Skip to main content
SpringerLink
Log in

A Model for Cell Volume Regulation

  • Chapter
  • First Online:
Mathematical Models with Singularities

Part of the book series: Atlantis Briefs in Differential Equations ((ABDE,volume 1))

  • 895 Accesses

Abstract

Living cells may experience volume changes as a result of osmosis. This chapter is devoted to the study of a recent model that describes the basic aspects of the dynamics of cell volume produced by active and passive transport of water and a solute across the cell membrane.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    In fact the proof is very similar to that of Theorem 8.2.

  2. 2.

    For \(n=2\), system (11.3) can be written as (11.8) with \(x=w_2,y=\sqrt{\sigma }w_1,x_{np}=\frac{\varepsilon }{\sigma },b_2=\beta /\sqrt{\sigma }, M_1(t)=\frac{\gamma (t)}{\sqrt{\sigma }}-\frac{\sqrt{\sigma }}{\beta }\alpha (t),M_2(t)=\frac{\sqrt{\sigma }}{\beta }\alpha (t)\).

References

  1. Benson, J.D., Chicone, C.C., Critser, J.K.: Exact solutions of a two parameter flux model and cryobiological applications. Cryobiology 50(3), 308–316 (2005)

    Article  Google Scholar 

  2. Benson, J.D., Chicone, C.C., Critser, J.K.: A general model for the dynamics of cell volume, global stability and optimal control. J. Math. Biol. 63(2), 339–359 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bernardi, M., DePalma, R., Trevisani, F., Capani, F., Santini, C., Baraldini, M., Gasbarrini, G.: Serum potassium circadian rhythm. Relationship with aldosterone. Horm. Metab. Res. 17(12), 695 (1985)

    Article  Google Scholar 

  4. Fijorek, K., Puskulluoglu, M., Polak, S.: Circadian models of serum potassium, sodium, and calcium concentrations in healthy individuals and their application to cardiac electrophysiology simulations at individual level. Comput. Math. Methods Med. 2013, Article ID 429037 (8pp.) (2013)

    Google Scholar 

  5. Haydon, M.J., Bell, L.J., Webb, A.A.R.: Interactions between plant circadian clocks and solute transport. J. Exp. Bot. 62(7), 2333–2348 (2011)

    Article  Google Scholar 

  6. Hernández, J.A.: A general model for the dynamics of the cell volume. Bull. Math. Biol. 69(5), 1631–1648 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. Kanabrocki, E.L., Scheving, L.E., Halberg, F.: Circadian variations in presumably healthy men under conditions of peace time army reserve unit training. Space Life Sci. 4(2), 258–270 (1973)

    Google Scholar 

  8. Katkov, I.: A two-parameter model of cell membrane permeability for multisolute systems. Cryobiology 40(1), 64–83 (2000)

    Article  Google Scholar 

  9. Katkov, I.: The point of maximum cell water volume excursion in case of presence of an impermeable solute. Cryobiology 44(3), 193–203 (2002)

    Article  MathSciNet  Google Scholar 

  10. Kleinhans, F.W.: Membrane permeability modeling: Kedem-Katchalsky vs a two-parameter formalism. Cryobiology 37(4), 271–289 (1998)

    Article  Google Scholar 

  11. Sennels, H.P., Jørgensen, H.L., Goetze, J.P., Fahrenkrug, J.: Rhythmic 24-hour variations of frequently used clinical biochemical parameters in healthy young males-the Bispebjerg study of diurnal variations. Scand. J. Clin. Lab. Invest. 72, 287–295 (2012)

    Article  Google Scholar 

  12. Sothern, R.B., Vesely, D.L., Kanabrocki, E.L., et al.: Circadian relationships between circulating atrial natriuretic peptides and serum sodium and chloride in healthy humans. Am. J. Nephrol. 16(6), 462–470 (1996)

    Article  Google Scholar 

  13. Torres, P.J.: Periodic oscillations of a model for membrane permeability with fluctuating environmental conditions. J. Math. Biol., in press, doi:10.1007/s00285-014-0815-6

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, University of Granada, Granada, Spain

    Pedro J. Torres

Authors
  1. Pedro J. Torres
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pedro J. Torres .

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Atlantis Press and the authors

About this chapter

Cite this chapter

Torres, P.J. (2015). A Model for Cell Volume Regulation. In: Mathematical Models with Singularities. Atlantis Briefs in Differential Equations, vol 1. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-106-2_11

Download citation

Publish with us

Policies and ethics

Search

Navigation