cell mechanics with atomic force microscopy. J. R. Soc. Interface 12, 20140970 (2015).
Gautier, H. O. B. et al. in Methods in Cell Biology Vol. 125 (ed. Paluch, E. K.) 211–235 (Academic, 2015).
Dufrêne, Y. F. et al. Imaging modes of atomic force microscopy for application in molecular and cell biology. Nat. Nanotechnol. 12, 295–307 (2017).
Wu, P.-H. et al. A comparison of methods to assess cell mechanical properties. Nat. Methods 15, 491–498 (2018).
Vahabikashi, A. et al. Probe sensitivity to cortical versus intracellular cytoskeletal network stiffness. Biophys. J. 116, 518–529 (2019).
Iyer, S., Gaikwad, R. M., Subba-Rao, V., Woodworth, C. D. & Sokolov, I. Atomic force microscopy detects differences in the surface brush of normal and cancerous cells. Nat. Nanotechnol. 4, 389–393 (2009).
Solon, J., Levental, I., Sengupta, K., Georges, P. C. & Janmey, P. A. Fibroblast adaptation and stiffness matching to soft elastic substrates. Biophys. J. 93, 4453–4461 (2007).
Tee, S.-Y., Fu, J., Chen, C. S. & Janmey, P. A. Cell shape and substrate rigidity both regulate cell stiffness. Biophys. J. 100, L25–L27 (2011).
Liu, H., Sun, Y. & Simmons, C. A. Determination of local and global elastic moduli of valve interstitial cells cultured on soft substrates. J. Biomech. 46, 1967–1971 (2013).
Rianna, C. & Radmacher, M. Comparison of viscoelastic properties of cancer and normal thyroid cells on different stiffness substrates. Eur. Biophys. J. 46, 309–324 (2017).
Chopra, A., Tabdanov, E., Patel, H., Janmey, P. A. & Kresh, J. Y. Cardiac myocyte remodeling mediated by N-cadherin-dependent mechanosensing. Am. J. Physiol. Heart Circ. Physiol. 300, H1252–H1266 (2011).
Hertz, H. Über die berührung fester elastischer körper. J. Reine Angew. Math. 92, 156–171 (1882).
Harris, A. R. & Charras, G. T. Experimental validation of atomic force microscopy-based cell elasticity measurements. Nanotechnology 22, 345102 (2011).
Ivanovska, I. L. et al. Cross-linked matrix rigidity and soluble retinoids synergize in nuclear lamina regulation of stem cell differentiation. Mol. Biol. Cell 28, 2010–2022 (2017).
Kronenberg, N. M. et al. Long-term imaging of cellular forces with high precision by elastic resonator interference stress microscopy. Nat. Cell Biol. 19, 864–872 (2017).
Liehm, P., Kronenberg, N. M. & Gather, M. C. Analysis of the precision, robustness, and speed of elastic resonator interference stress microscopy. Biophys. J. 114, 2180–2193 (2018).
Boussinesq, J. Application des Potentiels à l'Étude de l'Équilibre et du Mouvement des Solides Élastiques, Principalement au Calcul des Déformations et des Pressions Que Produisent, dans ces Solides, des Efforts Quelconques Exercés sur une Petite Partie de Leur Surface ou de Leur Intérieur: Mémoire Suivi de Notes Étendues sur Divers Points de Physique Mathématique et d’Analyse (L. Danel, 1885).
Boudou, T., Ohayon, J., Picart, C. & Tracqui, P. An extended relationship for the characterization of Young’s modulus and Poisson’s ratio of tunable polyacrylamide gels. Biorheology 43, 721–728 (2006).
Sneddon, I. N. The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47–57 (1965).
Bilodeau, G. G. Regular pyramid punch problem. J. Appl. Mech. 59, 519–523 (1992).
Guz, N., Dokukin, M., Kalaparthi, V. & Sokolov, I. If cell mechanics can be described by elastic modulus: study of different models and probes used in indentation experiments. Biophys. J. 107, 564–575 (2014).
Simon, M. et al. Load rate and temperature dependent mechanical properties of the cortical neuron and its pericellular layer measured by atomic force microscopy. Langmuir 32, 1111–1119 (2016).
Chrzanowska-Wodnicka, M. & Burridge, K. Rho-stimulated contractility drives the formation of stress fibers and focal adhesions. J. Cell Biol. 133, 1403–1415 (1996).
Pelham, R. J. & Wang, Y.-l Cell locomotion and focal adhesions are regulated by substrate flexibility. Proc. Natl Acad. Sci. USA 94, 13661–13665 (1997).
Engler, A. J. et al. Myotubes differentiate optimally on substrates with tissue-like stiffness. J. Cell Biol. 166, 877–887 (2004).
Bollmann, L. et al. Microglia mechanics: immune activation alters traction forces and durotaxis. Front. Cell. Neurosci. 9, 363 (2015).
Han, S. J., Bielawski, K. S., Ting, L. H., Rodriguez, M. L. & Sniadecki, N. J. Decoupling substrate stiffness, spread area, and micropost density: a close spatial relationship between traction forces and focal adhesions. Biophys. J. 103, 640–648 (2012).
Moshayedi, P. et al. The relationship between glial cell mechanosensitivity and foreign body reactions in the central nervous system. Biomaterials 35, 3919–3925 (2014).
Chen, C. S., Mrksich, M., Huang, S., Whitesides, G. M. & Ingber, D. E. Geometric control of cell life and death. Science 276, 1425–1428 (1997).
Discher, D. E., Janmey, P. A. & Wang, Y. Tissue cells feel and respond to the stiffness of their substrate. Science 310, 1139–1143 (2005).
