Skip to main content
Log in

Coexistent Fluid-Phase Equilibria in Biomembranes with Bending Elasticity

  • Published:
Journal of Elasticity Aims and scope Submit manuscript

Abstract

The theory of fluid surfaces with elastic resistance to bending is applied to coexistent phase equilibria in biomembranes composed of lipid bilayers. A simplified version of the model is used to simulate the necking and budding of closed vesicles.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Ericksen, J.L.: Theory of Cosserat surfaces and its applications to shells, interfaces and cell membranes. In: Glockner, P.G., Epstein, M., Malcolm, D.J. (eds.) Proc. Int. Symp. on Recent Developments in the Theory and Application of Generalized and Oriented Media, pp. 27–39. Calgary, Canada (1979)

  2. Jenkins, J.T.: The equations of mechanical equilibrium of a model membrane. SIAM J. Appl. Math. 32, 755–764 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  3. Jenkins, J.T.: Static equilibrium configurations of a model red blood cell. J. Math. Biol. 4, 149–169 (1977)

    MATH  Google Scholar 

  4. Helfrich, W.: Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. 28c, 693–703 (1973)

    Google Scholar 

  5. Rosso, R., Virga, E.G.: Adhesive borders of lipid membranes. Proc. R. Soc. Lond. A 455, 4145–4168 (1999)

    Article  MATH  ADS  Google Scholar 

  6. Steigmann, D.J.: Fluid films with curvature elasticity. Arch. Ration. Mech. Anal. 150, 127–152 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. Nitsche, J.C.C.: Boundary value problems for variational integrals involving surface curvatures. Quart. Appl. Math. 51, 363–387 (1993)

    MATH  MathSciNet  Google Scholar 

  8. Steigmann, D.J.: On the relationship between the Cosserat and Kirchhoff-Love theories of elastic shells. Math. Mech. Solids 4, 275–288 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  9. Murdoch, A.I., Cohen, H.: Symmetry considerations for material surfaces. Arch. Ration. Mech. Anal. 72, 61–89 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ou-Yang, Z.-C., Liu, J.-X., Xie, Y.-Z.: Geometric Methods in the Elastic Theory of Membranes in Liquid Crystal Phases. World Scientific, Singapore (1999)

    MATH  Google Scholar 

  11. McMahon, H.T., Gallop, J.L.: Membrane curvature and mechanisms of dynamic cell membrane remodelling. Nature 438, 590–596 (2005)

    Article  ADS  Google Scholar 

  12. Baumgart, T., Hess, S.T., Webb, W.W.: Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension. Nature 425, 821–824 (2003)

    Article  ADS  Google Scholar 

  13. Baumgart, T., Das, S., Webb, W.W., Jenkins, J.T.: Membrane elasticity in giant vesicles with fluid phase coexistence. Biophys. J. 89, 1067–1080 (2005)

    Article  Google Scholar 

  14. Ericksen, J.L.: Equilibrium of bars. J. Elast. 5, 191–202 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  15. Hilgers, M.G., Pipkin, A.C.: Energy-minimizing deformations of elastic sheets with bending stiffness. J. Elast. 31, 125–139 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  16. Eremeyev, V.A., Pietraszkiewicz, W.: The nonlinear theory of elastic shells with phase transitions. J. Elast. 74, 67–86 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  17. Todhunter, I., Pearson, K.: A History of the Theory of Elasticity and of the Strength of Materials. Dover, New York (1960)

    MATH  Google Scholar 

  18. Steigmann, D.J.: Irreducible function bases for simple fluids and liquid crystal films. Z. Angew. Math. Phys. 54, 462–477 (2003)

    MATH  MathSciNet  Google Scholar 

  19. Zheng, Q.-S.: Irreducible function bases for simple fluids and liquid crystal films: A new derivation. Z. Angew. Math. Phys. 54, 478–483 (2003)

    MATH  MathSciNet  Google Scholar 

  20. Steigmann, D.J., Baesu, E., Rudd, R.E., Belak, J., McElfresh, M.: On the variational theory of cell-membrane equilibria. Interfaces Free Bound. 5, 357–366 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  21. Gelfand, I.M., Fomin, S.V.: Calculus of Variations. Prentice-Hall, New York (1963)

    Google Scholar 

  22. Graves, L.M.: The Weierstrass condition for multiple integral variation problems. Duke Math. J. 5, 656–660 (1939)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to David J. Steigmann.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Agrawal, A., Steigmann, D.J. Coexistent Fluid-Phase Equilibria in Biomembranes with Bending Elasticity. J Elasticity 93, 63–80 (2008). https://doi.org/10.1007/s10659-008-9165-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10659-008-9165-1

Keywords

Mathematics Subject Classification (2000)

Navigation