Extended Data Fig. 3: Effect of the elasticity of the intracellular part of molecular clutches on cell adhesion.
(a, b) Graphs of the cell traction and retrograde actin flow curves calculated using the linear WT model for various values of the spring constant (kc) describing the elastic properties of the intracellular part of molecular clutches. The solid curves denote stable branches of the graphs, and the dashed curves indicate unstable branches, see Extended Data Fig. 1 for details. It can be seen from the plots that the spring constant kc has a strong influence on the cell adhesion behaviour in the case of rigid substrates (E > 10 kPa), while there is almost no change on soft substrates (E ≤ 10 kPa). In addition, the figure shows that in the case of stiff molecular clutches (kc > 2.6 pN/nm), the molecular clutch system undergoes bifurcation, leading to bistability of the cell traction and retrograde actin flow curves on rigid substrates. To demonstrate the bifurcation, the model parameter values used in the calculations were the same as for the case of low fibronectin density (1 μg/ml) shown in Fig. 3(a) in the main text. (c) Representative trajectories demonstrating the time evolution of the molecular clutch system obtained by solving the master equation [Eq. (B10), SI] for points A, B and C (kc = 5 pN/nm) shown in panel (b) by using stochastic simulations and finite-difference calculations. From the plot it can be seen that if at low values of Young’s modulus of the substrate (E < 2 MPa) there is a unique stationary solution that attracts trajectories to its neighborhood (point A), then at higher values of Young’s modulus (E > 2 MPa) there is a pair of such stationary solutions (points B and C), which indicates the bistable behaviour of the molecular clutch system. Notably, stochastic simulations demonstrate that both strong and weak cell adhesion states corresponding to points B and C are very stable and can last for many minutes without experiencing stochastic transitions between each other.
