Synchronization in stress p53 network

We study transition of the temporal behaviours of $p53$ and $MDM2$ in a stress p53-MDM2-NO regulatory network induced by a bioactive molecule $NO$ (Nitric Oxide). We further study synchronization among a group of identical stress systems arranged in a 3D array with nearest neighbour diffusive coupling. The role of $NO$ and the effect of noise are investigated. In the single system study, we found three distinct types of temporal behaviour of $p53$ , namely oscillation death, damped oscillation and sustained oscillation, depending on the amount of stress induced by $NO$ , indicating how $p53$ responds to incoming stress. The correlation among coupled systems increases as the value of the coupling constant ( $\epsilon$ ) is increased ( $\gamma$ increases) and becomes constant after a certain value of $\epsilon$ . The permutation entropy spectra $H(\epsilon )$ for $p53$ and $MDM2$ as a function of $\epsilon$ are found to be different due to direct and indirect interaction of $NO$ with respective proteins. We find $\gamma$ versus $\epsilon$ for $p53$ and $MDM2$ to be similar in a deterministic approach but different in a stochastic approach, and the separation between $\gamma$ of the respective proteins as a function of $\epsilon$ decreases as system size increases. The role of $NO$ is found to be two-fold: stress induced by NO is prominent at small and large values of $\epsilon$ but synchrony induced by it dominates in the moderate range of $\epsilon$ . Excess stress induces apoptosis.