Table 1 Parameters and their default values for the model

k₁

Synthesis of HOTAIR

0.2 nM•min^− 1

[23, 28]

k₂

Degradation of HOTAIR

0.1 min^− 1

[23, 28]

V₃

Inhibition of WIF-1 synthesis

1 nM•min^− 1

[23, 28]

k_+ 4

Inhibition of Wnt synthesis

1 nM^− 1•min^− 1

[23, 28]

k_− 4

Dissociation of WIF-1 from the [WIF-1.Wnt] complex

1 min^− 1

[20]

k_+ 5

Binding of LRP5/6 to Fzl to form [LRP5/6.Fzl]

0.1 nM^− 1•min^− 1

[30,31,32]

k_− 5

Dissociation of [LRP5/6] into LRP5/6 and Fzl

1 min^− 1

[30,31,32]

k_+ 6

Binding of Wnt to [LRP5/6.Fzl] to form [Wnt.LRP5/6.Fzl]

1 nM^− 1•min^− 1

[30,31,32]

k₋₆

Dissociation of [Wnt.LRP5/6.Fzl] into Wnt and [LRP5/6. Fzl]

1 min^− 1

[30,31,32]

k_+ 7

Binding of LRP5/6 to Axin to form [LRP5/6.Axin]

1 nM^− 1•min^− 1

[30,31,32]

k₋₇

Dissociation of [LRP5/6.Axin] into LRP5/6 and Axin

1 min^− 1

[30,31,32]

k₈

Activation of Dsh

0.182 min^− 1

[30,31,32]

k₉

Deactivation of Dsh

0.0182 min^− 1

[30,31,32]

k₁₀

Dissociation of GSK3 from the destruction complex

0.05 nM^− 1•min^− 1

[30,31,32]

k_+ 11

Binding of GSK3 to [Axin.APC] to form [GSK3. APC.Axin]

0.0909 nM^− 1•min^− 1

[30,31,32]

k_− 11

Dissociation of [GSK3.APC.Axin] into GSK3 and [Axin.APC]

100 min^− 1

[30,31,32]

k_+ 12

Phosphorylation of Axin and APC

0.267 min^− 1

[30,31,32]

k_− 12

Dephosphorylation of Axin and APC

1 min^− 1

[30,31,32]

k_+ 13

Binding of APC to Axin to form [APC.Axin]

1 nM^− 1•min^− 1

[30,31,32]

k_− 13

Dissociation of [APC.Axin] into APC and Axin

100 min^− 1

[30,31,32]

k_+ 14

Binding of β-catenin to [GSK3.APC*.Axin*] to form [GSK3.APC*.Axin*.β-catenin]

120 nM^− 1•min^− 1

[30,31,32]

k_− 14

Dissociation of [GSK3.APC*.Axin*.β-catenin] into β-catenin and [GSK3.APC*.Axin*]

1 min^− 1

[30,31,32]

k₁₅

Phosphorylation of β-catenin

206 min^− 1

[30,31,32]

k₁₆

Dissociation of phosphorylated β-catenin

0.5 min^− 1

[30,31,32]

k₁₇

Degradation of phosphorylated β-catenin

0.417 min^− 1

[30,31,32]

k₁₈

Synthesis of Axin

8.22*10^− 5 nM•min^− 1

[30,31,32]

k₁₉

Degradation of Axin

0.167 min^− 1

[30,31,32]

k_+ 20

Binding of APC to β-catenin to form [APC.β-catenin]

1 nM^− 1•min^− 1

[30,31,32]

k_− 20

Dissociation of [APC.β-catenin] into APC and β-catenin

120 min^− 1

[30,31,32]

k₂₁

Synthesis of β-catenin

0.423 nM•min^− 1

[30,31,32]

k₂₂

Degradation of β-catenin

0.000257 min^− 1

[30,31,32]

k_+ 23

Binding of TCF to β-catenin to form [TCF.β-catenin]

2 nM^− 1•min^− 1

[30,31,32]

k_− 23

Dissociation of [TCF.β-catenin] into TCF and β-catenin

20 min^− 1

[30,31,32]

k₂₄

Synthesis of Axin induced by [TCF.β-catenin]

0.02 min^− 1

[30,31,32]

k₂₅

Synthesis of MMP-13

0.1 nM•min^− 1

[21]

k₂₆

Degradation of MMP-13

0.1 min^− 1

[21]

V₂₇

Activation of MMP-13 synthesis

0.1 nM•min^− 1

[21]

K₃

Inhibition constant of WIF-1 by HOTAIR

0.1 nM

[23, 28]

K₈

Activation constant of Dsh by Wnt

10 nM

[30, 31]

K₂₇

Activation constant of MMP-13 by [TCF.β-catenin]

1 nM

[21]

m₃

Degree of cooperativity of repression of WIF-1 expression by HOTAIR

4

[23, 28]

m₂₇

Degree of cooperativity of activation of MMP-13 expression by [TCF.β-catenin]

4

[23, 28]

Wnt

Initial concentration of Wnt

10 nM

[30, 31, 33]

Fzl

Initial concentration of Fzl

10 nM

[30, 31, 33]

WIF-1

Initial concentration of WIF-1

10 nM

[30, 31, 33]

Dsh

Initial concentration of Dsh

100 nM

[30, 31, 33]

APC

Initial concentration of APC

100 nM

[30, 31, 33]

TCF

Initial concentration of TCF

15 nM

[30, 31, 33]

GSK3

Initial concentration of GSK3

50 nM

[30, 31, 33]