  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.
