These cell forces can be measured with traction force microscopy which inverts the equations of elasticity theory to calculate them from the deformations of soft polymer substrates .

Here we have introduced a novel method to reconstruct cellular forces from the deformation of elastic substrates .

Compared to earlier studies that used truss models to evaluate a few stress fiber tensions on pillar arrays [43,44], we have implemented this procedure for cells on flat elastic substrates with hundreds of FAs.

Forces at FAs have been measured with traction force microscopy (TFM) on soft elastic substrates [8—10], pillar arrays [11,12], and fluorescent force sensors [13—18].

Active cable models have been shown to correctly predict shapes of adherent cells on micro-patterned substrates and yield force distributions that are robust with respect to local changes in network geometry or topography [45].

Substrates used in our experiments are isotropic with a Young's modulus of several kPa.

The elastic problem is stated as a boundary value problem (BVP), where cellular traction stress defines the boundary condition at the substrate’s top surface.

Polyacrylamide substrates for traction force microscopy

Polyacrylamide (PAA) substrates containing far-red fluorescent microbeads (Invitrogen, d = 40 nm) were prepared on glass coverslips using previously published methodslo’37.

Data for three representative UZOS-cells on soft elastic polyacrylamide substrates (E = 8.4 kPa).