Minimal model of calcium dynamics in two heterogeneous coupled cells

© 2018 Elsevier B.V. Intercellular calcium (Ca2+) waves are an important signalling mechanism in a wide variety of cells within the body, crucial for cellular coordination and control. In order to investigate calcium dynamics in coupled cells, a minimal model describing intracellular Ca2+ dynamics in a single cell is extended to describe two adjacent cells coupled by a flux of Ca2+ via gap junctions. The Ca2+ dynamics of the single cell system are either excitable, nonexcitable or oscillatory, depending on the strength of external stimulus to the inositol trisphosphate (IP3) dependent Ca2+ release pathway. We investigate how the stability and asymptotic dynamics of a system of two heterogeneous cells depend on the single-cell dynamics and the coupling strength. We show analytically that, in the case of very strong coupling, the asymptotic dynamics are the same as in a single cell whose IP3 stimulus strength is the average of the two coupled cells. In cases where one or both cells have an unstable steady state when uncoupled, coupling causes a qualitative change in behaviour. This can include amplitude-modulated oscillations, mixed mode oscillations, and the coalescence of multiple frequencies as the cells eventually become synchronised