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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