The role of time delays in P53 gene regulatory network stimulated by growth factor

In this paper, a delayed mathematical model for the P53-Mdm2 network is developed. The P53-Mdm2 network we study is triggered by growth factor instead of DNA damage and the amount of DNA damage is regarded as zero. We study the influences of time delays, growth factor and other important chemical reaction rates on the dynamic behaviors in the system. It is shown that the time delay is a critical factor and its length determines the period, amplitude and stability of the P53 oscillation. Furthermore, as for some important chemical reaction rates, we also obtain some interesting results through numerical simulation. Especially, S (growth factor), k(3) (rate constant for Mdm2(p) dephospho rylation), k(10) (basal expression of PTEN) and k(14) (Rate constant for PTEN-induced Akt dephosphorylation) could undermine the dynamic behavior of the system in different degree. These findings are expected to understand the mechanisms of action of several carcinogenic and tumor suppressor factors in humans under normal conditions.