Figure 6.

Integrated α-catenin dimer concentration over the cell volume from the numerical solution of the whole model. This quantity is plotted as a function of the α-catenin influx $j_{\alpha }^{\text{0}}$ (A), the β-catenin degradation rate in the cytoplasm, r_β (B), and the rates of unbinding, $k_{\beta }^{\text{off}}$ (C), and binding , $k_{\beta }^{\text{on}}$ (D), of the β-catenin protein complex from and to the membrane. The same constants are used as in Fig. 4. In B, r^{m, d}_β = r_β is assumed. Contact inhibition occurs when the concentration of α-catenin dimers, C_αα, is large. The contact inhibition breaks down for low production, $j_{\alpha }^{\text{0}}$, of α-catenin (A) and for an increased degradation of β-catenin (B). It also breaks down for an increased membrane off rate (C), which corresponds to mutations of E-cadherins leading to less efficient formation of cell-cell E-cadherin bonds. This results in an insufficient trapping of β-catenins on the membrane in the presence of cell-cell contact. Finally, contact inhibition breaks down for small values of $k_{\beta }^{\text{on}}$ (D), which could correspond to a less efficient binding of β-catenin to the membrane due to a decreased expression of E-cadherins.