Abstract
Numerous organs in the bodies of animals, including the lung, kidney, and mammary gland, contain ramified networks of epithelial tubes. These structures arise during development via a process known as branching morphogenesis. Previous studies have shown that mechanical forces directly impact this process, but the patterns of mechanical stress exerted by branching embryonic epithelia are not well understood. This is, in part, owing to a lack of experimental tools. Traditional traction force microscopy assays rely on the use of compliant hydrogels with well-defined mechanical properties. Isolated embryonic epithelial explants, however, have only been shown to branch in three-dimensional matrices of reconstituted basement membrane protein, or Matrigel, a biomaterial with poorly characterized mechanical behavior, especially in the regime of large deformations. Here, to compute the traction stresses generated by branching epithelial explants, we quantified the finite-deformation constitutive behavior of gels of reconstituted basement membrane protein subjected to multi-axial mechanical loads. We then modified the mesenchyme-free assay for the ex vivo culture of isolated embryonic airway epithelial explants by suspending fluorescent microspheres within the surrounding gel and tracking their motion during culture. Surprisingly, the tracked bead motion was non-zero in regions of the gel far away from the explants, suggestive of passive swelling deformations within the matrix. To compute accurate traction stresses, these swelling deformations must be decomposed from those generated by the branching explants. We thus tracked the motion of beads suspended within cell-free matrices and quantified spatiotemporal patterns of gel swelling. Taken together, these passive swelling data can be combined with the measured mechanical properties of the gel to compute the traction forces exerted by intact embryonic epithelial explants.


taken from an individual lot of Matrigel. Mean ± SD shown for n = 19 specimens.







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Affolter, M., R. Zeller, and E. Caussinus. Tissue remodelling through branching morphogenesis. Nat. Rev. Mol. Cell Biol. 10:831–842, 2009
Aisenbrey, E. A., and W. L. Murphy. Synthetic alternatives to Matrigel. Nat. Rev. Mater. 5:539–551, 2020
Alcaraz, J., R. Xu, H. Mori, C. M. Nelson, R. Mroue, V. A. Spencer, D. Brownfield, D. C. Radisky, C. Bustamante, and M. J. Bissell. Laminin and biomimetic extracellular elasticity enhance functional differentiation in mammary epithelia. EMBO J. 27:2829–2838, 2008
Bellusci, S., J. Grindley, H. Emoto, N. Itoh, and B. L. Hogan. Fibroblast growth factor 10 (FGF10) and branching morphogenesis in the embryonic mouse lung. Development 124:4867–4878, 1997
Beningo, K. A., and Y.-L. Wang. Flexible substrata for the detection of cellular traction forces. Trends Cell Biol. 12:79–84, 2002
Boudou, T., J. Ohayon, C. Picart, R. I. Pettigrew, and P. Tracqui. Nonlinear elastic properties of polyacrylamide gels: implications for quantification of cellular forces. Biorheology 46:191–205, 2009
Butler, J. P., I. M. Tolić-Nørrelykke, B. Fabry, and J. J. Fredberg. Traction fields, moments, and strain energy that cells exert on their surroundings. Am. J. Physiol. Cell Physiol. 282:C595–C605, 2002
Campàs, O., T. Mammoto, S. Hasso, R. A. Sperling, D. O’Connell, A. G. Bischof, R. Maas, D. A. Weitz, L. Mahadevan, and D. E. Ingber. Quantifying cell-generated mechanical forces within living embryonic tissues. Nat. Methods 11:183–189, 2014
Cardoso, W. V., A. Itoh, H. Nogawa, I. Mason, and J. S. Brody. FGF-1 and FGF-7 induce distinct patterns of growth and differentiation in embryonic lung epithelium. Dev. Dyn. 208:398–405, 1997
Chanet, S., C. J. Miller, E. D. Vaishnav, B. Ermentrout, L. A. Davidson, and A. C. Martin. Actomyosin meshwork mechanosensing enables tissue shape to orient cell force. Nat. Commun. 8:15014, 2017
