Fig. 5
From: A Theoretical Model of the Wnt Signaling Pathway in the Epithelial Mesenchymal Transition
In each subfigure, Dvl (d) is varied along the x-axis. Along the y-axis, the nondimensional parameters A 1 (a), A 2 (b), A 3 (c), C 1 (d), C 2 (e), C 3 (f), F 1 (g), F 2 (h), n 1 (i), n 2 (j), n 3 (k), n 4 (l) are varied one at a time. For those parameter values where the cell begins in Region I and remains in Region I, or crosses L1 into Region II, as Dvl (d) is increased, the cell is committed to the epithelial steady state. For those parameter values where the cell begins in Region III and remains in Region III, or crosses L2 into Region II, as Dvl changes, the cell is committed to the mesenchymal steady state. For parameter values that allow the cell to begin in region two, the starting steady state depends on the system’s initial conditions. If the cell begins in the epithelial steady state and crosses L2 into Region III with a change in Dvl (d), the cell will switch to the mesenchymal steady state. If the cell begins in the mesenchymal steady state in Region II and crosses L1 into Region I with changes in Dvl (d), the cell will switch to the epithelial steady state. The parameter values used in this system are marked with a dashed line. In this model, the cell begins in Region II with epithelial initial conditions