Figure 4.

(a) Plot of the type 1 family talin concentration A_Iϕ₁(w₀x)/K_m for parameter values taken from Table 1. (Dashed curve) Approximate analytical solution with c = 0 (see the Supporting Material). Otherwise, numerical solutions and thick curves corresponding to type 1 solutions of the β_∞ model coincide on the scale of the figure. (Thin curve) Asymptotic expansion of the analytical solution given by Eq. S10 in the Supporting Material. It shows that asymptotic results are already reliable even if $\sqrt{D/b}=0.28w_0$ as in the case of this figure. Color-code (from the top to the bottom curve) indicates that 1/2βk_bh₀² decreases stepwise (15, 7.5, 4.5 to 3), with the largest value in green. (b) Plot of the type 2 family solutions A_Iϕ₂(w₀x)/K_m. (Dashed curves) Numerical solutions. Thick and dashed curves coincide when ϕ₃^∗ goes to zero smoothly as |x| goes to infinity. (Circles) Boundary points x₀ for type 2 solutions where the solution passes through the singularity of the β_∞ model. Decreasing h₀ changes the solution until it matches a type 1 solution at the bifurcation point. The color code (from the top to the bottom curve) for panel b is the same as for panel a. (c) Plot of the density of engaged integrin n_b(w₀x) for centered type 1 and type 2 solutions for the same parameters (½βk_bh₀² = 4.5). For convenience, type 1 solutions have been scaled down by a factor 10 (w₀ = 10 μm).