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Three-dimensional force microscopy of cells in biopolymer networks


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.

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Figure 1: Macrorheology of collagen type I gels and semi-affine model description.
Figure 2: Experimental validation of the constitutive equation for collagen gels.
Figure 3: Reconstruction of cellular forces inside a 1.2–mg ml−1 collagen gel.
Figure 4: Contractility of MDA-MB-231 cells in gels with different collagen concentrations.
Figure 5: Time-lapse force microscopy of a breast carcinoma cell inside collagen gel.


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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.

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Authors and Affiliations



J.S., B.F., S.M., I.T., N.L. and K.S. designed the setup and performed the experiments; J.S., C. Metzner and K.E.A. developed the material model and mathematical tools; J.S., C. Metzner and C. Mark wrote the data-acquisition and analysis software; J.S., S.M. and B.F. wrote the article.

Corresponding author

Correspondence to Julian Steinwachs.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

Supplementary Notes 1–21 (PDF 7969 kb)

Supplementary Software

Unconstrained force reconstruction software as used in the manuscript. (ZIP 19048 kb)

Time lapse video of force density of an MEF cell over 22h

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 video of force densities of 20 MDA-MB-231 cells over 2h

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)

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

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