We describe a technique for the quantitative measurement of cell-generated forces in highly nonlinear three-dimensional biopolymer networks that mimic the physiological situation of living cells. We computed forces of MDA-MB-231 breast carcinoma cells from the measured network deformations around the cells using a finite-element approach based on a constitutive equation that captures the complex mechanical properties of diverse biopolymers such as collagen gels, fibrin gels and Matrigel. Our measurements show that breast carcinoma cells cultured in collagen gels generated nearly constant forces regardless of the collagen concentration and matrix stiffness. Furthermore, time-lapse force measurements showed that these cells migrated in a gliding motion with alternating phases of high and low contractility, elongation, migratory speed and persistence.
This is a preview of subscription content, access via your institution
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Rent or buy this article
Prices vary by article type
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Friedl, P., Zanker, K.S. & Brocker, E.B. Cell migration strategies in 3-D extracellular matrix: differences in morphology, cell matrix interactions, and integrin function. Microsc. Res. Tech. 43, 369–378 (1998).
Zaman, M.H. et al. Migration of tumor cells in 3D matrices is governed by matrix stiffness along with cell-matrix adhesion and proteolysis. Proc. Natl. Acad. Sci. USA 103, 10889–10894 (2006).
Friedl, P. & Wolf, K. Proteolytic interstitial cell migration: a five-step process. Cancer Metastasis Rev. 28, 129–135 (2009).
Friedl, P., Wolf, K. & Lammerding, J. Nuclear mechanics during cell migration. Curr. Opin. Cell Biol. 23, 55–64 (2011).
Koch, T.M., Muenster, S., Bonakdar, N., Buttler, J.P. & Fabry, B. 3D traction forces in cancer cell invasion. PLoS ONE 7, e33476 (2012).
Lämmermann, T. et al. Rapid leukocyte migration by integrin-independent flowing and squeezing. Nature 453, 51–55 (2008).
Dembo, M. & Wang, Y.L. Stresses at the cell-to-substrate interface during locomotion of fibroblasts. Biophys. J. 76, 2307–2316 (1999).
Butler, J.P., Tolic-Norrelykke, 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).
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).
Legant, W.R. et al. Multidimensional traction force microscopy reveals out-of-plane rotational moments about focal adhesions. Proc. Natl. Acad. Sci. USA 110, 881–886 (2013).
Legant, W.R. et al. Measurement of mechanical tractions exerted by cells in three-dimensional matrices. Nat. Methods 7, 969–971 (2010).
Storm, C., Pastore, J.J., MacKintosh, F.C., Lubensky, T.C. & Janmey, P.A. Nonlinear elasticity in biological gels. Nature 435, 191–194 (2005).
Arevalo, R.C., Urbach, J.S. & Blair, D.L. Size-dependent rheology of type-I collagen networks. Biophys. J. 99, L65–L67 (2010).
Münster, 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).
Voytik-Harbin, S.L., Roeder, B.A., Sturgis, J.E., Kokini, K. & Robinson, J.P. Simultaneous mechanical loading and confocal reflection microscopy for three-dimensional microbiomechanical analysis of biomaterials and tissue constructs. Microsc. Microanal. 9, 74–85 (2003).
Vader, D., Kabla, A., Weitz, D. & Mahadevan, L. Strain-induced alignment in collagen gels. PLoS ONE 4, e5902 (2009).
Roeder, B.A., Kokini, K. & Voytik-Harbin, S.L. Fibril microstructure affects strain transmission within collagen extracellular matrices. J. Biomech. Eng. 131, 031004 (2009).
Brown, A.E., Litvinov, R.I., Discher, D.E., Purohit, P.K. & Weisel, J.W. Multiscale mechanics of fibrin polymer: gel stretching with protein unfolding and loss of water. Science 325, 741–744 (2009).
Onck, P.R., Koeman, T., van Dillen, T. & van der Giessen, E. Alternative explanation of stiffening in cross-linked semiflexible networks. Phys. Rev. Lett. 95, 178102 (2005).
Heussinger, C., Schaefer, B. & Frey, E. Nonaffine rubber elasticity for stiff polymer networks. Phys. Rev. E 76, 031906 (2007).
Stein, A.M., Vader, D.A., Weitz, D.A. & Sander, L.M. The micromechanics of three-dimensional collagen-I gels. Complexity 16, 22–28 (2011).
Sheinman, M., Broedersz, C.P. & MacKintosh, F.C. Nonlinear effective-medium theory of disordered spring networks. Phys. Rev. E 85, 021801 (2012).
Stylianopoulos, T. & Barocas, V.H. Volume-averaging theory for the study of the mechanics of collagen networks. Comput. Methods Appl. Mech. Eng. 196, 2981–2990 (2007).
