Propagation and Synchronization of Ca2+ Spiral Waves in Excitable Media

Ca spiral wave is observed in a large number of cell types. Based on a Ca model presented by Atri et al., the propagation and synchronization of the intracellular Ca spiral waves are numerically studied and some interesting results are obtained. (i) The largest Lyapunov exponents versus bifurcation parameter is calculated to investigate the oscillation of Ca and it is found that almost all of the largest Lyapunov exponents are negative except for some others that are very close to zero (with an order of magnitude about 10−4 to 10−5). (ii) The two controllable parameters — the concentration of inositol 1,4,5-trisphosphate (IP3) and the diffusion coefficient — play an important role in inducing and supporting the rotating spiral wave, and the critical thresholds for supporting Ca spiral wave are identified by calculating the statistical factor of synchronization in two-dimensional space. (iii) The driving layer (layer-1) can activate the Ca oscillations in the driven layer (layer-2), and Ca spiral wave in the driven layer can also be developed to synchronize the Ca spiral wave in the drive with appropriate coupling intensity no matter whether mono-directional or mutual coupling of Ca is being used. (iv) An optimal synchronization is observed for an intermediate amount of noise in the presence of Gaussian white noise, and for this noise amount, the Ca waves in the two layers reach complete synchronization most quickly, it is a resonance-like behavior due to noise.