Entrainment and multi-stability of the p53 oscillator in human cells.

The tumor suppressor p53 responds to cellular stress and activates transcription programs critical for regulating cell fate. DNA damage triggers oscillations in p53 levels with a robust period. Guided by the theory of synchronization and entrainment, we developed a mathematical model and experimental system to test the ability of the p53 oscillator to entrain to external drug pulses of various periods and strengths. We found that the p53 oscillator can be locked and entrained to a wide range of entrainment modes. External periods far from p53's natural oscillations increased the heterogeneity between individual cells whereas stronger inputs reduced it. Single-cell measurements allowed deriving the phase response curves (PRCs) and multiple Arnold tongues of p53. In addition, multi-stability and non-linear behaviors were mathematically predicted and experimentally detected, including mode hopping, period doubling, and chaos. Our work revealed critical dynamical properties of the p53 oscillator and provided insights into understanding and controlling it. A record of this paper's transparent peer review process is included in the supplemental information.