Long-range paracrine coupling-induced Ca2+ patterns in two-dimensional cell networks under inositol 1,4,5-triphosphate-cytosolic Ca2+ interaction

A two-dimensional model is designed for intercellular calcium (Ca2+) waves in the presence of long-range (LR) paracrine coupling due to the action of extracellular messengers and Ca2+-activated degradation of inositol 1,4,5-triphosphate (IP3) by a 3-kinase. Using mean-field theory, a statistical variable is defined to detect the emergence of intercellular spiral waves of Ca2+. 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 IP3 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 IP3 degradation and stronger LR degree disintegrate spiral symmetry with increased hormonal stimulation. Strong IP3 degradation has the opposite effect.