Extended Data Fig. 4: Cell traction, retrograde actin flow and time evolution of NAs in cells grown on elastic-like and liquid-like substrates.

(a-c) Quasi-steady-state cell traction (a) and retrograde actin flow (b), as well as the dynamics of NA growth (c) in the case where large-scale substrate deformations are represented by the Maxwell model (liquid-like substrate) and the Kelvin-Voigt model (elastic-like substrate), respectively. It can be seen that in the case of liquid-like substrates, the model predicts that cell traction increases, and retrograde actin flow decreases with increasing viscosity of liquid-like substrates, which is in good agreement with previously published experimental data shown in the figure that were digitalized from ref. ⁷³. Furthermore, maturation of NAs is greatly hampered in the case of low-viscosity liquid-like substrates compared to elastic-like substrates due to the slower accumulation of vinculin in NAs, which is also consistent with previous experimental data⁷³ (from left to right N = 11, 12, 17 samples, data are presented as mean ± SD). The calculations were performed for E = 1 MPa Young’s modulus of the substrate. The results shown in panels (a-c) were obtained by numerically solving the master equation [Eq. (I1) and Eq. (I3), SI] describing the time evolution of the molecular clutch system using the finite-difference method. The values of the model parameters used in the calculations were the same as in Table T1 and Table T4, SI.