Synchronized Anti-Phase and In-Phase Oscillations of Intracellular Calcium Ions in Two Coupled Hepatocytes System

We study the dynamic behaviour of two intracellular calcium oscillators that are coupled through gap junctions both to Ca²⁺ and inositol(1,4,5)-trisphosphate (IP₃). It is found that synchronized anti-phase and in-phase
oscillations of cytoplasmic calcium coexist in parameters space. Especially, synchronized anti-phase oscillations only occur near the onset of a Hopf bifurcation point when the velocity of IP₃ synthesis is increased. In addition, two kinds of coupling effects, i.e., the diffusions of Ca²⁺ and IP₃ among cells on synchronous behaviour, are considered. We find that small coupling of
Ca²⁺ and large coupling of IP₃ facilitate the emergence of synchronized anti-phase oscillations. However, the result is contrary for the synchronized in-phase case. Our findings may provide a qualitative understanding about the mechanism of synchronous behaviour of intercellular calcium signalling.