Ion flux, transmembrane potential, and osmotic stabilization: A new electrophysiological dynamic model for Eukaryotic cells

Clair Poignard; Aude Silve; Frederic Campion; Lluis M. Mir; Olivier Saut; Laurent Schwartz

inria-00477372, version 1

Ion flux, transmembrane potential, and osmotic stabilization: A new electrophysiological dynamic model for Eukaryotic cells

Clair Poignard ( Author to contact preferably )^a^, 1, 2, Aude Silve ()^b^, 3, Frederic Campion ⁴, Lluis M. Mir ³, Olivier Saut ^1, 2, Laurent Schwartz ^5, 6

European Biophysics Journal: EBJ 40, 3 (2011)

Abstract: Survival of mammalian cells is achieved by tight control of cell volume while transmembrane potential is known to control many cellular functions since the seminal work of Hodgkin and Huxley. Regulation of cell volume and transmembrane potential have a wide range of implications in physiology, from neurological and cardiac disorders to cancer and muscle fatigue. Therefore understanding the relationship between transmembrane potential, ion fluxes, and cell volume regulation has become of great interest. In this paper we derive a system of differential equations that links transmembrane potential, ionic concentrations, and cell volume. This model demonstrates that volume stabilization occurs within minutes of changes in extracellular osmotic pressure. We infer a straightforward relationship between transmembrane potential and cell volume. Our model is a generalization of previous models in which either cell volume was constant or osmotic regulation instantaneous. When the extracellular osmotic pressure is constant, the cell volume varies as a function of transmembrane potential and ions fluxes thus providing an implicit link between transmembrane potential and cell growth. Numerical simulations of the model provide results that are consistent with experimental data in terms of time-related changes in cell volume and dynamics of the phenomena.

a – INRIA
b – Institut Gustave Roussy
1: Institut de Mathématiques de Bordeaux (IMB)
CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
2: MC2 (INRIA Bordeaux - Sud-Ouest)
INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR
3: Vectorology and Anticancer Therapies
Institut Gustave Roussy – CNRS : UMR8203 – Université Paris XI - Paris Sud
4: The Copenhaguen Muscle Research Centre (CMRC)
Copenhagen Hospital Cooperation – Panum Institute – University of Copenhagen
5: Hôpital Pitié-Salpétrière
Assistance publique - Hôpitaux de Paris (AP-HP) – Université Pierre et Marie Curie [UPMC] - Paris VI
6: Laboratoire d'informatique de l'école polytechnique (LIX)
CNRS : UMR7161 – Polytechnique - X

inria-00477372, version 1
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From: Clair Poignard <>
Submitted on: Wednesday, 28 April 2010 20:31:16
Updated on: Monday, 30 January 2012 17:17:31

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DOI: 10.1007/s00249-010-0641-8

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%% inria-00477372, version 1
%% http://hal.inria.fr/inria-00477372
@article{poignard:inria-00477372,
    hal_id = {inria-00477372},
    url = {http://hal.inria.fr/inria-00477372},
    title = {{Ion flux, transmembrane potential, and osmotic stabilization: A new electrophysiological dynamic model for Eukaryotic cells}},
    author = {Poignard, Clair and Silve, Aude and Campion, Frederic and Mir, Lluis, M. and Saut, Olivier and Schwartz, Laurent},
    abstract = {{Survival of mammalian cells is achieved by tight control of cell volume while transmembrane potential is known to control many cellular functions since the seminal work of Hodgkin and Huxley. Regulation of cell volume and transmembrane potential have a wide range of implications in physiology, from neurological and cardiac disorders to cancer and muscle fatigue. Therefore understanding the relationship between transmembrane potential, ion fluxes, and cell volume regulation has become of great interest. In this paper we derive a system of differential equations that links transmembrane potential, ionic concentrations, and cell volume. This model demonstrates that volume stabilization occurs within minutes of changes in extracellular osmotic pressure. We infer a straightforward relationship between transmembrane potential and cell volume. Our model is a generalization of previous models in which either cell volume was constant or osmotic regulation instantaneous. When the extracellular osmotic pressure is constant, the cell volume varies as a function of transmembrane potential and ions fluxes thus providing an implicit link between transmembrane potential and cell growth. Numerical simulations of the model provide results that are consistent with experimental data in terms of time-related changes in cell volume and dynamics of the phenomena.}},
    language = {English},
    affiliation = {Institut de Math{\'e}matiques de Bordeaux - IMB , MC2 - INRIA Bordeaux - Sud-Ouest , Vectorology and Anticancer Therapies , The Copenhaguen Muscle Research Centre - CMRC , H{\^o}pital Piti{\'e}-Salp{\'e}tri{\`e}re , Laboratoire d'informatique de l'{\'e}cole polytechnique - LIX},
    publisher = {Springer},
    journal = {European Biophysics Journal: EBJ},
    volume = {40},
    number = {3 },
    note = {RR-7269 RR-7269 ARC C3MB },
    audience = {international },
    doi = {10.1007/s00249-010-0641-8 },
    year = {2011},
    month = Jan,
    pdf = {http://hal.inria.fr/inria-00477372/PDF/RR-7269.pdf},
}

%F inria-00477372, version 1
%0 Journal Article
%U http://hal.inria.fr/inria-00477372
%2 SDV:BC:BC;MATH:MATH_AP
%T Ion flux, transmembrane potential, and osmotic stabilization: A new electrophysiological dynamic model for Eukaryotic cells
%A Poignard, Clair
%A Silve, Aude
%A Campion, Frederic
%A Mir, Lluis
%A Saut, Olivier
%A Schwartz, Laurent
%+ Institut de Mathématiques de Bordeaux - IMB , MC2 - INRIA Bordeaux - Sud-Ouest , Vectorology and Anticancer Therapies , The Copenhaguen Muscle Research Centre - CMRC , Hôpital Pitié-Salpétrière , Laboratoire d'informatique de l'école polytechnique - LIX
%X Survival of mammalian cells is achieved by tight control of cell volume while transmembrane potential is known to control many cellular functions since the seminal work of Hodgkin and Huxley. Regulation of cell volume and transmembrane potential have a wide range of implications in physiology, from neurological and cardiac disorders to cancer and muscle fatigue. Therefore understanding the relationship between transmembrane potential, ion fluxes, and cell volume regulation has become of great interest. In this paper we derive a system of differential equations that links transmembrane potential, ionic concentrations, and cell volume. This model demonstrates that volume stabilization occurs within minutes of changes in extracellular osmotic pressure. We infer a straightforward relationship between transmembrane potential and cell volume. Our model is a generalization of previous models in which either cell volume was constant or osmotic regulation instantaneous. When the extracellular osmotic pressure is constant, the cell volume varies as a function of transmembrane potential and ions fluxes thus providing an implicit link between transmembrane potential and cell growth. Numerical simulations of the model provide results that are consistent with experimental data in terms of time-related changes in cell volume and dynamics of the phenomena.
%G English
%J European Biophysics Journal: EBJ
%8 2011-01-00
%2 international
%I Springer
%V 40
%N 3
%R 10.1007/s00249-010-0641-8
%Z RR-7269
%Z ARC C3MB

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