Three-dimensional model of intracellular and intercellular Ca²⁺ waves propagation in endothelial cells

Intracellular and intercellular Ca²⁺ waves play key roles in cellular functions, and focal stimulation triggers Ca²⁺ wave propagation from stimulation points to neighboring cells, involving localized metabolism reactions and specific diffusion processes. Among these, inositol 1,4,5-trisphosphate (IP₃) is produced at membranes and diffuses into the cytoplasm to release Ca²⁺ from endoplasmic reticulum (ER). In this study, we developed a three-dimensional (3D) simulation model for intercellular and intracellular Ca²⁺ waves in endothelial cells (ECs). 3D model of 2 cells was reconstructed from confocal microscopic images and was connected via gap junctions. Cells have membrane and cytoplasm domains, and metabolic reactions were divided into each domain. Finally, the intracellular and intercellular Ca²⁺ wave propagations were induced using microscopic stimulation and were compared between numerical simulations and experiments. The experiments showed that initial sharp increases in intracellular Ca²⁺ occurred approximately 0.3 s after application of stimuli. In addition, Ca²⁺ wave speeds remained constant in cells, with intracellular and intercellular speeds of approximately 35 and 15 μm/s, respectively. Simulations indicated initial increases in Ca²⁺ concentrations at points of stimulation, and these were then propagated across stimulated and neighboring cells. In particular, initial rapid increases in intracellular Ca²⁺ were delayed and subsequent intracellular and intercellular Ca²⁺ wave speeds were approximately 25 and 12 μm/s, respectively. Simulation results were in agreement with those from cell culture experiments, indicating the utility of our 3D model for investigations of intracellular and intercellular messaging in ECs.