Fig. 2. Increases of average integrin cluster size and substrate stiffness contributed to lengthened lifetimes of integrin clusters.

(A) An integrin cluster could bind to a substrate of ECM proteins on its extracellular end and to actomyosin-based sarcomere-like contractile units (CUs) on its intracellular end. Each integrin molecule was modeled as one spring. (B) The ECM substrate to which the integrin cluster attached was modeled as a spring, and the dynamics of the integrin cluster–ECM substrate was modeled as a catch-slip bond that was pulled by CUs with a displacement boundary condition. (C) The lifetimes of α₅β₁ and α_vβ₃ integrin clusters changed differently with substrate stiffnesses. Talin/vinculin binding can enhance cluster lifetime. (D to E) Two important assumptions: force-mediated ligand binding rate increases and Kank-mediated unbinding rate changes. (F and G) With a limited displacement of CU-mediated pulling, the lifetime of integrin clusters on a stiff substrate (~100 kPa) is longer than that on an intermediate substrate (~1 kPa). (H and I) Integrin count at the initial of computation (N_int), and substrate stiffness (k_ecm) affects the average integrin count (N_b) during disassembly. (J and K) Integrin clusters can rupture at the edge of the cell and then slide with inward actin flow and later rebind to the substrate. The number of clustered integrins, W_t, was obtained from the number of clustered integrins, W_n, and the average number of integrins per cluster, W_a = 50. W_t increased with substrate stiffness to a plateau value. (L) A Hill function can be used to describe the relationship between W_t and substrate stiffness. (M) The Hill function can also describe the experimental data well (5, 32), which showed that the total clustered integrin increased with increasing stiffness. (N) Average integrin count (N_a) mainly influences the values of K and W_max parameters in the Hill function, while cluster number (M_a) only influences the values of the W_max parameter.