Ionic permeabilities of the human red blood cell: insights of a simple mathematical model
Stéphane Égée1 ; Marie Postel2 ; Benoît Sarels2
1 Sorbonne Université, CNRS, Laboratory of Integrative Biology of Marine Models (LBI2M), Station Biologique de Roscoff (SBR), F-29688 Roscoff, France
2 Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions (LJLL), F-75005 Paris, France
MathematicS In Action, Tome 13 (2024) no. 1, pp. 1-31.

We are interested in the system of ion channels present at the membrane of the human red blood cell. The cell, under specific experimental circumstances, presents important variations of its membrane potential coupled to variations of the main ions’ concentration ensuring its homeostasis.

In this collaborative work between biologists and mathematicians a simple mathematical model is designed to explain experimental measurements of membrane potential and ion concentrations. Its construction is presented, as well as illustrative simulations and a calibration of the model on real data measurements. A sensitivity analysis of the model parameters is performed. The impact of blood sample storage on ion permeabilities is discussed.

Publié le :
DOI : 10.5802/msia.39
Classification : 00X99
Mots clés : Red blood cell, erythrocytes, ions transfer, permeability, ODE model, calibration
Stéphane Égée 1 ; Marie Postel 2 ; Benoît Sarels 2

1 Sorbonne Université, CNRS, Laboratory of Integrative Biology of Marine Models (LBI2M), Station Biologique de Roscoff (SBR), F-29688 Roscoff, France
2 Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions (LJLL), F-75005 Paris, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Stéphane Égée; Marie Postel; Benoît Sarels. Ionic permeabilities of the human red blood cell: insights of a simple mathematical model. MathematicS In Action, Tome 13 (2024) no. 1, pp. 1-31. doi : 10.5802/msia.39. https://msia.centre-mersenne.org/articles/10.5802/msia.39/

[1] James Bassingthwaighte; Peter Hunter; Denis Noble The Cardiac Physiome: perspectives for the future, Exp. Physiol., Volume 94 (2009) no. 5, pp. 597-605 | DOI

[2] Anne Cueff; Rachel Seear; Agnieszka Dyrda; Guillaume Bouyer; Stéphane Egée; Alessandro Esposito; Jeremy Skepper; Teresa Tiffert; Virgilio L. Lew; Serge L. Y. Thomas Effects of elevated intracellular calcium on the osmotic fragility of human red blood cells, Cell Calcium, Volume 47 (2010) no. 1, pp. 29-36 | DOI

[3] Agnieszka Dyrda; Urszula Cytlak; Anna Ciuraszkiewicz; Agnieszka Lipinska; Anne Cueff; Guillaume Bouyer; Stéphane Egée; Poul Bennekou; Virgilio L. Lew; Serge L. Y. Thomas Local membrane deformations activate Ca2+-dependent K+ and anionic currents in intact human red blood cells, PLoS ONE, Volume 5 (2010) no. 2, e9447

[4] Emilie Fleur Gautier; Marjorie Leduc; Cochet Sylvie; Bailly Karine; Lacombe Catherine; Mohandas Narla; Guillonneau François; El Nemer Wassim; Mayeux Patrick Absolute proteome quantification of highly purified populations of circulating reticulocytes and mature erythrocytes, Blood Adv., Volume 2 (2018) no. 20, pp. 2646-2657 | DOI

[5] David E. Goldman Potential, impedance, and rectification in membranes, J. Gen. Physiol., Volume 27 (1943) no. 1, p. 37–60 | DOI

[6] Nikolaus Hansen The CMA Evolution Strategy: A Tutorial, 2023 | arXiv

[7] Jonathan Herman; William Usher SALib: An open-source Python library for Sensitivity Analysis, J. Open Source Softw., Volume 2 (2017) no. 9 | DOI

[8] Takuya Iwanaga; William Usher; Jonathan Herman Toward SALib 2.0: Advancing the accessibility and interpretability of global sensitivity analyses, Socio-Environ. Sys. Model., Volume 4 (2022), p. 18155 | DOI

[9] Julia Jansen; Min Qiao; Laura Hertz; Xijia Wang; Elisa Fermo; Anna Zaninoni; Raffaella Colombatti; Ingolf Bernhardt; Paola Bianchi; Lars Kaestner Mechanistic ion channel interactions in red cells of patients with Gárdos channelopathy, Blood Adv., Volume 5 (2021) no. 17, pp. 3303-3308 | DOI

[10] J. P. Keener; J. Sneyd Mathematical Physiology, Interdisciplinary Applied Mathematics, 2, Springer, 2009 | DOI

[11] Virgilio L. Lew; Robert M. Bookchin Volume, pH, and ion-content regulation in human red cells: analysis of transient behavior with an integrated model, J. Membrane Biol., Volume 92 (1986) no. 1, pp. 57-74

[12] Virgilio L. Lew; Teresa Tiffert The terminal density reversal phenomenon of aging human red blood cells, Front. Physiol., Volume 4 (2013), p. 171

[13] Daniel V. Olivença; Jacob D. Davis; Carla M. Kumbale; Conan Y. Zhao; Samuel P. Brown; Nael A. McCarty; Eberhard O. Voit Mathematical models of cystic fibrosis as a systemic disease, WIREs Mech. Dis., Volume 15 (2023) no. 6, e1625

[14] Simon Rogers; Virgilio L. Lew User guide to the red blood cell model (RCM), a multiplatform JAVA-based model of human red blood cell homeostasis (2020) (https://www.biorxiv.org/content/early/2020/09/12/2020.03.07.981779) | DOI

[15] I. M Sobol Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Math. Comput. Simul., Volume 55 (2001) no. 1, pp. 271-280 | DOI | MR | Zbl

[16] Geoffrey R. Tanner; Anastasios V. Tzingounis The mammalian nodal action potential: new data bring new perspectives, Advances in Physiology Education, Volume 46 (2022) no. 4, pp. 693-702 | DOI

[17] Ciyou Zhu; Richard H. Byrd; Peihuang Lu; Jorge Nocedal Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization, ACM Trans. Math. Softw., Volume 23 (1997) no. 4, pp. 550-560 | MR

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