  The Notch pathway plays a vital role in determining whether cells in the
intestinal epithelium adopt a secretory or an absorptive phenotype. Cell fate
specification is coordinated via Notch's interaction with the canonical Wnt
pathway. Here, we propose a new mathematical model of the Notch and Wnt
pathways, in which the Hes1 promoter acts as a hub for pathway crosstalk.
Computational simulations of the model can assist in understanding how healthy
intestinal tissue is maintained, and predict the likely consequences of
biochemical knockouts upon cell fate selection processes. Chemical reaction
network theory (CRNT) is a powerful, generalised framework which assesses the
capacity of our model for monostability or multistability, by analysing
properties of the underlying network structure without recourse to specific
parameter values or functional forms for reaction rates. CRNT highlights the
role of beta-catenin in stabilising the Notch pathway and damping oscillations,
demonstrating that Wnt-mediated actions on the Hes1 promoter can induce
dynamical transitions in the Notch system, from multistability to
monostability. Time-dependent model simulations of cell pairs reveal the
stabilising influence of Wnt upon the Notch pathway, in which beta-catenin- and
Dsh-mediated action on the Hes1 promoter are key in shaping the subcellular
dynamics. Where Notch-mediated transcription of Hes1 dominates, there is Notch
oscillation and maintenance of fate flexibility; Wnt-mediated transcription of
Hes1 favours bistability akin to cell fate selection. Cells could therefore
regulate the proportion of Wnt- and Notch-mediated control of the Hes1 promoter
to coordinate the timing of cell fate selection as they migrate through the
intestinal epithelium and are subject to reduced Wnt stimuli.
