Mathematical modelling of Wnt/β-catenin signalling

The Wnt/β-catenin pathway plays an important role in development and disease. Theoretical approaches have been used to describe this pathway and have provided intriguing insights into its signalling characteristics. In the present paper, we review mathematical models of the pathway. We focus on a quantitative kinetic model for canonical Wnt/β-catenin signalling describing the reactions of the pathway's core compounds [Lee, Salic, Krüger, Heinrich and Kirschner (2003) PLoS Biol. 1, 116–132]. Numerous modifications and further analyses with respect to signalling characteristics, transcriptional feedback and cross-talk were performed. In addition, the role of β-catenin in gene expression and cell–cell adhesion as well as spatial aspects of signalling are investigated in various theoretical models.