  Dynamics of p53 is known to play important roles in the regulation of cell fate decisions in response to various stresses, and PDCD5 functions as a co-activator of p53 to modulate the p53 dynamics. In the present paper, we investigate how p53 dynamics are modulated by PDCD5 during the DNA damage response using methods of bifurcation analysis and potential landscape. Our results reveal that p53 activities can display rich dynamics under different PDCD5 levels, including monostability, bistability with two stable steady states, oscillations, and co-existence of a stable steady state and an oscillatory state. Physical properties of the p53 oscillations are further shown by the potential landscape, in which the potential force attracts the system state to the limit cycle attractor, and the curl flux force drives the coherent oscillation along the cyclic. We also investigate the effect of PDCD5 efficiency on inducing the p53 oscillations. We show that Hopf bifurcation is induced by increasing the PDCD5 efficiency, and the system dynamics show clear transition features in both barrier height and energy dissipation when the efficiency is close to the bifurcation point. This study provides a global picture of how PDCD5 regulates p53 dynamics via the interaction with the p53-Mdm2 oscillator and can be helpful in understanding the complicate p53 dynamics in a more complete p53 pathway. 
Bifurcation analysis and potential landscape of the p53-Mdm2 oscillator   regulated by the co-activator PDCD5