Table 1 Parameter Definitions for ODE Model
From: A Theoretical Model of the Wnt Signaling Pathway in the Epithelial Mesenchymal Transition
Parameter | Definition | Units | Assumed Value | Source |
|---|---|---|---|---|
α1 | Basal production of E-cadherin | \( \frac{nM}{\mathit{\min}} \) | 0.01 | estimated |
α2 | Basal production of β-catenin | \( \frac{nM}{\mathit{\min}} \) | 0.01 | [13] |
α3 | Basal production of Slug | \( \frac{nM}{\mathit{\min}} \) | 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 | \( \frac{nM}{\mathit{\min}} \) | 3.7 ∙ 10−3 | estimated |
k 1 | Rate at which E-cadherin sequesters β-catenin at the cell membrane | \( \frac{nM}{\mathit{\min}} \) | 0.01 | estimated |
k 2 | Rate at which β-catenin upregulates Slug in the cell nucleus | \( \frac{nM}{\mathit{\min}} \) | 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 |