Simulation of waves in calcium models with 3D spherical geometry

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.

Calcium Dynamics: Spatio‐Temporal Organization from the Subcellular to the Organ Level

Many essential physiological processes are controlled by calcium. To ensure reliability and specificity, calcium signals are highly organized in time and space in the form of oscillations and waves. Interesting findings have been obtained at various scales, ranging from the stochastic opening of a single calcium channel to the intercellular calcium wave spreading through an entire organ. A detailed understanding of calcium dynamics thus requires a link between observations at different scales. It appears that some regulations such as calcium-induced calcium release or PLC activation by calcium, as well as the weak diffusibility of calcium ions play a role at all levels of organization in most cell types. To comprehend how calcium waves spread from one cell to another, specific gap-junctional coupling and paracrine signaling must also be taken into account. On the basis of a pluridisciplinar approach ranging from physics to physiology, a unified description of calcium dynamics is emerging, which could help understanding how such a small ion can mediate so many vital functions in living systems.

Simulation of calcium waves in ascidian eggs: insights into the origin of the pacemaker sites and the possible nature of the sperm factor

Fertilization triggers repetitive waves of cytosolic Ca2+ in the egg of many species. The mechanism involved in the generation of Ca2+ waves has been studied in much detail in mature ascidian eggs, by raising artificially the level of inositol 1,4,5-trisphosphate [Ins(1,4,5)P3] or of its poorly metabolizable analogue, glycero-myo-phosphatidylinositol 4,5-bisphosphate [gPtdIns(4,5)P2]. Here, we use this strategy and the experimental results it provides to develop a realistic theoretical model for repetitive Ca2+ wave generation and propagation in mature eggs. The model takes into account the heterogeneous spatial distribution of the endoplasmic reticulum. Our results corroborate the hypothesis that Ca2+ wave pacemakers are associated with cortical accumulations of endoplasmic reticulum. The model is first tested and validated by the adequate match between its theoretical predictions and the observed effects of localized injections of massive amounts of Ins(1,4,5)P3 analogues. In a second step, we use the model to make some propositions about the possible characteristics of the sperm factor. We find that to account for the spatial characteristics of the first series of Ca2+ waves seen at fertilization in ascidian eggs, it has to be assumed that, if the sperm factor is a phospholipase C, it is Ca2+-sensitive and highly diffusible. Although the actual state of knowledge does not allow us to explain the observed relocalization of the Ca2+ wave pacemaker site, the model corroborates the assumption that PtdIns(4,5)P2, the substrate for phospholipase C is distributed over the entire egg. We also predict that the dose of sperm factor injected into the egg should modulate the temporal characteristics of the first, long-lasting fertilization wave.