Global Stability and Tipping Point Prediction of the cell fate decision making model

This study investigates global stability and tipping point prediction in cell fate decision-making systems through non-equilibrium landscape flux theory. We demonstrate that cell fate dynamics are governed by the interplay between potential landscape and curl flux, where the landscape guides systems toward stable states while curl flux mediates transitions between them. Our analysis reveals that non-zero curl flux generates irreversible dominant pathways between multi-stable states. We identify several quantitative measures for transition prediction, including barrier heights, kinetic switching times, entropy production rates, and average flux. We introduce novel non-equilibrium early warning indicators based on time irreversibility of cross-correlations ({Delta}C), average flux, and entropy production rate. These indicators exhibit significant changes near bifurcations, enabling transition prediction before state stability loss, with superior predictive capability compared to traditional critical slowing down theory. The rotational nature of curl flux is shown to destabilize attractor states, providing a dynamical foundation for phase transitions in cell differentiation, reprogramming, and transdifferentiation processes. These findings advance our understanding of non-equilibrium dynamics in cell fate decisions and offer practical implications for stem cell research and regenerative medicine, potentially enabling more precise therapeutic strategies in stem cell applications.