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

Abstract

Nonlinear excitations of ${\mathrm{C}\mathrm{a}}^{2+}$ 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 ${\mathrm{C}\mathrm{a}}^{2+}$ 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 $\left(G^{\prime }/G\right)$-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.

Keywords:

• Modulational instability
• calcium waves
• paracrine signaling
• spiral waves

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

CBT has received research grant from the Botswana International University of Science and Technology [grant number DVC/RDI/2/1/16I (25)]. CBT also thanks the Kavli Institute for Theoretical Physics (KITP), University of California Santa Barbara (USA), where this work was supported in part by the National Science Foundation [grant number NSF PHY-1748958], and the Gordon and Betty Moore Foundation [grant number 2919.01].