Engler, A. J., Sen, S., Sweeney, H. L. & Discher, D. E. Matrix elasticity directs stem cell lineage specification. Cell 126, 677–689 (2006).
Kasza, K. E. et al. The cell as a material. Curr. Opin. Cell Biol. 19, 101–107 (2007).
Gupta, M. et al. Adaptive rheology and ordering of cell cytoskeleton govern matrix rigidity sensing. Nat. Commun. 6, 7525 (2015).
Soine, J. R. et al. Model-based traction force microscopy reveals differential tension in cellular actin bundles. PLoS Comput. Biol. 11, e1004076 (2015).
Humphrey, D., Duggan, C., Saha, D., Smith, D. & Käs, J. Active fluidization of polymer networks through molecular motors. Nature 416, 413–416 (2002).
Kovacs, M., Toth, J., Hetenyi, C., Malnasi-Csizmadia, A. & Sellers, J. R. Mechanism of blebbistatin inhibition of myosin II. J. Biol. Chem. 279, 35557–35563 (2004).
Gardel, M. L., Kasza, K. E., Brangwynne, C. P., Liu, J. & Weitz, D. A. in Methods in Cell Biology Vol. 89 (eds J.J. Correia & H.W. Detrich) 487–519 (Academic Press, 2008).
Dimitriadis, E. K., Horkay, F., Maresca, J., Kachar, B. & Chadwick, R. S. Determination of elastic moduli of thin layers of soft material using the atomic force microscope. Biophys. J. 82, 2798–2810 (2002).
Charras, G. T., Lehenkari, P. P. & Horton, M. A. Atomic force microscopy can be used to mechanically stimulate osteoblasts and evaluate cellular strain distributions. Ultramicroscopy 86, 85–95 (2001).
Moshayedi, P. et al. Mechanosensitivity of astrocytes on optimized polyacrylamide gels analyzed by quantitative morphometry. J. Phys. Condens. Matter 22, 194114 (2010).
Wilby, M. J. et al. N-cadherin inhibits Schwann cell migration on astrocytes. Mol. Cell. Neurosci. 14, 66–84 (1999).
Syed, Y. A. et al. Inhibition of oligodendrocyte precursor cell differentiation by myelin-associated proteins. Neurosurg. Focus 24, E5 (2008).
Cook, S. M. et al. Practical implementation of dynamic methods for measuring atomic force microscope cantilever spring constants. Nanotechnology 17, 2135–2145 (2006).
Pogoda, K. et al. Soft substrates containing hyaluronan mimic the effects of increased stiffness on morphology, motility, and proliferation of glioma cells. Biomacromolecules 18, 3040–3051 (2017).
Charrier, E. E., Pogoda, K., Wells, R. G. & Janmey, P. A. Control of cell morphology and differentiation by substrates with independently tunable elasticity and viscous dissipation. Nat. Commun. 9, 449 (2018).
Gavara, N. Combined strategies for optimal detection of the contact point in AFM force–indentation curves obtained on thin samples and adherent cells. Sci. Rep. 6, 21267 (2016).
Han, S. J., Oak, Y., Groisman, A. & Danuser, G. Traction microscopy to identify force modulation in subresolution adhesions. Nat. Methods 12, 653–656 (2015).
McGill, R., Tukey, J. W. & Larsen, W. A. Variations of box plots. Am. Stat. 32, 12–16 (1978).
Acknowledgements
We thank P. Janmey, B. Fabry and U. Schwarz for critical discussions and comments on the manuscript, T. Schäffer for personal support and A. Winkel (JPK) for technical support, as well as J. Tavares and M. Kotter for microglial cells and B. Colledge for NIH 3T3 fibroblasts. We acknowledge funding from the German Science Foundation (DFG grant numbers RH 147/1-1 to J.R., EXC 1003 CiM to T.B.), the Herchel Smith Foundation (postdoctoral fellowship to A.D.), the Royal Society (University Research Fellowship to K.J.C.), the UK EPSRC (programme grant number EP/P030017/1 to M.C.G.), the Human Frontier Science Program (HFSP grant number RGP0018/2017 to T.B.), the European Research Council (consolidator grant numbers 772798 to K.J.C., 771201 to T.B., 647186 to G.C. and 772426 to K.F.), and the UK BBSRC (equipment grant number BB/R000042/1 to G.C. and research project grant number BB/N006402/1 to K.F.).
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J.R. and K.F. conceived the study. J.R. conducted all AFM experiments, analysed all AFM data and developed the model. A.D. conducted all optical imaging and traction force microscopy experiments and analysed data. B.W. and T.B. custom-designed PAA beads. N.M.K. and M.C.G. conducted and analysed ERISM measurements. K.J.C. helped with imaging and data analysis. G.C. helped with AFM experiments. All authors discussed the study. J.R. and K.F. wrote the paper with contributions from all co-authors.
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Supplementary Figs. 1–10, discussion and refs. 51–56.
Supplementary Video 1
Indentation of a microglial cell cultured on a stiff substrate by AFM.
Supplementary Video 2
Indentation of a microglial cell cultured on a soft substrate by AFM.
Supplementary Video 3
Indentation of a fibroblast cultured on a stiff substrate by AFM.
Supplementary Video 4
Indentation of a fibroblast cultured on a soft substrate by AFM.
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Rheinlaender, J., Dimitracopoulos, A., Wallmeyer, B. et al. Cortical cell stiffness is independent of substrate mechanics. Nat. Mater. 19, 1019–1025 (2020). https://doi.org/10.1038/s41563-020-0684-x
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DOI: https://doi.org/10.1038/s41563-020-0684-x
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