ArticleJournal of mathematical biology2012
Mathematical properties of pump-leak models of cell volume control and electrolyte balance.
Article in Journal of mathematical biology, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 16 papers.
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16 citing papers in PubMed, 46 citations in OpenAlex.
- Stability and Robustness of a Generalized Pump-Leak Model for Epithelial Vesicles.Bulletin of mathematical biology · 2026Article
- Electrodiffusion active pump model with asymmetric immersed chemical potentials.bioRxiv : the preprint server for biology · 2026Article
- Pore size dynamics control complex volume swelling in pyroptosis.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
- A Mathematical Exploration of SDH-b Loss in Chromaffin Cells.Bulletin of mathematical biology · 2025Article
- Mathematical modeling of intracellular osmolarity and cell volume stabilization: The Donnan effect and ion transport.The Journal of general physiology · 2024Article
- Physical basis of the cell size scaling laws.eLife · 2023Article
- A hydro-osmotic coarsening theory of biological cavity formation.PLoS computational biology · 2021Article
- Article
- Hydrogen, Bicarbonate, and Their Associated Exchangers in Cell Volume Regulation.Frontiers in cell and developmental biology · 2021Article
- Gap junctions amplify spatial variations in cell volume in proliferating tumor spheroids.Nature communications · 2020Article
- The importance of water and hydraulic pressure in cell dynamics.Journal of cell science · 2020Review
- On the Effects of Mechanical Stress of Biological Membranes in Modeling of Swelling Dynamics of Biological Systems.Scientific reports · 2020Article
- Evolution of our understanding of cell volume regulation by the pump-leak mechanism.The Journal of general physiology · 2019Review
- Different approaches to modeling analysis of mitochondrial swelling.Mitochondrion · 2018Review
- How Cells Can Control Their Size by Pumping Ions.Frontiers in cell and developmental biology · 2017Article
- Electrophysiology.Communications on pure and applied mathematics · 2013Article
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1 author at 1 institution in 1 country.
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Abstract
Homeostatic control of cell volume and intracellular electrolyte content is a fundamental problem in physiology and is central to the functioning of epithelial systems. These physiological processes are modeled using pump-leak models, a system of differential algebraic equations that describes the balance of ions and water flowing across the cell membrane. Despite their widespread use, very little is known about their mathematical properties. Here, we establish analytical results on the existence and stability of steady states for a general class of pump-leak models. We treat two cases. When the ion channel currents have a linear current-voltage relationship, we show that there is at most one steady state, and that the steady state is globally asymptotically stable. If there are no steady states, the cell volume tends to infinity with time. When minimal assumptions are placed on the properties of ion channel currents, we show that there is an asymptotically stable steady state so long as the pump current is not too large. The key analytical tool is a free energy relation satisfied by a general class of pump-leak models, which can be used as a Lyapunov function to study stability.
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