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 (ϵ) is increased (γ increases) and becomes constant after a certain value of ϵ. The permutation entropy spectra H(ϵ) for p53 and MDM2 as a function of ϵ are found to be different due to direct and indirect interaction of NO with respective proteins. We find γ versus ϵ for p53 and MDM2 to be similar in a deterministic approach but different in a stochastic approach, and the separation between γ of the respective proteins as a function of ϵ 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 ϵ but synchrony induced by it dominates in the moderate range of ϵ. Excess stress induces apoptosis.

Switching p53 states by calcium: dynamics and interaction of stress systems.

The integration of calcium and a p53-Mdm2 oscillator model is studied using a deterministic as well as a stochastic approach, to investigate the impact of a calcium wave on single cell dynamics and on the inter-oscillator interaction. The high dose of calcium in the system activates the nitric oxide synthase, synthesizing nitric oxide which then downregulates Mdm2 and influences drastically the p53-Mdm2 network regulation, lifting the system from a normal to a stressed state. The increase in calcium level switches the system to different states, as identified by the different behaviours of the p53 temporal dynamics, i.e. oscillation death to sustain the oscillation state via a mixed state of dampened and oscillation death states. Further increase of the calcium dose in the system switches the system from sustained to oscillation death state again, while an excess of calcium shifts the cell to an apoptotic state. Another important property of the calcium ion is its ability to behave as a synchronizing agent among the interacting systems. The time evolution of the p53 dynamics of the two diffusively coupled systems at stress condition via Ca(2+) shows synchronization between the two systems. The noise contained in the system interestingly helps the system to maintain its stabilized state (normal condition). However, noise has the tendency to destruct the synchronization effect, which means that it tries to restrict the system from external signals to maintain its normal condition. However, at the stress condition, the synchronization rate is found to be faster.

Stochastic synchronization of interacting pathways in testosterone model.

We examine the possibilities of various coupling mechanisms among a group of identical stochastic oscillators via Chemical Langevin formalism where each oscillator is modeled by stochastic model of testosterone (T) releasing pathway. Our results show that the rate of synchrony among the coupled oscillators depends on various parameters namely fluctuating factor, coupling constants [symbol; see text], and interestingly on system size. The results show that synchronization is achieved much faster in classical deterministic system rather than stochastic system. Then we do large scale simulation of such coupled pathways using stochastic simulation algorithm and the detection of synchrony is measured by various order parameters such as synchronization manifolds, phase plots etc and found that the proper synchrony of the oscillators is maintained in different coupling mechanisms and support our theoretical claims. We also found that the coupling constant follows power law behavior with the systems size (V) by [symbol; see text] ~ AV(-γ), where γ=1 and A is a constant. We also examine the phase transition like behavior in all coupling mechanisms that we have considered for simulation. The behavior of the system is also investigated at thermodynamic limit; where V → ∞, molecular population, N → ∞ but N/V → finite, to see the role of noise in information processing and found the destructive role in the rate of synchronization.

The enhancement of stability of p53 in MTBP induced p53-MDM2 regulatory network.

We have modeled an MTBP-MDM2-p53 regulatory network by integrating p53-MDM2 autoregulatory model (Proctor and Gray, 2008) with the effect of a cellular protein MTBP (MDM2 binding protein) which is allowed to bind with MDM2 (Brady et al., 2005). We study this model to investigate the activation of p53 and MDM2 steady state levels induced by MTBP protein under different stress conditions. Our simulation results in three approaches namely deterministic, Chemical Langevin equation and stochastic simulation of Master equation show a clear transition from damped limit cycle oscillation to fixed point oscillation during a certain time period with constant stress condition in the cell. This transition is the signature of transition of p53 and MDM2 levels from activated state to stabilized steady state levels. We present various phase diagrams to show the transition between unstable and stable states of p53 and MDM2 concentration levels and also their possible relations among critical value of the parameters at which the respective protein level reach stable steady states. In the stochastic approach, the dynamics of the proteins become noise induced process depending on the system size. We found that this noise enhances the stability of the p53 steady state level.

Intercellular synchronization of diffusively coupled Ca(2+) oscillators.

We examine the synchrony in the dynamics of localized [Ca(2 + )](i) oscillations among a group of cells exhibiting such complex Ca(2 + ) oscillations, connected in the form of long chain, via diffusing coupling where cytosolic Ca(2 + ) and inositol 1,4,5-triphosphate are coupling molecules. Based on our numerical results, we could able to identify three regimes, namely desynchronized, transition and synchronized regimes in the (T - k(e)) (time period-coupling constant) and (A - k(e)) (amplitude-coupling constant) spaces which are supported by phase plots (Δϕ verses time) and recurrence plots, respectively. We further show the increase of synchronization among the cells as the number of coupling molecules increases in the (T - k(e)) and (A - k(e)) spaces.

Intercellular synchronization of coupled smooth muscle cells via Ca2+ propagation.

The propagation of Ca2+ wave through gap junction in smooth muscle cell is studied as a function of electrical coupling parameter (g) modulated by Ca2+ level in the cell. The range of activation time of Ca2+ propagation with amplitude is found to increase as increase in electrical coupling parameter g, which is identified by increase in critical time of activation, T(F) as a function of g. Then identical Ca2+ oscillators are allowed to interact via electrical and diffusive coupling of Ca2+ ions diffused through gap junctions, and rate of intercellular synchronization among them is studied. The phase diagrams in (T(F) - g) and (T(F) - epsilon) parameter spaces separate oscillation death and damped oscillations regimes which correspond to deactivated and activated regimes of Ca2+ level. The effect of on T(F) is significantly very slow, however it enhances the rate of synchronization among the coupled oscillators. The increase in g comparatively slows down the rate of synchronization of the coupled oscillators as shown in the phase diagram in (epsilon - g) parameter space which separates desynchronized and synchronized regimes.

Measurement of phase synchrony of coupled segmentation clocks.

The temporal behavior of segmentation clock oscillations shows phase synchrony via mean field like coupling of delta protein restricting to nearest neighbors only, in a configuration of cells arranged in a regular three dimensional array. We found the increase of amplitudes of oscillating dynamical variables of the cells as the activation rate of delta-notch signaling is increased, however, the frequencies of oscillations are decreased correspondingly. Our results show the phase transition from desynchronized to synchronized behavior by identifying three regimes, namely, desynchronized, transition and synchronized regimes supported by various qualitative and quantitative measurements.