Figure 5.

Distinct regions in parameter space are distinguished by their dependence on ligand binding. (A) A bifurcation diagram of adhesion area A with respect to [Ligand] is given, showing branches of stable (solid lines) and unstable (dashed lines) steady states separated by thresholds of transcritical bifurcation points (open circles). Decreasing K_on from 0.7 (black lines) to 0.3 (gray lines) shifts the transcritical bifurcation point to the left, allowing for the unclustered stable steady state to be attained at [Ligand] = 0. (B) Two-parameter bifurcation of adhesion area A with respect to [Ligand] and K_on is given, showing the boundary (black line) between the regions of unclustered (region 1) and clustered steady states lying below and above the boundary, respectively. The region of clustered steady states is further divided into three regions: region 2, defined by [Ligand]^‡ > 0, requiring the presence of both ligand and integrin to induce clustering; region 3, defined by [Ligand]^‡ < 0 with A₀ < 0, requiring the presence of integrin, but not necessarily ligand, to form stable adhesion plaques; and the unphysiological region 4, defined by A₀ > 0, which exhibits clustering irrespective of integrin or ligand densities.