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. 2024 Dec 3;90(1):2.
doi: 10.1007/s00285-024-02163-z.

Mathematical properties of pump-leak-cotransport models

Vincent Ouellet  1   2 , Nicolas Doyon  3   4 , Antoine G Godin  5   6 , Pierre Marquet  5   6
Affiliations

Mathematical properties of pump-leak-cotransport models

Vincent Ouellet et al. J Math Biol. .

Abstract

Models of ordinary differential equations are often used to describe the electrical, ionic and volumetric responses of cells to external stimuli. Although these cellular models are often solved numerically, rigorous evidence regarding their steady state solutions is scarce. In this work, we provide a formalism defining the conditions ensuring the existence and uniqueness of a steady-state solution in a large class of models including leak channels, a pump and cotransporters. Our work generalizes previous results and provides explicit conditions that a model must satisfy to guarantee the existence and uniqueness of a steady state.

Keywords: Cell swelling models; Cell volume control; Cellular resilience; Chloride-cation cotransporters; Differential algebraic system; Electrolyte balance; Existence and unicity of steady states; Homotopy; Mathematical model of cell swelling; Mathematical model of water transport; Ordinary differential equation model of cell activity.

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Conflict of interest statement

Declarations. Conflict of interest: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential Conflict of interest.

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