Landscape and flux quantify the stochastic transition dynamics for p53 cell fate decision.

The p53 transcription factor is a key mediator in cellular responses to various stress signals including DNA repair, cell cycle arrest, and apoptosis. In this work, we employ landscape and flux theory to investigate underlying mechanisms of p53-regulated cell fate decisions. Based on a p53 regulatory network, we quantified the potential landscape and probabilistic flux for the p53 system. The landscape topography unifies and quantifies three cell fate states, including the limit cycle oscillations (representing cell cycle arrest), high p53 state (characterizing apoptosis), and low p53 state (characterizing the normal proliferative state). Landscape and flux results provide a quantitative explanation for the biphasic dynamics of the p53 system. In the oscillatory phase (first phase), the landscape attracts the system into the ring valley and flux drives the system cyclically moving, leading to cell cycle arrest. In the fate decision-making phase (second phase), the ring valley shape of the landscape provides an efficient way for cells to return to the normal proliferative state once DNA damage is repaired. If the damage is unrepairable with larger flux, the system may cross the barrier between two states and switch to the apoptotic state with a high p53 level. By landscape-flux decomposition, we revealed a trade-off between stability (guaranteed by landscape) and function (driven by flux) in cellular systems. Cells need to keep a balance between appropriate speed to repair DNA damage and appropriate stability to survive. This is further supported by flux landscape analysis showing that flux may provide the dynamical origin of phase transition in a non-equilibrium system by changing landscape topography.