Oscillating two-dimensional Ca2+ waves in cell networks with bidirectional paracrine signaling

Abstract

Nonlinear excitations of Ca2+ waves are investigated in a two-dimensional cell network with bidirectional paracrine signaling, both in the longitudinal and transversal directions. The semi-discrete approximation is used to show that the dynamics of the intercellular Ca2+ waves can be reduced to complex Ginzburg–Landau equations, depending on the high- or low-frequency regime. The onset of modulational instability is addressed, where the instability features of the low- and high-frequency modes are compared via the instability growth rate. The (G′/G)-expansion method is employed to find analytically spiral-like wave solutions for the two dynamical regimes. Their response to the effect of paracrine coupling is also addressed.