Chaudhuri, O., J. Cooper-White, P. A. Janmey, D. J. Mooney, and V. B. Shenoy. Effects of extracellular matrix viscoelasticity on cellular behaviour. Nature 584:535–546, 2020
Chaudhuri, O., S. T. Koshy, C. B. da Cunha, J.-W. Shin, C. S. Verbeke, K. H. Allison, and D. J. Mooney. Extracellular matrix stiffness and composition jointly regulate the induction of malignant phenotypes in mammary epithelium. Nat. Mater. 13:970–978, 2014
Dembo, M., and Y.-L. Wang. Stresses at the cell-to-substrate interface during locomotion of fibroblasts. Biophys. J. 76:2307–2316, 199
Eiraku, M., N. Takata, H. Ishibashi, M. Kawada, E. Sakakura, S. Okuda, K. Sekiguchi, T. Adachi, and Y. Sasai. Self-organizing optic-cup morphogenesis in three-dimensional culture. Nature 472:51–56, 2011
Filas, B. A., I. R. Efimov, and L. A. Taber. Optical coherence tomography as a tool for measuring morphogenetic deformation of the looping heart. Anat. Rec. 290:1057–1068, 2007
Franck, C., S. Hong, S. A. Maskarinec, D. A. Tirrell, and G. Ravichandran. Three-dimensional full-field measurements of large deformations in soft materials using confocal microscopy and digital volume correlation. Exp. Mech. 47:427–438, 2007
Gjorevski, N., A. S. Piotrowski, V. D. Varner, and C. M. Nelson. Dynamic tensile forces drive collective cell migration through three-dimensional extracellular matrices. Sci. Rep. 5:11458, 2015
Gjorevski, N., N. Sachs, A. Manfrin, S. Giger, M. E. Bragina, P. Ordóñez-Morán, H. Clevers, and M. P. Lutolf. Designer matrices for intestinal stem cell and organoid culture. Nature 539:560–564, 2016
Gómez-González, M., E. Latorre, M. Arroyo, and X. Trepat. Measuring mechanical stress in living tissues. Nat. Rev. Phys. 2:300–317, 2020
Goodwin, K., S. Mao, T. Guyomar, E. Miller, D. C. Radisky, A. Košmrlj, and C. M. Nelson. Smooth muscle differentiation shapes domain branches during mouse lung development. Development 146:dev181172, 2019
Goodwin, K., and C. M. Nelson. Branching morphogenesis. Development 147:dev184499, 2020
Goodwin, K., and C. M. Nelson. Mechanics of development. Dev. Cell 56:240–250, 2020
Gordon, V. D., M. T. Valentine, M. L. Gardel, D. Andor-Ardó, S. Dennison, A. A. Bogdanov, D. A. Weitz, and T. S. Deisboeck. Measuring the mechanical stress induced by an expanding multicellular tumor system: a case study. Exp. Cell Res. 289:58–66, 2003
Hamburger, V., and H. L. Hamilton. A series of normal stages in the development of the chick embryo. J. Morphol. 88:49–92, 1951
Holzapfel, G. A. Nonlinear Solid Mechanics: A Continuum Approach for Engineering. Hoboken: Wiley, 2000
Hughes, C. S., L. M. Postovit, and G. A. Lajoie. Matrigel: a complex protein mixture required for optimal growth of cell culture. Proteomics 10:1886–1890, 2010
Hur, S. S., Y. Zhao, Y.-S. Li, E. Botvinick, and S. Chien. Live cells exert 3-dimensional traction forces on their substrata. Cell. Mol. Bioeng. 2:425–436, 2009
Iber, D., and D. Menshykau. The control of branching morphogenesis. Open Biol. 3:130088, 2013
Karzbrun, E., A. Kshirsagar, S. R. Cohen, J. H. Hanna, and O. Reiner. Human brain organoids on a chip reveal the physics of folding. Nat. Phys. 14:515–522, 2018
Kim, H. Y., M.-F. Pang, V. D. Varner, L. Kojima, E. Miller, D. C. Radisky, and C. M. Nelson. Localized smooth muscle differentiation is essential for epithelial bifurcation during branching morphogenesis of the mammalian lung. Dev. Cell 34:719–726, 2015
Kleinman, H. K., and G. R. Martin. Matrigel: basement membrane matrix with biological activity. Semin. Cancer Biol. 15:378–386, 2005
Lai, V. K., D. S. Nedrelow, S. P. Lake, B. Kim, E. M. Weiss, R. T. Tranquillo, and V. H. Barocas. Swelling of collagen-hyaluronic acid co-gels: an in vitro residual stress model. Ann. Biomed. Eng. 44:2984–2993, 2016
Legant, W. R., J. S. Miller, B. L. Blakely, D. M. Cohen, G. M. Genin, and C. S. Chen. Measurement of mechanical tractions exerted by cells in three-dimensional matrices. Nat. Methods 7:969–971, 2010
