Cell volume control in three dimensions: Water movement without solute movement

Cell volume primarily represents the amount of water in a cell. Osmotically active metabolites and mechanical forces can cause changes in cell volume, but cell volume is under feedback control around a characteristic set point. Traditionally, the analysis of cell volume regulation treats the cell as a semipermeable bag with osmotic pressure converted to hydrostatic pressure at the membrane. However, newer data show that in cells with a cross-linked cytoskeleton, osmotic stress is distributed throughout the cell volume and not confined to the cortex. Cyto-skeletal cross-linking creates a sponge-like interior bonded to the membrane at the periphery. The cytoskeleton can be strong enough to allow a cell to withstand hours-long exposure to distilled water without lysing. The elastic energy stored in a swollen, cross-linked cytoskeleton is much larger than that in the cell cortex (see Appendix) and hence is a critical variable to include when model-ing cell volume regulation. Traditional analyses of cell volume regulation have used a Donnan equilibrium model that treats the cell as a semipermeable bag containing mobile and immobile The physics of this " poroelas-tic " system is well understood (Biot, 1941; Hill, 2012) but has usually not been incorporated into discussions and models of osmotic balance and cellular volume changes. Poroelasticity describes the interaction between fluid flow and solid deformation within a porous medium. When an external load is applied sponge, the fluid filled pores of the sponge experience a change in pressure , and this leads to fluid flow causing deformation of the elastic skeleton of the sponge. Poroelasticity is a common model for inhomogeneous materials containing fluids. Correspondence to Frederick Sachs: s a c h s @ b u f f a l o. e d u Abbreviations used in this paper: AFM, atomic force microscopy; BAEC, bovine aortic endothelial cell; MSC, mechanosensitive ion channel. Modeling poroelasticity combines two laws: Darcy's law describes the fluid motion and pressure in a porous medium (Whitaker, 1986) and states that the fluid velocity is proportional to the pressure gradient, the fluid viscosity , and the material's ability to disrupt the flow. The second law describes the mechanics of the matrix under the combined action of forces in the sponge network and the hydrostatic pressure in the pores. Biot (1941) merged these two laws. In the Appendix, we present an analysis of a swollen cell, demonstrating that the elastic energy stored in the cytoskeleton is much larger …