Long-range paracrine coupling-induced Ca^{2+} patterns in two-dimensional cell networks under inositol 1,4,5-triphosphate-cytosolic Ca^{2+} interaction.

A two-dimensional model is designed for intercellular calcium (Ca^{2+}) waves in the presence of long-range (LR) paracrine coupling due to the action of extracellular messengers and Ca^{2+}-activated degradation of inositol 1,4,5-triphosphate (IP_{3}) by a 3-kinase. Using mean-field theory, a statistical variable is defined to detect the emergence of intercellular spiral waves of Ca^{2+}. The latter are generated by the local heterogeneity caused by asymmetrical stimulation of the network. It is confirmed that spiral waves may develop when the synchronization degree is low. It is found that balanced LR coupling and IP_{3} degradation, under appropriate external hormonal stimulation, can effectively control the creation and propagation of spiral waves. A higher LR degree disrupts network synchronization, and only specific ranges of stimulation factor support spiral waves. Weak IP_{3} degradation and stronger LR degree disintegrate spiral symmetry with increased hormonal stimulation. Strong IP_{3} degradation has the opposite effect.