Lu, P., and Z. Werb. Patterning mechanisms of branched organs. Science 322:1506–1509, 2008
Makarenkova, H. P., M. P. Hoffman, A. Beenken, A. V. Eliseenkova, R. Meech, C. Tsau, V. N. Patel, R. A. Lang, and M. Mohammadi. Differential interactions of FGFs with heparan sulfate control gradient formation and branching morphogenesis. Sci. Signal. 2:ra55, 2009
Mammoto, A., K. M. Connor, T. Mammoto, C. W. Yung, D. Huh, C. M. Aderman, G. Mostoslavsky, L. E. H. Smith, and D. E. Ingber. A mechanosensitive transcriptional mechanism that controls angiogenesis. Nature 457:1103–1108, 2009
Martiel, J.-L., A. Leal, L. Kurzawa, M. Balland, I. Wang, T. Vignaud, Q. Tseng, and M. Théry. Measurement of cell traction forces with ImageJ. Methods Cell Biol. 125:269–287, 2015
Miller, C. J., and L. A. Davidson. The interplay between cell signalling and mechanics in developmental processes. Nat. Rev. Genet. 14:733–744, 2013
Mongera, A., P. Rowghanian, H. J. Gustafson, E. Shelton, D. A. Kealhofer, E. K. Carn, F. Serwane, A. A. Lucio, J. Giammona, and O. Campàs. A fluid-to-solid jamming transition underlies vertebrate body axis elongation. Nature 561:401–405, 2018
Nam, S., K. H. Hu, M. J. Butte, and O. Chaudhuri. Strain-enhanced stress relaxation impacts nonlinear elasticity in collagen gels. Proc. Natl. Acad. Sci. U.S.A. 113:5492–5497, 2016
Nam, S., J. Lee, D. G. Brownfield, and O. Chaudhuri. Viscoplasticity enables mechanical remodeling of matrix by cells. Biophys. J. 111:2296–2308, 2016
Nelson, C. M., and J. P. Gleghorn. Sculpting organs: mechanical regulation of tissue development. Annu. Rev. Biomed. Eng. 14:129–154, 2012
Nelson, C. M., J. P. Gleghorn, M.-F. Pang, J. M. Jaslove, K. Goodwin, V. D. Varner, E. Miller, D. C. Radisky, and H. A. Stone. Microfluidic chest cavities reveal that transmural pressure controls the rate of lung development. Development 144:4328–4335, 2017
Nogawa, H., and T. Ito. Branching morphogenesis of embryonic mouse lung epithelium in mesenchyme-free culture. Development 121:1015–1022, 199
Nogawa, H., K. Morita, and W. V. Cardoso. Bud formation precedes the appearance of differential cell proliferation during branching morphogenesis of mouse lung epithelium in vitro. Dev. Dyn. 213:228–235, 1998
Nogawa, H., and Y. Takahashi. Substitution for mesenchyme by basement-membrane-like substratum and epidermal growth factor in inducing branching morphogenesis of mouse salivary epithelium. Development 112:855–861, 1991
Park, W. Y., B. Miranda, D. Lebeche, G. Hashimoto, and W. V. Cardoso. FGF-10 is a chemotactic factor for distal epithelial buds during lung development. Dev. Biol. 201:125–134, 1998
Piotrowski, A. S., V. D. Varner, N. Gjorevski, and C. M. Nelson. Three-dimensional traction force microscopy of engineered epithelial tissues. Methods Mol. Biol. 1189:191–206, 2015
Poincloux, R., O. Collin, F. Lizárraga, M. Romao, M. Debray, M. Piel, and P. Chavrier. Contractility of the cell rear drives invasion of breast tumor cells in 3D Matrigel. Proc. Natl. Acad. Sci. U.S.A. 108:1943–1948, 2011
Polacheck, W. J., and C. S. Chen. Measuring cell-generated forces: a guide to the available tools. Nat. Methods 13:415–423, 2016
Qiao, J., H. Sakurai, and S. K. Nigam. Branching morphogenesis independent of mesenchymal–epithelial contact in the developing kidney. Proc. Natl. Acad. Sci. U.S.A. 96:7330–7335, 1999
Reed, J., W. J. Walczak, O. N. Petzold, and J. K. Gimzewski. In situ mechanical interferometry of Matrigel films. Langmuir 25:36–39, 2009
Rivlin, R. S. Large elastic deformations of isotropic materials. I. Fundamental concepts. Philos. Trans. A 240:459–490, 1948
Sanz-Herrera, J. A., J. Barrasa-Fano, M. Cóndor, and H. V. Oosterwyck. Inverse method based on 3D nonlinear physically constrained minimisation in the framework of traction force microscopy. Soft Matter 17:10210–10222, 2020
