Systems-Level Mathematical Modeling of Cell Cycle Regulation, DNA Damage Response, and Repair Kinetics: A Unifying Dynamical Framework

The preservation of genomic stability requires precise coordination between cell cycle progression, DNA damage response (DDR) mechanisms, and structural repair kinetics. While individual subsystems have been extensively studied, their dynamic integration into discrete cell fate decisions remains highly complex. This paper presents a comprehensive systems-level mathematical framework that unifies the Novak-Tyson bistable mitotic engine, the ATM/ATR-p53-MDM2-Wip1 sensory network, and the clearance kinetics of non-homologous end joining (NHEJ) and homologous recombination (HR). By coupling non-linear ordinary and delay differential equations, the model demonstrates how continuous genotoxic stress is decoded into excitable, digital p53 pulses. These signals are dynamically translated via the p21 checkpoint gate into a tripartite bifurcating landscape of macroscopic cell fates: transient cell cycle arrest with successful recovery, permanent senescence, or programmed apoptosis. Ultimately, this unified quantitative model establishes a predictive computational foundation for analyzing cancer-associated mutations and optimizing targeted combination therapies.