Dynamics of stress p53: Nitric oxide induced transition of states and synchronization

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.