Inhibitors play a significant role in the monitoring of cellular pathways. In this investigation, we evaluate the impact of p53 protein production in the CycD/Cdk4(6) subsystem. This protein assumes a crucial role in the regulation of cellular processes, including DNA repair, cell quiescence, and apoptosis. The occurrence of these processes takes place during the \(\hbox {G}_\textbf{1}\) phase, which represents the growth stage of a cell. Although the expression of the p53 protein is not fully understood, it is known to be pulsatile and produced in response to DNA damage. As a result, the severity of cell DNA damage directly affects the level of p53 protein expression within the cell system. To further comprehend the cancerous activity of a cell in this subsystem, we have developed a novel mathematical model for the behaviour of the CycD/CDK4(6) subsystem. Our observations reveal that the system exhibits a Hopf-bifurcation, which is consistent with laboratory findings. In addition to the mathematical analysis, we have also conducted simulations of the cell processes, which successfully mimic the results obtained in the laboratory. We hope that this model will contribute to a deeper understanding of the impact of the p53 protein on cellular processes in averting oncogenic activities.
