Department of Physics, Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
Thomas J Grundy
Children's Cancer Research Unit, The Children's Hospital at Westmead, Sydney, Australia; School of Medical Sciences and Children’s Hospital at Westmead Clinical School, University of Sydney, Sydney, Australia
Pamela L Strissel
Department of Gynecology and Obstetrics, Laboratory for Molecular Medicine, University Hospital Erlangen, Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
David Böhringer
Department of Physics, Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
Nadine Grummel
Department of Physics, Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
Richard Gerum
Department of Physics, Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
Julian Steinwachs
Department of Physics, Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
Carolin C Hack
Department of Gynecology and Obstetrics, Laboratory for Molecular Medicine, University Hospital Erlangen, Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
Matthias W Beckmann
Department of Gynecology and Obstetrics, Laboratory for Molecular Medicine, University Hospital Erlangen, Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
Markus Eckstein
Institute of Pathology, University Hospital Erlangen, Erlangen, Germany
Reiner Strick
Department of Gynecology and Obstetrics, Laboratory for Molecular Medicine, University Hospital Erlangen, Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
Geraldine M O'Neill
Children's Cancer Research Unit, The Children's Hospital at Westmead, Sydney, Australia; School of Medical Sciences and Children’s Hospital at Westmead Clinical School, University of Sydney, Sydney, Australia
Ben Fabry
Department of Physics, Friedrich-Alexander University Erlangen-Nürnberg, Erlangen, Germany
We describe a method for quantifying the contractile forces that tumor spheroids collectively exert on highly nonlinear three-dimensional collagen networks. While three-dimensional traction force microscopy for single cells in a nonlinear matrix is computationally complex due to the variable cell shape, here we exploit the spherical symmetry of tumor spheroids to derive a scale-invariant relationship between spheroid contractility and the surrounding matrix deformations. This relationship allows us to directly translate the magnitude of matrix deformations to the total contractility of arbitrarily sized spheroids. We show that our method is accurate up to strains of 50% and remains valid even for irregularly shaped tissue samples when considering only the deformations in the far field. Finally, we demonstrate that collective forces of tumor spheroids reflect the contractility of individual cells for up to 1 hr after seeding, while collective forces on longer timescales are guided by mechanical feedback from the extracellular matrix.
