Stability analysis of Wnt-ERK cellular signalling by using Nyquist criterion

We have previously reported an analysis method for intracellular signal transduction systems by using Nyquist criterion in which we provided a proof-of-principle study with the Goodwin oscillator as a simple model that is a three-dimensional small system with a negative feedback regulation. In this study, we try to apply our method based on Nyquist criterion to a practical cancer cell signalling model on the Wnt-ERK pathway that is a 31-dimensional ordinary differential equation system with the six multiple feedback regulations. In this study, two different feedback loops that are mediated by a same signalling molecule are investigated. By applying our method to the analysis of each feedback loop independently, the effect of them on the stability of the whole system is compared.