Abstract
The conservation of the cell volume within values compatible with the overall cell functions represents an ubiquitous property, shared by cells comprising the whole biological world. Water transport across membranes constitutes the main process associated to the dynamics of the cell volume, its chronic and acute regulations therefore represent crucial aspects of cell homeostasis. In spite of the biological diversity, the dynamics of the cell volume exhibits common basic features in the diverse types of cells. The purpose of this study is to show that there is a general model capable to describe the basic aspects of the dynamics of the cell volume. It is demonstrated here that the steady states of this model represent asymptotically stable configurations. As illustrations, several cases of non-polarized (i.e., symmetrical) and polarized (e.g., epithelial) cells performing water transport are shown here to represent particular cases of the general model. From a biological perspective, the existence of a general model for the dynamics of the cell volume reveals that, in spite of physiological and morphological peculiarities, there is a basic common design of the membrane transport processes. In view of its stability properties, this basic design may represent an ancestral property that has proven to be successful regarding the overall homeostatic properties of cells.
Similar content being viewed by others
References
Baumgarten, C.M., Feher J.J., 1995. Osmosis and the regulation of the cell volume. In: Sperelakis, N. (Ed.), Cell Physiology. Source Book. Academic Press, New York, pp. 180–211.
Byrne, J.H., Schultz, S.G., 1988. An Introduction to Membrane Transport and Bioelectricity. Raven Press, New York, pp. 66–92.
Csonka, L.N., Hanson, A.D., 1991. Prokariotic osmoregulation: Genetics and physiology. Annu. Rev. Microbiol. 15, 569–606.
Diamond, J.M., 1982. Transcellular cross-talk between epithelial cell membranes. Nature 300, 683–685.
Falciatore, A., d’Alcalà, M.R., Croot, P., Bowler, C., 2000. Perception of environmental signals by a marine diatom. Science 288, 2363–2366.
Hallows, K.R., Knauf, P.A., 1994. Principles of cell volume regulation. In: Strange, K. (Ed.), Cellular and Molecular Physiology of Cell Volume Regulation. CRC Press, Boca Raton, FL, pp. 3–29.
Hernández, J.A., Cristina, E., 1998. Modeling cell volume regulation in nonexcitable cells: The roles of the Na+ pump and of cotransport systems. Am. J. Physiol. 275, C1067–C1080.
Hernández, J.A., 2003. Stability properties of elementary dynamic models of membrane transport. Bull. Math. Biol. 65, 175–197.
Keener, J., Sneyd, J., 1998. Mathematical Physiology. Springer-Verlag, New York, pp. 33–73.
Lang, F., Busch, G.L., Ritter, M., Volkl, H., Waldegger, S., Gulbins, E., Häussinger, D., 1998. Functional significance of cell volume regulatory mechanisms. Physiol. Rev. 78, 247–306.
MacKnight, A.D.C., 1987. Volume maintenance in isosmotic conditions. Curr. Top. Membr. Transp. 30, 3–43.
Minton, A.P., 1983. The effect of volume occupancy upon the thermodynamic activity of proteins: Some biochemical consequences. Mol. Cell. Biochem. 55, 119–140.
Moo Kwon, H., Handler, J.S., 1995. Cell volume regulated transporters of compatible osmolytes. Curr. Opin. Cell Biol. 7, 465–471.
Parker, J.C., 1993. In defense of cell volume? Am. J. Physiol. 265, C1191–C1200.
Reuss, L., Cotton, C.U., 1994. Volume regulation in epithelia: Transcellular transport and cross-talk. In: Strange, K. (Ed.), Cellular and Molecular Physiology of Cell Volume Regulation. CRC Press, Boca Raton, FL, pp. 31–47.
Sánchez, J.M., Li, Y., Rubashkin, A., Iserovich, P., Wen, Q., Ruberti, J.W., Smith, R.W., Rittenband, D., Kuang, K., Diecke, F.P.J., Fischbarg, J., 2002. Evidence for a central role for electro-osmosis in fluid transport in corneal endothelium. J. Membr. Biol. 187, 37–50.
Schultz, S.G., 1981. Homocellular regulatory mechanisms in sodium-transporting epithelia: Avoidance of extinction by “flush-through.” Am. J. Physiol. 242, F579–F590.
Stein, W.D., 1990. Channels, Carriers and Pumps. An Introduction to Membrane Transport. Academic Press, New York, pp. 271–310.
Stein, W.D., 2002. Cell volume homeostasis: Ionic and nonionic mechanisms. In: Zeuthen, T., Stein, W.D. (Eds.), Molecular Mechanisms of Water Transport Across Biological Membranes. Academic Press, London, pp. 231–258.
Tosteson, D.C., Hoffman, J.F., 1960. Regulation of cell volume by active cation transport in high and low potassium sheep red cells. J. Gen. Physiol. 44, 169–194.
Weinstein, A.M., 1992. Analysis of volume regulation in an epithelial cell model. Bull. Math. Biol. 54, 537–561.
Weinstein, A.M., 1997. Dynamics of cellular homeostasis: recovery time for a perturbation from equilibrium. Bull. Math. Biol. 59, 451–481.
Weinstein, A.M., 2004. Modeling epithelial cell homeostasis: assessing recovery and control mechanisms. Bull. Math. Biol. 66, 1201–1240.
Weiss, T.F., 1996. Cellular Biophysics. Vol. 1: Transport. MIT Press, Cambridge, MA, pp. 571–643.
Whittembury, G., Reuss, L., 1992. Mechanisms of coupling of solute and solvent transport in epithelia. In: Seldin, D.W., Giebishch, G. (Eds.), The Kidney: Physiology and Pathophysiology, 2nd edn. Raven Press, New York, pp. 317–360.
Yancey, P.H., Clark, M.E., Hand, S.C., Bowlus, R.D., Somero, G.N., 1982. Living with water stress: Evolution of osmolyte systems. Science 217, 1214–1222.
Zeuthen, T., 1996. Molecular Mechanisms of Water Transport. Springer-Verlag, Heidelberg, pp. 1–10.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hernández, J.A. A General Model for the Dynamics of the Cell Volume. Bull. Math. Biol. 69, 1631–1648 (2007). https://doi.org/10.1007/s11538-006-9183-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-006-9183-8