Mathematical Modeling of Cell Volume Alterations under Different Osmotic Conditions
Cell volume, together with membrane potential and intracellular hydrogen ion concentration, is an essential biophysical parameter for normal cellular activity. Cell volumes can be altered by osmotically active compounds and extracellular tonicity. In this study, a simple mathematical model of osmotically induced cell swelling and shrinking is presented. Emphasis is given to water diffusion across the membrane. The mathematical description of the cellular behavior consists in a system of coupled ordinary differential equations. We compare experimental data of cell volume alterations driven by differences in osmotic pressure with mathematical simulations under hypotonic and hypertonic conditions. Implications for a future model are also discussed.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1099533Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1675
 G.I. Evan, K.H. Vousden, “Proliferation, cell cycle and apoptosis in cancer,” in Nature, vol. 411, pp. 342-348, 2001.
 F.Q. Alenzi, “Links between apoptosis, proliferation and the cell cycle,” in Br J Biomed Sci, vol. 61, pp. 99-102, 2004.
 R.S. Wong, “Apoptosis in cancer: from pathogenesis to treatment,” in J Exp Clin Cancer Res, 30:87, 2011.
 D.L. Grossmann, L. Huc, X. Terkli, “A role of NHE-1 in cell proliferation and migration,” in Cell Apoptotic Signaling Pathways, (ed. Ch.O. Pickens), Nova Science Publishers, pp. 86-109, 2007.
 Y. Okada, E. Maeno, “Apoptosis, cell volume regulation and volumeregulatory chloride channels,” in Comp Biochem Physiol A Mol Integr Physiol, vol. 130, pp. 377–383, 2001.
 M.B. Friis, C.R. Friborg, L. Schneider, “Cell shrinkage as a signal to apoptosis in NIH 3T3 fibroblasts, ” in J Physiol, vol. 567, pp. 427–443, 2005.
 C.D. Bortner, J.A. Cidlowski, „Cell shrinkage and monovalent cation fluxes: role in apoptosis” in Arch Biochem Biophys, vol. 462, pp. 176- 188, 2007.
 B. Nilius, J. Eggermont, T. Voets, G. Buyse, V. Manolopoulos, G. Droogmans, “Properties of volume-regulated anion channels in mammalian cells,” in Prog Biophys Mol Biol, vol. 68, pp. 69–119, 1997.
 A. S. Werkman, “Aquaporins at glance,“ in J of Cell Sci, vol 124, pp. 2107- 2112, 2011.
 J. Pouyssegur, C. Sardet, A. Franchi, G. Allemain, A. Paris, “A specific mutation abolishing Na+/H+ antiport activity in hamster fibroblasts precludes growth at neutral and acidic pH,” in Proc Natl Acad Sci USA, vol. 81, pp. 4833– 4837, 1984.
 On-line database: http://bionumbers.hms.harvard.edu/ bionumber.aspx?&id=105877&ver=2#
 A. Finkelstein, “Water and nonelectrolyte permeability of lipid bilayer membranes,” in J Gen Physiol, vol. 68, pp.127-135, 1976.
 K. Olbrich, W. Rawicz, D. Needham, F. Evans,” Water permeability and mechanical strength in polyunsaturated lipid bilayers,“ in Biophys J, vol. 79, pp. 321-327, 2000.
 C.A. Berry, A.S. Verkman, ”Osmotic gradient dependence of osmotic water permeability in rabbit proximal convoluted tubule, ” in J Membr Biol, vol. 105, pp. 33-43, 1988.
 C.L. Chou, M.A. Knepper, A.N. VanHeok, D. Brown, T. Ma, A.S. Verkman, ”Reduced water permeability and altered ultrascructure in thin descending limb of Henle in aquaporin-1 null mice,” in J Clin Invest, vol. 103, pp. 491-496, 1999.
 A. Eckhart, M. Műller, A. Salt, J. Smolders, H. Rask-Andersen, H. Löwenheim, ”Water permeability of mammalian cochlea: functional features of an aquaporin-facilitated water shunt at the perilymphendolymph barrier,” in Eur J Physiol, vol. 466, pp. 1963- 1985, 2014.
 R.I. Macey, “Transport of water and urea in red blood cells, “ in Am J Physiol, vol. 246, pp. C195-C203, 1984.
 A.S Werkman, A.N. VanHoek, T. Ma, A. Frigeri, W.R. Skach, A. Mitra, B.K. Tamarappoo, J. Farinas, “Water transport across mammalian cell membranes,” in Am J Physiol, vol. 270, pp. C12-C30, 1996.