Exploring the implicit interlayer regulatory mechanism between cells and tissue: stochastic mathematical analyses of the spontaneous ordering in beating synchronization.

The present study focused on beating synchronization, and tried to elucidate the interlayer regulatory mechanisms between the cells and clump in beating synchronization with using the stochastic simulations which realize the beating synchronizations in beating cells with low cell-cell conductance. Firstly, the fluctuation in interbeat intervals (IBIs) of beating cells encouraged the process of beating synchronization, which was identified as the stochastic resonance. Secondly, fluctuation in the synchronized IBIs of a clump decreased as the number of beating cells increased. The decrease in IBI fluctuation due to clump formation implied both a decline of the electrophysiological plasticity of each beating cell and an enhancement of the electrophysiological stability of the clump. These findings were identified as the community effects. Because IBI fluctuation and the community effect facilitated the beating stability of the cell and clump, these factors contributed to the spontaneous ordering in beating synchronization. Thirdly, the cellular layouts in clump affected the synchronized beating rhythms. The synchronized beating rhythm in clump was implicitly regulated by a complicated synergistic effect among IBI fluctuation of each beating cell, the community effect and the cellular layout. This finding was indispensable for leading an elucidation of mechanism of emergence. The stochastic simulations showed the necessity of considering the synergistic effect, to elucidate the interlayer regulatory mechanisms in biological system.