Calcium wave propagation in chains of endothelial cells with nonlinear reaction dynamics: Green's function approach

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 wave propagation in networks of endothelial cells: model-based theoretical and experimental study

In this paper, we present a combined theoretical and experimental study of the propagation of calcium signals in multicellular structures composed of human endothelial cells. We consider multicellular structures composed of a single chain of cells as well as a chain of cells with a side branch, namely a “T” structure. In the experiments, we investigate the result of applying mechano-stimulation to induce signaling in the form of calcium waves along the chain and the effect of single and dual stimulation of the multicellular structure. The experimental results provide evidence of an effect of architecture on the propagation of calcium waves. Simulations based on a model of calcium-induced calcium release and cell-to-cell diffusion through gap junctions shows that the propagation of calcium waves is dependent upon the competition between intracellular calcium regulation and architecture-dependent intercellular diffusion.

Calcium wave signal has been found in a wide variety of cell types. Over the last years, a large number of calcium experiments have shown that calcium signal is not only an intracellular regulator but is also able to be transmitted to surrounding cells as intercellular signal. This paper focuses on the development of an approach with complementary integration of theoretical and experimental methods for studying the multi-level interactions in multicellular architectures and their effect on collective cell dynamic behavior. We describe new types of higher-order (across structure) behaviors arising from lower-order (within cells) phenomena, and make predictions concerning the mechanisms underlying the dynamics of multicellular biological systems. The theoretical approach describes numerically the dynamics of non-linear behavior of calcium-based signaling in model networks of cells. Microengineered, geometrically constrained networks of human umbilical vein endothelial cells (HUVEC) serve as platforms to arbitrate the theoretical predictions in terms of the effect of network topology on the spatiotemporal characteristics of emerging calcium signals.