Figure 4.

Cytosolic concentration profiles of β-catenin (A), α-catenin (B), and α-catenin dimers (C) resulting from the reaction-diffusion system described by Eqs. 1a–1d, with the boundary conditions without cell-cell contact (Eq. 6) or with cell-cell contact (Eq. 7), as functions of the distance from the center of a cell with spherical symmetry. The different parameters are as follows. The Golgi apparatus of the cell is located at r₀ = 1 μm and the total radius of the cell is R = 10 μm. The β-catenin influx is j⁰_β = 5.0 μm μM s⁻¹. The diffusion constants of α- and β-catenin are equal to 1 μm² s⁻¹, and the one for α-catenin dimers is 0.5 μm² s⁻¹ (30). In these plots, the reaction rate of α-catenin with β-catenin is 0.01 μM⁻¹ s⁻¹, and that of α-catenin with itself is 0.005 μM⁻¹ s⁻¹ (31). The protein degradation rates of α-catenin and β-catenin are equal to 10⁻³ s⁻¹, and the consumption and degradation rates of α-catenin dimers are 0.5 × 10⁻³ s⁻¹. Finally, the membrane binding and unbinding rates, k^on_β and k^off_β, of the β-catenin protein complex are equal to 1 μm s⁻¹ and 1 s⁻¹, respectively.