How Cells Can Control Their Size by Pumping Ions

Abstract

The ability of all cells to set and regulate their size is a fundamental aspect of cellular physiology. It has been known for sometime but not widely so, that size stability in animal cells is dependent upon the operation of the sodium pump, through the so-called pump-leak mechanism (Tosteson and Hoffman, 1960). Impermeant molecules in cells establish an unstable osmotic condition, the Donnan effect, which is counteracted by the operation of the sodium pump, creating an asymmetry in the distribution of Na+ and K+ staving off water inundation. In this paper, which is in part a tutorial, I show how to model quantitatively the ion and water fluxes in a cell that determine the cell volume and membrane potential. The movement of water and ions is constrained by both osmotic and charge balance, and is driven by ion and voltage gradients and active ion transport. Transforming these constraints and forces into a set of coupled differential equations allows us to model how the ion distributions, volume and voltage change with time. I introduce an analytical solution to these equations that clarifies the influence of ion conductances, pump rates and water permeability in this multidimensional system. I show that the number of impermeant ions (x) and their average charge have a powerful influence on the distribution of ions and voltage in a cell. Moreover, I demonstrate that in a cell where the operation of active ion transport eliminates an osmotic gradient, the size of the cell is directly proportional to x. In addition, I use graphics to reveal how the physico-chemical constraints and chemical forces interact with one another in apportioning ions inside the cell. The form of model used here is applicable to all membrane systems, including mitochondria and bacteria, and I show how pumps other than the sodium pump can be used to stabilize cells. Cell biologists may think of electrophysiology as the exclusive domain of neuroscience, however the electrical effects of ion fluxes need to become an intimate part of cell biology if we are to understand a fundamental process like cell size regulation.

Biophysical models reveal the relative importance of transporter proteins and impermeant anions in chloride homeostasis

“…4A,[A]i = 155 mM). Analytically, it can be shown that the number of moles of X 304 determines completely the volume of the compartment, while the permeant ions alone cannot be 305 used to predict steady state volume(Kay, 2017). Similarly, all initial impermeant anion concentrations 306 resulted in identical steady state values of ECl (-83.8 mV), EK (-95.1 mV) and Vm (-72.6 mV) (Fig.…”

“…Our theoretical approach is based on the pump-612 leak formulation (Tosteson and Hoffman, 1960). It suggests that mammalian cells maintain their 613 volume under osmotic stress generated by impermeant anions and the Donnan effect by employing 614 active transport of Na + and K + using the Na + /K + -ATPase (Armstrong, 2003;Kay, 2017). A Donnan 615 equilibrium, a true thermodynamic equilibrium requiring no energy to maintain it, is not possible in 616 cells with pliant membranes like neurons (Sperelakis, 2012).…”

Bioelectrical understanding and engineering of cell biology

“…IMFs can arise from selective transport or differential permeability to charged molecules, or can be generated through membrane-bound redox reactions of the respiratory chain [3,4]. A key point to recognize is that IMF and MP are coupled to each other and further to cell volume and metabolism [17,18]. The connection to volume arises from the distribution of ions and charged molecules (essential for the formation of MP), determining also the osmotic forces on cells [17].…”

“…A key point to recognize is that IMF and MP are coupled to each other and further to cell volume and metabolism [17,18]. The connection to volume arises from the distribution of ions and charged molecules (essential for the formation of MP), determining also the osmotic forces on cells [17]. The connection to metabolism is achieved by four general mechanisms (figure 2b).…”

Water Homeostasis and Cell Volume Maintenance and Regulation

“…Thus, cells observe all the requirements for Gibbs-Donnan disequilibrium and they are under pressure to swell. The reason they maintain their volume is because they use cellular energy to fuel the Na + /K + -pump to constantly fight the leak of ions and the influx of water (Kay, 2017; Tosteson & Hoffman, 1960). The pump basically renders the membrane “impermeable” to Na + by actively extruding the Na + that enters the cell through leak pathways.…”