wnt -- shuttle model for Wnt signaling pathway

The cannonical Wnt/beta-catenin signaling pathway is important for essential cellular functions such as development, homeostasis, and is implicated in many diseases [MacLean, Rosen, Byrne, Harrington]. The Wnt shuttle model includes an abstraction of the signal transduction pathway [Gross, Harrington, Rosen, Sturmfels].

i1 : wnt()

o1 = X_1-->X_2
     X_2-->X_1
     X_2-->X_3
     X_2+X_4-->Y_4
     Y_4-->X_2+X_4
     Y_4-->X_2+X_5
     X_5+X_8-->Y_6
     Y_6-->X_5+X_8
     Y_6-->X_4+X_8
     X_4+Y_0-->Y_8
     Y_8-->X_4+Y_0
     Y_8-->X_4
     0-->Y_0
     Y_0-->0
     Y_0-->Y_1
     X_3+X_6-->Y_5
     Y_5-->X_3+X_6
     Y_5-->X_3+X_7
     X_7+X_9-->Y_7
     Y_7-->X_7+X_9
     Y_7-->X_6+X_9
     X_6+Y_1-->Y_9
     Y_9-->X_6+Y_1
     Y_9-->X_6
     Y_1-->0
     Y_1-->Y_0
     Y_1+Y_2-->Y_3
     Y_3-->Y_1+Y_2
     X_3-->X_2
     X_5-->X_7
     X_7-->X_5

o1 : ReactionNetwork

In the Wnt shuttle model, the symbols used in the chemical reactions have the following meaning:

X_1 - X_3: dishevelled species; X_4 - X_7: destruction complex (APC/Axin/GSK3 beta); X_8 - X_9: phosphatase; Y_0 - Y_1: beta-catenin; Y_2: transcription factor; Y_3 - Y_9: intermediate complex; 0: empty set;

For more details see Algebraic Systems Biology: A Case Study for the Wnt Pathway: Gross, Harrington, Rosen, Sturmfels.

To rename species, use substitute(ReactionNetwork,List).