Landscape and kinetic path quantify critical transitions in epithelial-mesenchymal transition.

Epithelial-mesenchymal transition (EMT), a basic developmental process that might promote cancer metastasis, has been studied from various perspectives. Recently, the early warning theory has been used to anticipate critical transitions in EMT from mathematical modeling. However, the underlying mechanisms of EMT involving complex molecular networks remain to be clarified. Especially, how to quantify the global stability and stochastic transition dynamics of EMT and what the underlying mechanism for early warning theory in EMT is remain to be fully clarified. To address these issues, we constructed a comprehensive gene regulatory network model for EMT and quantified the corresponding potential landscape. The landscape for EMT displays multiple stable attractors, which correspond to E, M, and some other intermediate states. Based on the path-integral approach, we identified the most probable transition paths of EMT, which are supported by experimental data. Correspondingly, the results of transition actions demonstrated that intermediate states can accelerate EMT, consistent with recent studies. By integrating the landscape and path with early warning concept, we identified the potential barrier height from the landscape as a global and more accurate measure for early warning signals to predict critical transitions in EMT. The landscape results also provide an intuitive and quantitative explanation for the early warning theory. Overall, the landscape and path results advance our mechanistic understanding of dynamical transitions and roles of intermediate states in EMT, and the potential barrier height provides a new, to our knowledge, measure for critical transitions and quantitative explanations for the early warning theory