  We study the temporal and the synchronous behaviours in p53-Mdm2 regulatory
network due to the interaction of its complex network components with the
nitric oxide molecule. In single cell process, increase in nitric oxide
concentration gives rise the transition to various p53 temporal behaviours,
namely fixed point oscillation, damped oscillation and sustain oscillation
indicating stability, weakly activated and strongly activated states. The noise
in stochastic system is found to help to reach these states much faster as
compared to deterministic case which is evident from permutation entropy
dynamics. In coupled system with nitric oxide as diffusively coupling molecule,
we found nitric oxide as strong coupling molecule within a certain range of
coupling strength \epsilon beyond which it become weak synchronizing agent. We
study these effects by using correlation like synchronization indicator \gamma
obtained from permutation entropies of the coupled system, and found five
important regimes in (\epsilon-\gamma) phase diagram, indicating
desynchronized, transition, strongly synchronized, moderately synchronized and
weakly synchronized regimes respectively. We claim that there is the
competition between the toxicity and the synchronizing role of nitric oxide
that lead the cell in different stressed conditions.
