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.
Immune cells such as natural killer (NK) cells migrate with high speeds of several μm/min through dense tissue, but the traction forces are unknown. We present a method to measure dynamic traction forces of fast migrating cells in non-linear biopolymer matrices. We find that NK cells display bursts of large traction forces that increase with matrix stiffness and facilitate migration through tight constrictions.
We describe a technique for simultaneous quantification of the contractile forces and cytosolic calcium dynamics of muscle fibers embedded in three-dimensional biopolymer gels. We derive a scaling law for linear elastic matrices such as basement membrane extract hydrogels (Matrigel) that allows us to measure contractile force from the shape of the relaxed and contracted muscle cell and the Young's modulus of the matrix, without further knowledge of the matrix deformations surrounding the cell and without performing computationally intensive inverse force reconstruction algorithms. We apply our method to isolated mouse flexor digitorum brevis (FDB) fibers that are embedded in 10 mg/ml Matrigel. Upon electrical stimulation, individual FDB fibers show twitch forces of 0.37 µN ± 0.15 µN and tetanic forces (100 Hz stimulation frequency) of 2.38 µN ± 0.71 µN, corresponding to a tension of 0.44 kPa ± 0.25 kPa and 2.53 kPa ± 1.17 kPa, respectively. Contractile forces of FDB fibers increase in response to caffeine and the troponin-calcium-stabilizer Tirasemtiv, similar to responses measured in whole muscle.From simultaneous high-speed measurements of cell length changes and cytosolic calcium concentration using confocal line scanning at a frequency of 2048 Hz, we show that twitch and tetanic force responses to electric pulses follow the low-pass filtered calcium signal. In summary, we present a technically simple high speed and high throughput method for measuring contractile forces and cytosolic calcium dynamics of single muscle fibers. We expect that our method will help to reduce preparation time, costs, and the number of sacrificed animals needed for experiments such as drug testing. Statement of significanceWe describe a high speed, high throughput method for the simultaneous measurement of contractile force and cytoplasmic calcium dynamics following electrical pulse stimulation of muscle fibers embedded in a 3-dimensional biopolymer matrix. In contrast to the classical approach of attaching muscle fibers to a force-transducer, our method allows for a highly efficient, parallel analysis of large numbers of fibers under different treatment conditions.
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