To investigate the possible coupling mechanisms, a mathematical model based on calcium induced calcium release with positive feedback on InsP3 production is extended to a set of coupled cells with gap junctional diffusion of calcium, and InsP3 alternatively. In the case of coupling an arbitrary number of identical cells, the behavior of the system near bifurcation can be analytically separated in terms of synchronous and asynchronous modes. In addition, in numerical studies we consider both the cases of identical and non-identical cells.
In accordance with our simulations, gap junctional diffusion of calcium leads to rapid synchronization both in sets of identical and non-identical cells. By diffusion of InsP3 on the other hand no synchronization is achieved in sets of identical cells. Coupling non-identical cells (showing differences in their oscillation frequencies when not coupled) results in a complex behavior: The cells oscillate with very slightly differing frequencies. As a consequence when observing the system for a short period, there seem to be fixed phase differences between the cells. But as these phase differences change slowly, during a longer period any phase difference occurs. This gives reason for the assumption that InsP3 diffusion can support the establishment of an approximate common frequency of calcium oscillations in a cluster of connected cells but is not responsible for synchronization.