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.
[1] G.I. Evan, K.H. Vousden, “Proliferation, cell cycle and apoptosis in
cancer,” in Nature, vol. 411, pp. 342-348, 2001.
[2] F.Q. Alenzi, “Links between apoptosis, proliferation and the cell cycle,”
in Br J Biomed Sci, vol. 61, pp. 99-102, 2004.
[3] R.S. Wong, “Apoptosis in cancer: from pathogenesis to treatment,” in J
Exp Clin Cancer Res, 30:87, 2011.
[4] 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.
[5] 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.
[6] 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.[7] 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.
[8] 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.
[9] A. S. Werkman, “Aquaporins at glance,“ in J of Cell Sci, vol 124, pp.
2107- 2112, 2011.
[10] 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.
[11] On-line database: http://bionumbers.hms.harvard.edu/
bionumber.aspx?&id=105877&ver=2#
[12] A. Finkelstein, “Water and nonelectrolyte permeability of lipid bilayer
membranes,” in J Gen Physiol, vol. 68, pp.127-135, 1976.
[13] 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.
[14] 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.
[15] 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.
[16] 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.
[17] R.I. Macey, “Transport of water and urea in red blood cells, “ in Am J
Physiol, vol. 246, pp. C195-C203, 1984.
[18] 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.
[1] G.I. Evan, K.H. Vousden, “Proliferation, cell cycle and apoptosis in
cancer,” in Nature, vol. 411, pp. 342-348, 2001.
[2] F.Q. Alenzi, “Links between apoptosis, proliferation and the cell cycle,”
in Br J Biomed Sci, vol. 61, pp. 99-102, 2004.
[3] R.S. Wong, “Apoptosis in cancer: from pathogenesis to treatment,” in J
Exp Clin Cancer Res, 30:87, 2011.
[4] 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.
[5] 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.
[6] 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.[7] 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.
[8] 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.
[9] A. S. Werkman, “Aquaporins at glance,“ in J of Cell Sci, vol 124, pp.
2107- 2112, 2011.
[10] 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.
[11] On-line database: http://bionumbers.hms.harvard.edu/
bionumber.aspx?&id=105877&ver=2#
[12] A. Finkelstein, “Water and nonelectrolyte permeability of lipid bilayer
membranes,” in J Gen Physiol, vol. 68, pp.127-135, 1976.
[13] 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.
[14] 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.
[15] 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.
[16] 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.
[17] R.I. Macey, “Transport of water and urea in red blood cells, “ in Am J
Physiol, vol. 246, pp. C195-C203, 1984.
[18] 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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:69185", author = "Juliana A. Knocikova and Yann Bouret and Médéric Argentina and Laurent Counillon", title = "Mathematical Modeling of Cell Volume Alterations under Different Osmotic Conditions", abstract = "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.
", keywords = "Eukaryotic cell, mathematical modeling, osmosis,
volume alterations.", volume = "8", number = "8", pages = "1164-5", }
