Extended Data Fig. 6: Time evolution of cell adhesion complexes in MEF WT cells on elastic-like substrates (Kelvin-Voigt model).
(a, b) Time evolution of cell traction (P) and retrograde actin flow (v) calculated by solving the master-equation [Eq. (B10), SI] using the finite-difference method, starting from an initial configuration with zero molecular clutches between the cell and the substrate. Three different values of the substrate Young’s modulus (E) and viscosity coefficient (ξs) were tested: 100 Pa, 1 kPa, 10 kPa and 0 pN ⋅ s/nm, 1 pN ⋅ s/nm, 1000 pN ⋅ s/nm, respectively. The values of the other model parameters were the same as in the linear WT model, see Table T1, SI. In all cases, cell traction and retrograde actin flow rapidly reach steady-state values within 10-20 s, regardless of the substrate viscosity. (c) Probability distribution (pon) of molecular clutch extension (l) after 20 s of time evolution of the molecular clutch system, calculated for three different values of the Young’s modulus (E) and viscosity coefficient (ξs) of the substrate. The graph shows that the molecular clutch system reaches the steady-state probability distribution given by Eq. (9) in the main text within 20 s (yellow dashed lines), regardless of the substrate viscosity. (d) Time evolution of substrate deformation (xs). The graph shows that the characteristic relaxation time of the substrate strongly depends on its viscosity, but it has little effect on the rapid convergence of the probability distribution of molecular clutch extension, cell traction, and retrograde actin flow to their steady-state values for elastic-like substrates described by the Kelvin-Voigt model, see panels (a-c). (e) The characteristic relaxation time of retrograde actin flow obtained by fitting the curves shown in panel (b) to an exponential decay function as a function of the Young’s modulus and viscosity coefficient of the substrate. It can be seen that the characteristic relaxation time decreases with increasing Young’s modulus of the substrate. However, it is practically independent of the viscous properties of elastic-like substrates.
