Bulletin of Mathematical Biology

, Volume 69, Issue 5, pp 1631–1648 | Cite as

A General Model for the Dynamics of the Cell Volume

  • Julio A. Hernández
Original Article


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.


Cell volume Membrane transport Mathematical models 


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  1. 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.Google Scholar
  2. Byrne, J.H., Schultz, S.G., 1988. An Introduction to Membrane Transport and Bioelectricity. Raven Press, New York, pp. 66–92.Google Scholar
  3. Csonka, L.N., Hanson, A.D., 1991. Prokariotic osmoregulation: Genetics and physiology. Annu. Rev. Microbiol. 15, 569–606.CrossRefGoogle Scholar
  4. Diamond, J.M., 1982. Transcellular cross-talk between epithelial cell membranes. Nature 300, 683–685.CrossRefGoogle Scholar
  5. Falciatore, A., d’Alcalà, M.R., Croot, P., Bowler, C., 2000. Perception of environmental signals by a marine diatom. Science 288, 2363–2366.CrossRefGoogle Scholar
  6. 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.Google Scholar
  7. 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.Google Scholar
  8. Hernández, J.A., 2003. Stability properties of elementary dynamic models of membrane transport. Bull. Math. Biol. 65, 175–197.CrossRefGoogle Scholar
  9. Keener, J., Sneyd, J., 1998. Mathematical Physiology. Springer-Verlag, New York, pp. 33–73.zbMATHGoogle Scholar
  10. 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.Google Scholar
  11. MacKnight, A.D.C., 1987. Volume maintenance in isosmotic conditions. Curr. Top. Membr. Transp. 30, 3–43.Google Scholar
  12. Minton, A.P., 1983. The effect of volume occupancy upon the thermodynamic activity of proteins: Some biochemical consequences. Mol. Cell. Biochem. 55, 119–140.CrossRefGoogle Scholar
  13. Moo Kwon, H., Handler, J.S., 1995. Cell volume regulated transporters of compatible osmolytes. Curr. Opin. Cell Biol. 7, 465–471.CrossRefGoogle Scholar
  14. Parker, J.C., 1993. In defense of cell volume? Am. J. Physiol. 265, C1191–C1200.Google Scholar
  15. 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.Google Scholar
  16. 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.CrossRefGoogle Scholar
  17. Schultz, S.G., 1981. Homocellular regulatory mechanisms in sodium-transporting epithelia: Avoidance of extinction by “flush-through.” Am. J. Physiol. 242, F579–F590.Google Scholar
  18. Stein, W.D., 1990. Channels, Carriers and Pumps. An Introduction to Membrane Transport. Academic Press, New York, pp. 271–310.Google Scholar
  19. 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.CrossRefGoogle Scholar
  20. 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.CrossRefGoogle Scholar
  21. Weinstein, A.M., 1992. Analysis of volume regulation in an epithelial cell model. Bull. Math. Biol. 54, 537–561.zbMATHGoogle Scholar
  22. Weinstein, A.M., 1997. Dynamics of cellular homeostasis: recovery time for a perturbation from equilibrium. Bull. Math. Biol. 59, 451–481.zbMATHCrossRefGoogle Scholar
  23. Weinstein, A.M., 2004. Modeling epithelial cell homeostasis: assessing recovery and control mechanisms. Bull. Math. Biol. 66, 1201–1240.CrossRefMathSciNetGoogle Scholar
  24. Weiss, T.F., 1996. Cellular Biophysics. Vol. 1: Transport. MIT Press, Cambridge, MA, pp. 571–643.Google Scholar
  25. 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.Google Scholar
  26. 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.CrossRefGoogle Scholar
  27. Zeuthen, T., 1996. Molecular Mechanisms of Water Transport. Springer-Verlag, Heidelberg, pp. 1–10.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Sección Biofísica, Facultad de CienciasUniversidad de la República, Iguá esq. MataojoMontevideoUruguay

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