Nonlinear dynamics of inositol 1,4,5-trisphosphate-induced Ca ^{2 +} patterns in two-dimensional cell networks with paracrine signaling interaction

Two-dimensional Ca^{2 +} oscillations are investigated in a cell network in the presence of bidirectional paracrine signaling interactions. The proposed model relies on Ca^{2 +}-induced Ca^{2 +} release, in which Ca^{2 +}-stimulated degradation of inositol 1,4,5-triphosphate (IP₃) by a3-kinase plays a significant role. Via predictions from the synchronization factor R in the parameter domain, the propagation of intercellular Ca^{2 +} wave is numerically studied. Large values of external stimulus are required for weak paracrine coupling to support synchronization, while the latter takes place for strong coupling when the hormonal stimulus is weak. Moreover, the rate of linear leak of Ca^{2 +} from the endoplasmic reticulum to the cytosol favors synchronous states when the paracrine coupling is weak. Considering particularly weak values of the synchronization factor, importance is given to the effect of paracrine signaling. Different scenarios are recorded, especially the appearance of spiral Ca^{2 +} waves and their disintegration to turbulent patterns under strong paracrine coupling. Additionally, weak paracrine coupling gives rise to target Ca^{2 +} waves. It is also reported that a suitable balance between the IP₃ degradation and the cell’s degree of stimulus is necessary for the robustness of spiral waves to be effective under appropriate paracrine coupling strength.