Sato, T., R. G. Vries, H. J. Snippert, M. van de Wetering, N. Barker, D. E. Stange, J. H. van Es, A. Abo, P. Kujala, P. J. Peters, and H. Clevers. Single Lgr5 stem cells build crypt-villus structures in vitro without a mesenchymal niche. Nature 459:262–265, 2009
Serwane, F., A. Mongera, P. Rowghanian, D. A. Kealhofer, A. A. Lucio, Z. M. Hockenbery, and O. Campàs. In vivo quantification of spatially varying mechanical properties in developing tissues. Nat. Methods 14:181–186, 2017
Song, D., L. Dong, M. Gupta, L. Li, O. Klaas, A. Loghin, M. Beall, C. S. Chen, and A. A. Oberai. Recovery of tractions exerted by single cells in three-dimensional nonlinear matrices. J. Biomech. Eng. 142:081012, 2020
Soofi, S. S., J. A. Last, S. J. Liliensiek, P. F. Nealey, and C. J. Murphy. The elastic modulus of MatrigelTM as determined by atomic force microscopy. J. Struct. Biol. 167:216–219, 2009
Steinwachs, J., C. Metzner, K. Skodzek, N. Lang, I. Thievessen, C. Mark, S. Münster, K. E. Aifantis, and B. Fabry. Three-dimensional force microscopy of cells in biopolymer networks. Nat. Methods 13:171–176, 2016
Style, R. W., R. Boltyanskiy, G. K. German, C. Hyland, C. W. MacMinn, A. F. Mertz, L. A. Wilen, Y. Xu, and E. R. Dufresne. Traction force microscopy in physics and biology. Soft Matter 10:4047–4055, 2014
Taber, L. A. Nonlinear Theory of Elasticity: Applications in Biomechanics. Singapore: World Scientific, 2004
Taber, L. A. Continuum Modeling in Mechanobiology. Cham: Springer Nature, 2020
Tinevez, J.-Y., N. Perry, J. Schindelin, G. M. Hoopes, G. D. Reynolds, E. Laplantine, S. Y. Bednarek, S. L. Shorte, and K. W. Eliceiri. TrackMate: an open and extensible platform for single-particle tracking. Methods 115:80–90, 2017
Varner, V. D., J. P. Gleghorn, E. Miller, D. C. Radisky, and C. M. Nelson. Mechanically patterning the embryonic airway epithelium. Proc. Natl. Acad. Sci. U.S.A. 112:9230–9235, 2015
Varner, V. D., and C. M. Nelson. Cellular and physical mechanisms of branching morphogenesis. Development 141:2750–2759, 2014.
Varner, V. D., D. A. Voronov, and L. A. Taber. Mechanics of head fold formation: investigating tissue-level forces during early development. Development 137:3801–3811, 2010
Vernon, R. B., J. C. Angello, M. L. Iruela-Arispe, T. F. Lane, and E. H. Sage. Reorganization of basement membrane matrices by cellular traction promotes the formation of cellular networks in vitro. Lab. Invest. 66:536–547, 1992
Vining, K. H., and D. J. Mooney. Mechanical forces direct stem cell behaviour in development and regeneration. Nat. Rev. Mol. Cell Biol. 18:728–742, 2017
Vukicevic, S., H. K. Kleinman, F. P. Luyten, A. B. Roberts, N. S. Roche, and A. H. Reddi. Identification of multiple active growth factors in basement membrane Matrigel suggests caution in interpretation of cellular activity related to extracellular matrix components. Exp. Cell Res. 202:1–8, 1992
Wang, J.H.-C., and J.-S. Lin. Cell traction force and measurement methods. Biomech. Model. Mechanobiol. 6:361, 2007
Wang, Y.-L., and R. J. Pelham. Preparation of a flexible, porous polyacrylamide substrate for mechanical studies of cultured cells. Methods Enzymol. 298:489–496, 1998
Weaver, M., N. R. Dunn, and B. L. Hogan. Bmp4 and Fgf10 play opposing roles during lung bud morphogenesis. Development 127:2695–2704, 2000
Yu, J. C., and R. Fernandez-Gonzalez. Local mechanical forces promote polarized junctional assembly and axis elongation in Drosophila. eLife 5:e10757, 2016
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This work was supported by a grant from the National Institutes of Health (R01HL145147).
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Patil, L.S., Varner, V.D. Toward Measuring the Mechanical Stresses Exerted by Branching Embryonic Airway Epithelial Explants in 3D Matrices of Matrigel. Ann Biomed Eng 50, 1143–1157 (2022). https://doi.org/10.1007/s10439-022-02989-y
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DOI: https://doi.org/10.1007/s10439-022-02989-y