Mathematical modeling of intracellular calcium in presence of receptor: a homeostatic model for endothelial cell.

ABSTRACT

Calcium is a ubiquitous molecule and second messenger that regulates many cellular functions ranging from exocytosis to cell proliferation at different time scales. In the vasculature, a constant adenosine triphosphate (ATP) concentration is maintained because of ATP released by red blood cells (RBCs). These ATP molecules continuously react with purinergic receptors on the surface of endothelial cells (ECs). Consequently, a cascade of chemical reactions are triggered that result in a transient cytoplasmic calcium (Ca[Formula see text]), followed by return to its basal concentration. The mathematical models proposed in the literature are able to reproduce the transient peak. However, the trailing concentration is always higher than the basal cytoplasmic Ca[Formula see text] concentrations, and the Ca[Formula see text] concentration in endoplasmic reticulum (ER) remains lower than its initial concentration. This means that the intracellular homeostasis is not recovered. We propose, herein, a minimal model of calcium kinetics. We find that the desensitization of EC surface receptors due to phosphorylation and recycling plays a vital role in maintaining calcium homeostasis in the presence of a constant stimulus (ATP). The model is able to capture several experimental observations such as refilling of Ca[Formula see text] in the ER, variation of cytoplasmic Ca[Formula see text] transient peak in ECs, the resting cytoplasmic Ca[Formula see text] concentration, the effect of removing ATP from the plasma on Ca[Formula see text] homeostasis, and the saturation of cytoplasmic Ca[Formula see text] transient peak with increase in ATP concentration. Direct confrontation with several experimental results is conducted. This work paves the way for systematic studies on coupling between blood flow and chemical signaling, and should contribute to a better understanding of the relation between (patho)physiological conditions and Ca[Formula see text] kinetics.