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The presence of impermeant molecules within a cell can lead to an increase in cell volume through the influx of water driven by osmosis. This phenomenon is known as the Donnan (or Gibbs–Donnan) effect. Animal cells actively transport ions to counteract the Donnan effect and regulate their volume, actively pumping Na+ out and K+ into their cytosol using the Na+/K+ ATPase (NKA) pump. The pump-leak equations (PLEs) are a system of algebraic-differential equations to model the membrane potential, ion (Na+, K+, and Cl−), and water flux across the cell membrane, which provide insight into how the combination of passive ions fluxes and active transport contribute to stabilizing cell volume. Our broad objective is to provide analytical insight into the PLEs through three lines of investigation: (1) we show that the provision of impermeant extracellular molecules can stabilize the volume of a passive cell; (2) we demonstrate that the mathematical form of the NKA pump is not as important as the stoichiometry for cell stabilization; and (3) we investigate the interaction between the NKA pump and cation–chloride co-transporters (CCCs) on cell stabilization, showing that NCC can destabilize a cell while NKCC and KCC can stabilize it. We incorporate extracellular impermeant molecules, NKA pump, and CCCs into the PLEs and derive the exact formula for the steady states in terms of all the parameters. This analytical expression enables us to easily explore the effect of each of the system parameters on the existence and stability of the steady states.
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This content will become publicly available on January 1, 2027
A kinetic study of multi-substrate uniporters
Not AvailableTransporters play key roles in regulating the movement of molecules into and out of cells. Uniporters, the simplest class of transporters, use facilitated diffusion to translocate molecules across membranes down their concentration gradient. This process can be affected by the presence of additional substrates in the intra- and extracellular environment, which can either increase the net transport rate of a molecule via trans acceleration or decrease it via competitive inhibition. In this study, we derived mathematical models to describe the net transport rate of uniporters in the presence of multiple extracellular substrates or inhibitors. Analyses of these models identified four possible states for the system when two substrates are present, with two states leading to trans acceleration and the other two states resulting in inhibition. Finally, we found that the relation between kinetic constants that controls the fraction of transporters in the inward-facing open state is responsible for these behaviors. Our theoretical results provide a mathematical framework for understanding the dynamic response of uniporters in the presence of multiple substrates and inhibitors, which could have implications for various processes, from nutrient utilization to metabolic engineering.
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- Award ID(s):
- 1942722
- PAR ID:
- 10651400
- Publisher / Repository:
- ScienceDirect
- Date Published:
- Journal Name:
- Journal of Theoretical Biology
- Volume:
- 616
- Issue:
- C
- ISSN:
- 0022-5193
- Page Range / eLocation ID:
- 112267
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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