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 ([Formula: see text]) 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 ordinary differential equation (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 ([Formula: see text]), 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. Ataxia-Telangiectasia and RAD3-related (ATR) production rate dependent on damage ([Formula: see text]), p53 activation rate dependent on ATR ([Formula: see text]), p53-dependent Mdm2 production rate ([Formula: see text]), p53-dependent Wip1 production rate ([Formula: see text], ATR degradation rate ([Formula: see text]) and Mdm2-dependent p53 degradation rate ([Formula: see text], which shorten the delay time ([Formula: see text]), and brakes (e.g. ATR-dependent Mdm2 degradation rate ([Formula: see text]), self-degradation rate of Mdm2 ([Formula: see text]) and self-degradation rate of Wip1 ([Formula: see text]), which prolong it. Sensitivity analysis showed that as parameter values increase, [Formula: see text] becomes less sensitive to [Formula: see text]. The sensitivity to [Formula: see text] exhibited an initial increase followed by a decrease, whereas the opposite trend was observed for [Formula: see text]. The remaining parameters ([Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text]) 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.