Jia Ya

Breakup of Spiral Waves in Coupled Hindmarsh–Rose Neurons

Breakup of spiral wave in the Hindmarsh–Rose neurons with nearest-neighbour couplings is reported. Appropriate initial values and parameter regions are selected to develop a stable spiral wave and then the Gaussian coloured noise with different intensities and correlation times is imposed on all neurons to study the breakup of spiral wave, respectively. Based on the mean field theory, the statistical factor of synchronization is defined to analyse the evolution of spiral wave. It is found that the stable rotating spiral wave encounters breakup with increasing intensity of Gaussian coloured noise or decreasing correlation time to certain threshold.

Effects of Nonlinear Time-Delay on a Stochastic Asymmetric System

We numerically investigate the effects of nonlinear time-delay on the stochastic system. With the delay time increasing, it is found that the peak of probability distribution in low steady states is decreased, and the peak of probability distribution in high steady states is increased. The mean of state variable, the normalized variance, and the normalized autocorrelation function which quantifies the concentrated degree are slowly varied for small delay time. However, the mean of state variable is rapidly increased, and the normalized variance and the normalized autocorrelation function is rapidly decreased for large delay time.

Noise-Induced Bursting and Coherence Resonance in Minimal Cytosolic Ca2+ Oscillation Model

A stochastic calcium oscillation model based on the minimal calcium oscillation model is investigated by numerical computation. When the extracellular stimulation is sub-threshold and random, the oscillations of cytosolic calcium show complex behaviour: a bursting-like phenomenon induced by noise, that is, the phase of glomerate spikes are separated by phase of quiescence (but fluctuations in the baseline values of calcium with small amplitude during the silent phase), in a pattern that occurs at irregular intervals. By using the histogram of interspike intervals of calcium concentration spikes, it is found that the noise-induced coherence resonance phenomenon occurs at the cellular level.

A mathematical model of a P53 oscillation network triggered by DNA damage

Taking the interaction between a DNA damage repair module, an ATM module, and a P53–MDM2 oscillation module into account, this paper presents a mathematical model of a P53 oscillation network triggered by a DNA damage signal in individual cells. The effects of the DNA damage signal and the delay time of P53-induced MDM2 expression on the behaviours of the P53 oscillation network are studied. In the oscillatory state of the P53–MDM2 oscillator, it is found that the pulse number of P53–P oscillation increases with the increase of the initial DNA damage signal, whereas the amplitude and the period of P53–P oscillation are fixed for different initial DNA damage signals, and the period numbers of P53–P oscillations decrease with the increase of time delay of MDM2 expression induced by P53. These theoretical predictions are consistent with previous experimental results. The combined negative feedback of P53–MDM2 with the time delay of P53-induced MDM2 expression causes oscillation behaviour in the P53 network.

Theoretical Study on Drift of Ca 2+ Spiral Waves Controlled by Electric Field

Based on the Tang–Othmer Ca2+ model, the drift behavior of intracellular Ca2+ spiral waves under the influence of weak electric field is investigated. Numerical results show that the dependence of drift velocity of the spiral tip on dc electric field is similar to experimental observations in BZ system. When an ac electric field is applied, interesting resonant-drift phenomenon is observed with ω = 2Ω0. All results can be explained analytically using a proximate method.

A Coarse Estimation of Cell Size Region from a Mesoscopic Stochastic Cell Cycle Model

Based on a deterministic cell cycle model of fission yeast, the effects of the finite cell size on the cell cycle regulation in wee1− cdc25Δ double mutant type are numerically studied by using of the chemical Langevin equations. It is found that at a certain region of cell size, our numerical results from the chemical Langevin equations are in good qualitative agreement with the experimental observations. The two resettings to the G2 phase from early stages of mitosis can be induced under the moderate cell size. The quantized cycle times can be observed during such a cell size region. Therefore, a coarse estimation of cell size is obtained from the mesoscopic stochastic cell cycle model.

Can a Correlation Ratchet Operate Under Spatial Symmetry and Temporal Symmetry

The simplest imaginable ratchet system which cantains two noises correlated with each other is discussed. It is found that (1) the correlation between noises can induce transport, even when the ratchet potential is completely symmetric in space and the driving forcing is symmetric in time, and (2) the system can exhibit a current in either direction, and the direction can be controlled by the intensity of the correlation between noises.

A NOVEL PHASE TRANSITION PHENOMENON IN BISTABLE SYSTEM

A bistable system driven by additive noise and multiplicative noise is studied, when the correlation time of the correlations between two noises is nonzero. It is found that the system undergoes a succession of two phase transitions as the strength of the correlations between two noises increases.

Cooperative Effects of Noise and Coupling on Stochastic Dynamics of a Membrane-Bulk Coupling Model

Based on a membrane-bulk coupling cell model proposed by Gomez–Marin et al. [Phys. Rev. Lett. 98 (2007) 168303], the cooperative effects of noise and coupling on the stochastic dynamical behavior are investigated. For parameters in a certain region, the oscillation can be induced by the cooperative effect of noise and coupling. Whether considering the coupling or not, corresponding coherence resonance phenomena are observed. Furthermore, the effects of two coupling parameters, cell size L and coupling intensity κ, on the noise-induced oscillation of membranes are studied. Contrary effects of noise are found in and out of the deterministic oscillatory regions.

Coupling Effect of Ion Channel Clusters on Calcium Signalling

Based on a modified intracellular Ca2+ model involving diffusive coupling of two calcium ion channel clusters, the effects of coupling on calcium signalling are numerically investigated. The simulation results indicate that the diffusive coupling of clusters together with internal noise determine the calcium dynamics of single cluster, and for either homogeneous or heterogeneous coupled clusters, the synchronization of clusters, which is important to calcium signalling, is enhanced by the coupling effect.