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

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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\(^{2+}\)), 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\(^{2+}\) concentrations, and the Ca\(^{2+}\) 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\(^{2+}\) in the ER, variation of cytoplasmic Ca\(^{2+}\) transient peak in ECs, the resting cytoplasmic Ca\(^{2+}\) concentration, the effect of removing ATP from the plasma on Ca\(^{2+}\) homeostasis, and the saturation of cytoplasmic Ca\(^{2+}\) 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\(^{2+}\) kinetics.

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Acknowledgements

We acknowledge the financial support from CNES (Centre National d’Etudes Spatiales) and for having access to data, and the French-German University Programme Living Fluids (Grant CFDA-Q1-14). The simulations were performed on the Cactus cluster of the CIMENT infrastructure, which is supported by the Rhône-Alpes region (Grant No. CPER07 13 CIRA).

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Authors and Affiliations

  1. CNRS, LIPhy, Université Grenoble Alpes, 38000, Grenoble, France

    Ananta Kumar Nayak, Zhe Gou & Chaouqi Misbah

  2. Indian Institute of Technology Palakkad, Palakkad, Kerala, 678557, India

    Sovan Lal Das

  3. LadHyX, CNRS, Ecole Polytechnique, Institut polytechnique de Paris, 91120, Palaiseau, France

    Abdul I. Barakat

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  1. Ananta Kumar Nayak
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  2. Zhe Gou
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  4. Abdul I. Barakat
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  5. Chaouqi Misbah
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Contributions

Ananta Kumar Nayak developed the calcium model and analyzed it. Zhe Gou, Sovan Lal Das, Abdul I. Barakat and Chaouqi Misbah participated to model development and interpretation. Chaouqi Misbah has designed the research topic and planes. All the authors have contributed to the paper writing and interpretations.

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Correspondence to Chaouqi Misbah.

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Nayak, A.K., Gou, Z., Das, S.L. et al. Mathematical modeling of intracellular calcium in presence of receptor: a homeostatic model for endothelial cell. Biomech Model Mechanobiol 22, 217–232 (2023). https://doi.org/10.1007/s10237-022-01643-9

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