Uncovering dual oscillatory regimes in p53-mdm2 dynamics: A data-driven modeling approach with implications for...

Quantifying the dynamic interplay between p53 and Mdm2 is critical for uncovering their roles in cancer suppression and therapeutic targeting. Experimental studies have shown that p53-Mdm2 interactions exhibit oscillatory behavior in response to DNA damage. However, several mathematical models fail to sustain these oscillations or do not fit well with the experimental data, instead converging to constant steady-state values of p53 and Mdm2, which is unrealistic. In this study, we develop a simple yet robust ordinary differential equation model that accurately quantifies different stable periodic solutions (limit cycles) for p53-Mdm2 dynamics. Specifically, using a two-step numerical calibration algorithm, we validate the model against four experimental datasets. The calibrated model fits the data well and reveals two distinct oscillatory regimes: one in which Mdm2 oscillates with an amplitude 2.67 times greater than that of p53, suggesting a strongly amplified feedback response, and another in which Mdm2 exhibits variable but consistently lower-amplitude oscillations relative to p53. The observed variability in oscillatory behavior may support tumor suppression by enabling context-dependent activation of p53 targets, allowing cells to fine-tune stress responses.