Fig. 5: Bistability of cell adhesion.

a,b, Stability diagrams of the linear KD (a) and linear WT (b) models. Three-dimensional red shapes and triangles denote the bistability regions and their projections, respectively. Yellow cylinders represent the model parameter ranges corresponding to MEF Talin 1 KO, Talin 2 shRNA and MEF WT cells. The blue dotted contour in a indicates a cross section of the bistability region detailed in c. Notably, talin-deficient MEF cells lie close to this region, whereas MEF WT cells are far from it, indicating that the high elasticity of talin stabilizes NAs and FAs. c, Close-up of a cross section of the bistability region indicated in a. Its boundaries are formed by the trajectories of the two saddle-node points shown in d. The bistability region arises from a cusp-type catastrophe when the rigidity of the intracellular part of molecular clutches is sufficiently large. d, Cusp catastrophe experienced by the molecular-clutch system. The pale green surface depicts cell traction (P) as a function of the retrograde actin flow (v) and substrate elasticity (E) in the linear KD model. The solid and dashed curves denote the stable and unstable branches of the solution for different myosin II densities (σ_m). Reducing σ_m to ~44 μm⁻² results in the appearance of two saddle-node bifurcation points, a typical sign of a cusp catastrophe. Further decreasing σ_m shifts these points along the surface, outlining an instability region that includes only the unstable branches of cell traction curves. e,f, Stability diagrams of cell adhesion complexes in the case of MEF Talin 1 KO, Talin 2 shRNA cells (e) and MEF WT cells (f) obtained by projecting the bistability regions shown in a and b onto the horizontal plane. The black, red and blue solid curves mark the onset of the cusp catastrophe and bifurcations due to saddle-node points moving to infinity, which lead to the formation of biphase–monophase boundaries (green dotted curves), which affect the shapes of cell traction curves both within and beyond the bistability region. The insets around the bistability region illustrate representative cell traction curves within each domain. The graphs show that the elasticity of the intracellular part of molecular clutches and the myosin II density have a profound effect on the mechanosensitive behaviour of cell adhesion.