Licup, A.J. et al. Stress controls the mechanics of collagen networks. Proc. Natl. Acad. Sci. USA 112, 9573–9578 (2015).
Kraning-Rush, C.M., Carey, S.P., Califano, J.P., Smith, B.N. & Reinhart-King, C.A. The role of the cytoskeleton in cellular force generation in 2D and 3D environments. Phys. Biol. 8, 015009 (2011).
Lautscham, L.A. et al. Migration in confined 3D environments is determined by a combination of adhesiveness, nuclear volume, contractility, and cell stiffness. Biophys. J. 109, 900–913 (2015).
Lang, N.R. et al. Estimating the 3D pore size distribution of biopolymer networks from directionally biased data. Biophys. J. 105, 1967–1975 (2013).
Metzner, C. et al. Superstatistical analysis and modelling of heterogeneous random walks. Nat. Commun. 6, 7516 (2015).
Mickel, W. et al. Robust pore size analysis of filamentous networks from 3D confocal microscopy. Biophys. J. 95, 6072–6080 (2008).
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).
Engler, A. et al. Substrate compliance versus ligand density in cell on gel responses. Biophys. J. 86, 617–628 (2004).
Reinhart-King, C.A., Dembo, M. & Hammer, D.A. The dynamics and mechanics of endothelial cell spreading. Biophys. J. 89, 676–689 (2005).
Bonakdar, N. et al. Biomechanical characterization of a desminopathy in primary human myoblasts. Biochem. Biophys. Res. Commun. 419, 703–707 (2012).
Faust, U. et al. Cyclic stress at mHz frequencies aligns fibroblasts in direction of zero strain. PLoS ONE 6, e28963 (2011).
Kollmannsberger, P. & Fabry, B. High-force magnetic tweezers with force feedback for biological applications. Rev. Sci. Instrum. 78, 114301 (2007).
Nelder, J.A. & Mead, R. A simplex method for function minimization. Comput. J. 7, 308–313 (1965).
Huber, P.J. Robust Statistics (John Wiley & Sons, 1981).
Tikhonov, A.N. Solution of incorrectly formulated problems and the regularization method. Soviet Mathematics Doklady 4, 1035–1038 (1963).
Hersch, N. et al. The constant beat: cardiomyocytes adapt their forces by equal contraction upon environmental stiffening. Biol. Open 2, 351–361 (2013).
We thank J.P. Butler (Harvard University) for helpful discussions and for developing a method to locate the force epicenter from a 3D vector field, and we thank P. Strissel (University Clinics Erlangen) for help with Matrigel experiments. We acknowledge E. Wagena (Radboud University Nijmegen) for generating dual-color HT1080 fibrosarcoma cells, which were a gift from K. Wolf (Radboud University Nijmegen, the Netherlands). This work was supported by the German Research Foundation (DFG) Research Training Group 1962 “Dynamic Interactions at Biological Membranes: From Single Molecules to Tissue,” the US National Institutes of Health (NIH-HL65960) and the Emerging Fields Initiative of the University of Erlangen–Nuremberg.
The authors declare no competing financial interests.
Supplementary Notes 1–21 (PDF 7969 kb)
Unconstrained force reconstruction software as used in the manuscript. (ZIP 19048 kb)
Time lapse image series showing force density around a primary MEF cell migrating inside a collagen gel over a time course of 22h. After 10h, the cell divides, which is associated with a strong but temporary reduction of traction forces. After division, the daughter cells migrate in opposite directions in a persistent gliding motion characterized by synchronous changes in elongation and contractility. (MOV 4116 kb)
Time lapse image series showing force density, morphology and motility of 20 MDA-MB-231 breast carcinoma cells inside a collagen gel recorded over 2h. Red arrows indicate the local force density. Green lines indicate the long and short axes of the cell. The intersection of the green lines coincides with the center of mass of the cell. Note that in general the highly mobile cells show large contractile forces and an elongated cell shape. (MOV 4749 kb)
About this article
Cite this article
Steinwachs, J., Metzner, C., Skodzek, K. et al. Three-dimensional force microscopy of cells in biopolymer networks. Nat Methods 13, 171–176 (2016). https://doi.org/10.1038/nmeth.3685
This article is cited by
AMPK is a mechano-metabolic sensor linking cell adhesion and mitochondrial dynamics to Myosin-dependent cell migration
Nature Communications (2023)
Nature Communications (2023)
Nature Reviews Bioengineering (2023)
Nature Reviews Molecular Cell Biology (2023)
Cellular and Molecular Bioengineering (2023)