Modelling Coupled Oscillations in the Notch, Wnt, and FGF Signaling Pathways during Somitogenesis: A Comprehensive Mathematical Model

Somite formation in the early stage of vertebrate embryonic development is controlled by a complicated gene network named segmentation clock, which is defined by the periodic expression of genes related to the Notch, Wnt, and the fibroblast growth factor (FGF) pathways. Although in recent years some findings about crosstalk among the Notch, Wnt, and FGF pathways in somitogenesis have been reported, the investigation of their crosstalk mechanisms from a systematic point of view is still lacking. In this study, a more comprehensive mathematical model was proposed to simulate the dynamics of the Notch, Wnt, and FGF pathways in the segmentation clock. Simulations and bifurcation analyses of this model suggested that the concentration gradients of both Wnt, and FGF signals along the presomitic mesoderm (PSM) are corresponding to the whole process from start to stop of the segmentation clock. A number of highly sensitive parameters to the segmentation clock's oscillatory pattern were identified. By further bifurcation analyses for these sensitive parameters, and several complementary mechanisms in respect of the maintenance of the stable oscillation of the segmentation clock were revealed.