Mathematical models for the Notch and Wnt signaling pathways and the crosstalk between them during somitogenesis

Somitogenesis is a fundamental characteristic feature of development in various animal embryos. Molecular evidence has proved that the Notch and Wnt pathways play important roles in regulating the process of somitogenesis and there is crosstalk between these two pathways. However, it is difficult to investigate the detailed mechanism of these two pathways and their interactions in somitogenesis through biological experiments. In recent years some mathematical models have been proposed for the purpose of studying the dynamics of the Notch and Wnt pathways in somitogenesis. Unfortunately, only a few of these models have explored the interactions between them.

In this study, we have proposed three mathematical models for the Notch signalling pathway alone, the Wnt signalling pathway alone, and the interactions between them. These models can simulate the dynamics of the Notch and Wnt pathways in somitogenesis, and are capable of reproducing the observations derived from wet experiments. They were used to investigate the molecular mechanisms of the Notch and Wnt pathways and their crosstalk in somitogenesis through the model simulations.

Three mathematical models are proposed for the Notch and Wnt pathways and their interaction during somitogenesis. The simulations demonstrate that the extracellular Notch and Wnt signals are essential for the oscillating expressions of both Notch and Wnt target genes. Moreover, the internal negative feedback loops and the three levels of crosstalk between these pathways play important but distinct roles in maintaining the system oscillation. In addition, the results of the parameter sensitivity analysis of the models indicate that the Notch pathway is more sensitive to perturbation in somitogenesis.