Analysis of the regulation of model parameters on Delay Time in the p53 dynamical response to Single-Stranded Breaks

The dynamic p53 response is a known determinant of cell fate. However, its temporal control, specifically the mechanisms regulating the delay time (t d ) of the graded p53 pulse following single-stranded breaks (SSBs), remains poorly understood. To systematically dissect this timing mechanism, we developed and analyzed a mechanistic ODE model of the p53-Mdm2-ATR network. We first established that increasing damage intensity reliably shortens the delay time, accelerating the cellular decision-making process. Our analysis revealed a critical finding: the delay time is most acutely sensitive to the p53-dependent Mdm2 production rate(β 3 ), highlighting the dominant role of the negative feedback loop in setting the pace. We further classified the model parameters into functional roles: accelerators (e.g., ATR production rate dependent on damage(β 1 ), p53 activation rate dependent on ATR(β 2 ),p53-dependent Mdm2 production rate(β 3 ), p53-dependent Wip1 production rate(β 4 ), ATR degradation rate(α 1 ) and Mdm2-dependent p53 degradation rate(α 2 )), which shorten the delay time(t d ), and brakes (e.g.,ATR-dependent Mdm2 degradation rate(α 4 ),self-degradation rate of Mdm2(α 5 ) and self-degradation rate of Wip1(α 6 )), which prolong it. Sensitivity analysis showed that as parameter values increase, t d becomes less sensitive to β 4 . The sensitivity to α 2 exhibited an initial increase followed by a decrease, whereas the opposite trend was observed for β 2 . The remaining parameters (β 1 , β 3 , α 1 , α 4 ,α 5 ,α 6 ) all showed a monotonic decrease in sensitivity. This work provides a quantitative blueprint for therapeutic interventions, suggesting that targeting the p53-Mdm2 feedback strength is the most effective strategy to sensitize cancer cells and shorten the critical delay to cell death.