Fig 1.
Main steps in TFM analyses and associated influential factors.
Fig 2.
Visualization of the in-silico testcase: A cell deforming a substrate with finite size.
Fig 3.
A) Reference traction field applied to the substrate, simulating a cell with 25 focal adhesions. The white arrows indicate the in-plane direction of the resulting traction force of each FA. B) Displacement field of the substrate surface resulting from the applied tractions. Both fields are plotted in the deformed configuration for material A and ν = 0.499.
Fig 4.
A) Stress-Stretch response for uniaxial tension (UA), pure shear (PS) and equibiaxial tension (EB) deformation modes for neo-Hookean (Material A, blue) and Ogden (Material B, red) materials for ν = 0.499. B) Displacement magnitude within each FA measured in the in-silico test-case plotted against traction. Reported are means (diamond shaped marker) with minima and maxima (errorbar) of each FA for the computations with both materials A (blue) and B (red).
Fig 5.
The relation between fluorescent markers distance (L0) and the quantity of fluorescent markers that are positioned within a focal adhesion (nFA).
Reported results have been evaluated numerically for 25000 elliptical focal adhesions (2μm x 1μm). The black solid line marks the average, the area shaded in grey the maximum and minimum.
Fig 6.
Magnitude of the reconstructed traction stress field for an in-silico generated displacement field on material A, with a displacement measurement resolution of L0 = 0.5μm.
Fig 7.
Example of the reference and reconstructed traction fields in the region of a single focal adhesion.
The white contour marks the border of the FA as defined in the in-silico model. The total traction force of the FA is plotted in both cases with a black arrow, whereas the white cross-shaped marker indicates the location with the highest traction stress within the FA.
Fig 8.
Detail of the applied (A)) and reconstructed (B)) traction field (x ∈ [0 6.5]μm, y ∈ [−15 −8.5]μm) with material A (ν = 0.499) for different displacement field resolutions and interpolation schemes.
The white contours indicate the borders of the FAs.
Fig 9.
Effect of different displacement field resolutions and interpolation methods for material A (ν = 0.499).
Reported are mean and standard deviation for 5 testcase repetitions (N = 125 FAs).
Fig 10.
Effect of noise affected displacement vectors (Gaussian noise, 30nm standard deviation) for different displacement measurement resolutions for material A (ν = 0.499), solid red line.
The results for the noise-free case are shown in blue. Reported are mean and standard deviation for 5 testcase repetitions (N = 125 FAs).
Fig 11.
Comparison of the traction reconstruction quality measures for the reconstruction including the out-of-plane displacement field on the substrate surface (3D applied displacement field, continuous bars) and without (2D applied displacement field, dashed bars).
The comparison is shown for a substrate of material A (ν = 0.499) and original traction fields with different out-of-plane traction angles: 10° (blue color) and 45° (red color).
Fig 12.
Principal Stretches λ2 (green cloud) and λ3 (violet cloud) vs. λ1 for the in-silico computation for material A and B.
The color intensity is proportional to the frequency. The solid, dashed and dotted lines indicate the relations of λ2(λ1) and λ3(λ1) for the cases of uniaxial tension, pure shear and equibiaxial deformation modes, respectively.
Fig 13.
Reconstruction quality measures against nominal focal adhesion traction stress tReal for material A and B with ν = 0.499.
Reported is mean (solid line) and standard deviation (shaded area) for N = 25.
Fig 14.
Influence of noise on the reconstruction for compressible (ν = 0.45, red bars) and nearly incompressible (ν = 0.499, blue bars) substrates.
The results are presented normalized to the respective noise free cases to highlight the relative change induced by the noise. Note that the same volumetric behaviour (νRec = νReal) was assumed for generating the test case and its reconstruction.
Fig 15.
Comparison of the reconstructed traction force (TMR) and traction stress peaks (PTR) of single FAs with different traction magnitude for the linear TFM and the fully non-linear TFM for materials A and B.
Reported is mean (solid line) and standard deviation (shaded area) for N = 25.
Fig 16.
A) Traction stress field reconstruction (resolution L0 = 1μm) achieved by additionally accounting for FA position and shape (constrained method). The same region as reported in Fig 8 is shown. B) and C) Comparison of the performance of the unconstrained (blue) and constrained (red) reconstruction scheme for the noise free case and Material A. Reported are mean and standard deviation for 5 testcase repetitions (N = 125 FAs).
Fig 17.
Cross-section of the substrate (dark grey, xz-plane) underneath the focal adhesion (coloured half-ellipse), highlighting the deformation and surface wrinkling under increasing FA traction tRef.