Table 1. State variables and initial conditions of the model.

Network components	Description	Initial Concentration	Initial number of molecules in simulations	References
	β-catenin in cytoplasm	20 nM	300	Tan et al, 2012
	destruction complex	60 nM	900	Choi et al, 2006
	Axin	20 nM	300	Tan et al, 2012
	APC	200 nM	3000	Estimated
	β-catenin bound destruction complex	4 nM	60	Choi et al, 2006
	GSK3	200 nM	3000	Tan et al, 2012
	APC/β-catenin complex	0.2 nM	3	Choi et al, 2006
	Axin/β-catenin complex	0.06 Nm	1	Choi et al, 2006
	Axin/APC complex	40 nM	600	Estimated
	CK1-phospho-β-catenin bound destruction complex	2 nM	30	Lee et al, 2003
	GSK3-phospho-β-catenin bound destruction complex	2 nM	30	Lee et al, 2003
	GSK3-phospho-β-catenin bound inactive-destruction complex	6 nM	90	Estimated
	inactive destruction complex	60 nM	900	Estimated
	active β-catenin	2 nM	30	Tan et al, 2012
	free cadherin on membrane surfaces	E-cad: depends on adhesion condition; N-cad: 0	E-cad: depends on adhesion condition; N-cad: 0	Tan et al, 2012
	cadherin/β-catenin complex	E-cad: depends on adhesion condition; N-cad: 0	E-cad: depends on adhesion condition; N-cad: 0	Tan et al, 2012
	cadherin/β-catenin complex in Golgi	60 nM	900	Estimated
	Wnt/receptors complex	0	0
	ABC/Bcl9 Complex	0.2 nM	30	Estimated
	ABC/Bcl9 Complex	0.2 nM	30	Estimated
	ABC/Bcl9/TCF Complex	0.2 nM	30	Estimated
	β-catenin/destruction complex bound Wnt/receptor Complex	0	0
	Wnt/receptor bound destruction complex	0	0
	Wnt/receptor bound destruction complex with CK1-phospho-β-catenin	0	0
	Wnt/receptor bound destruction complex with GSK3-phospho-β-catenin	0	0
	cadherin/β-catenin complex in trans-dimer	E-cad: depends on adhesion condition; N-cad: 0	E-cad: depends on adhesion condition; N-cad: 0
	cadherin/β-catenin in cis-cluster	E-cad: depends on adhesion condition; N-cad: 0	E-cad: depends on adhesion condition; N-cad: 0
	cadherin in trans-dimer	E-cad: depends on adhesion condition; N-cad: 0	E-cad: depends on adhesion condition; N-cad: 0
	cadherinin cis-cluster	E-cad: depends on adhesion condition; N-cad: 0	E-cad: depends on adhesion condition; N-cad: 0