Fig. 2

For τ = [0,20), the cell exists in the epithelial steady state where E-cadherin (e) level is high and both β-catenin (b) and Slug (s) are low. a If a small amount of Wnt signal is released by the microenvironment at τ = 20, a small amount of Dvl (d = 1.2) will accumulate at the membrane. E-cadherin will decrease slightly and both β-catenin and Slug will rise, but not enough to induce EMT. If, at τ = 50, the environment stops releasing Wnt signal, Dvl will detach from the membrane, meaning that the concentration of Dvl at the membrane will be 0 once again. Because EMT was not induced, the proteins all return to their initial epithelial values. b If enough Wnt signal is released by the microenvironment at τ = 20, enough Dvl will accumulate at the membrane (d = 5.4). The steady state values of β-catenin (b) and Slug (s) will rise and, thus, E-cadherin (e) will reach a very low steady state value. The lack of E-cadherin means that the cell will no longer be adhesive with the surrounding cells or its microenvironment, allowing it to move away from the primary tumor. If the concentration of membrane Dvl returns to 0 due to the cellular distance from the external Wnt signal at τ = 50, E-cadherin, β-catenin, and Slug will stabilize at values that allow the cell to maintain its mesenchymal state