Journal of Computer-Aided Materials Design

, Volume 14, Supplement 1, pp 103–109 | Cite as

Membrane fluctuations around inclusions

  • Christian D. Santangelo
  • Oded Farago


The free energy of inserting a protein into a membrane is determined by considering the variation in the spectrum of thermal fluctuations in response to the presence of a rigid inclusion. Both numerically and through a simple analytical approximation, we find that the primary effect of fluctuations is to reduce the effective surface tension, hampering the insertion at low surface tension. Our results, which should also be relevant for membrane pores, suggest (in contrast to classical nucleation theory) that a finite surface tension is necessary to facilitate the opening of a pore.


Membranes Proteins Thermal fluctuations Surface tension 


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  1. 1.
    Safran, S.A.: Statistical Thermodynamics of Surfaces, Interfaces, and Membranes. Addison-Wesley, New York (1994)Google Scholar
  2. 2.
    Lipowsky, R., Sackmann, E. (eds.): Structure and Dynamics of Membranes. Elsevier, Amsterdam (1995)Google Scholar
  3. 3.
    Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K., Watson, J.D.: Molecular Biology of the Cell. Garland, New York (1989)Google Scholar
  4. 4.
    Bruinsma, R., Pincus, P.: Protein aggregation in membranes. Curr. Opin. Solid State Mater. Sci. 1, 401–406 (1996); Kardar, M., Golestanian, R.: The “friction” of vacuum, and other fluctuation-induced forces. Rev. Mod. Phys. 71, 1233–1245 (1999), and references thereinGoogle Scholar
  5. 5.
    May, S.: Theories on structural perturbations of lipid bilayers. Curr. Opin. Colloid Interface Sci. 5, 244–249 (2000); Partenskii, M.B., Jordan, P.C.: Membrane deformation and the elastic energy of insertion: perturbation of membrane elastic constants due to peptide insertion. J. Chem. Phys. 117, 10768–10776 (2002), and references therein. An exception is the discussion in Netz, R.R.: Inclusions in fluctuating membranes: exact results. J. Phys. I (France) 7, 833–852 (1997)Google Scholar
  6. 6.
    Helfrich, W.: Elastic properties of liqid bilayers: theory and possible experiments. Z Naturforsch[C] 28, 693–703 (1973)Google Scholar
  7. 7.
    Ben-Shaul, A., Ben-Tal, N., Honig, B.: Statistical thermodynamic analysis of peptide and protein insertion in lipid membrances. Biophys. J. 71, 130–137 (1996)CrossRefGoogle Scholar
  8. 8.
    Lazaridis, T.: Effective energy function for proteins in liqid membrances. Proteins52, 176–192 (2003) and references thereinCrossRefGoogle Scholar
  9. 9.
    The conservation of the total membrane area [see Eq. (10)] introduces an implicit coupling between the equilibrium and fluctuation parts of the free energy. This coupling is removed by the assumption that H = H′ = 0. Furthermore, this assumption ensures that the inclusion has a circular projected area (which is not case when the inclusion tilts). Height fluctuations, as well as cases with arbitrary projected area, are discussed in a more detailed publication [12], where we show that these complications do not affect the membrane fluctuation part of the free energy (to order \({r_0^2}\))Google Scholar
  10. 10.
    Sens, P., Safran, S.A.: Pore formation and area exchange in tense membranes. Europhys. Lett. 43, 95–100 (1998)CrossRefGoogle Scholar
  11. 11.
    Koltover, I., Rädler, J.O., Safinya, C.R.: Membrane mediated attraction and ordered aggregation of colloidal particles bound to giant phospholipid vesicles. Phys. Rev. Lett. 82, 1991–1994 (1999)CrossRefGoogle Scholar
  12. 12.
    Farago, O., Santangelo, C.D.: Pore formation in fluctuating membrances. J. Chem. Phys. 122, 044901 (2005)CrossRefGoogle Scholar
  13. 13.
    Litster, J.D.: Stability of lipid bilayers and red blood cell membranes. Phys. Lett. A 53, 193–194 (1975)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of MassachusettsAmherstUSA
  2. 2.Department of Biomedical EngineeringBen Gurion UniversityBe’er ShevaIsrael

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