Quantifying the total mechanical tractions within aggregates of cells using microsphere traction force microscopy (MTFM)

Quantitative measurements of cell-generated mechanical forces have mostly been limited to two-dimensional substrates. While recent advances in three-dimensional measurements have provided useful insight, they have been limited to single-cell studies or only provide information on the local variations in these forces. Here we present the development of a force measurement method that uses cell-sized, compressible and elastic hydrogel microspheres (with diameters of 5-50 µm) as force sensors, thereby providing a solid cell-gel interface to promote natural cell-like interactions, and allowing measurements of nominal values of the cell-exerted forces, due to their inherent compressibility. In the analysis of the microsphere deformations, we use a boundary spectral method based on spherical harmonics decomposition of the traction field on the gel surface. Using the technique developed here, we quantify the total active traction profiles that aggregates of mammalian cells exert on the boundary of synthetic spherical hydrogel bodies and report the stress profiles within tumor-cell spheroids.