Table 1.

Parameter Definitions for ODE Model

Parameter	Definition	Units	Assumed Value	Source
α1	Basal production of E-cadherin	$\frac{\mathit{nM}}{\mathit{min}}$	0.01	estimated
α2	Basal production of β-catenin	$\frac{\mathit{nM}}{\mathit{min}}$	0.01	[13]
α3	Basal production of Slug	$\frac{\mathit{nM}}{\mathit{min}}$	0.001	estimated
β1	Basal degradation of E-cadherin	$\frac{1}{\mathit{min}}$	0.03	estimated
β2	Rate at which β-catenin binds to the GSK-3β / Axin/APC complex	$\frac{1}{\mathit{min}}$	0.03	estimated
β3	Basal degradation of Slug	$\frac{1}{\mathit{min}}$	0.03	estimated
k 0	Rate at which Dvl inactivates the GSK-3β/Axin/ APC complex	$\frac{\mathit{nM}}{\mathit{min}}$	3.7 ∙ 10−3	estimated
k 1	Rate at which E-cadherin sequesters β-catenin at the cell membrane	$\frac{\mathit{nM}}{\mathit{min}}$	0.01	estimated
k 2	Rate at which β-catenin upregulates Slug in the cell nucleus	$\frac{\mathit{nM}}{\mathit{min}}$	1	estimated
IC S	Half maximal concentration of Slug required to inhibit E-cadherin transcription	nM	3.3	estimated
IC B	Half maximal concentration of β-catenin needed up upregulate Slug	nM	0.33	estimated
IC E	Half maximal concentration of E-cadherin needed for sequestration of β-catenin at membrane	nM	0.033	estimated
IC D	Half maximal concentration of Dvl needed to inhibit the degradation of β-catenin by GSK-3β	nM	0.67	estimated
n 1	Hill Coefficient	–	3	estimated
n 2	Hill Coefficient	–	2	estimated
n 3	Hill Coefficient	–	2	estimated
n 4	Hill Coefficient	–	5	estimated