The European Physical Journal E

, Volume 14, Issue 3, pp 299–308 | Cite as

Tilt modulus of a lipid monolayer

Article

Abstract.

In addition to the familiar bending and stretching deformations, lipid monolayers and bilayers in their disordered state are often subjected to tilt deformations, occurring for instance in structural rearrangements accompanying membrane fusion, or upon insertion of “oblique” hydrophobic proteins into lipid bilayers. We study the elastic response of a flat lipid monolayer to a tilt deformation, using the spatial and conformational average of the chain end-to-end vector from the membrane normal to define a macroscopic membrane tilt. The physical origin and magnitude of the corresponding tilt modulus \(\kappa_t\) is analyzed using two complementary theoretical approaches. The first is a phenomenological model showing that the tilt and bending deformations are decoupled and the effects of inter-chain correlations on the tilt modulus is small. The second is based on a molecular-level mean-field theory of chain packing, enabling numerical evaluation of the tilt modulus for realistic, multi-conformation, chain models. Both approaches reveal that the tilt modulus involves two major contributions. The first is elastic in origin, arising from the stretching of the hydrocarbon chains upon a tilt deformation and reflecting the loss of chain conformational freedom associated with chain stretching. The second, purely entropic, contribution results from the constraints imposed by a tilt deformation on the fluctuations of chain director orientations. Using the chain-packing theory we compute the two contributions numerically as a function of the cross-sectional area per chain. The elastic and entropic terms are shown to dominate the value of \(\kappa_t\) for small and large areas per chain, respectively. For typical cross-sectional areas of lipid chains in biological membranes they areof comparable magnitude, yielding \(\kappa_t \approx 0.2k_{\rm B}T/\AA^2\).

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References

  1. 1.
    J.M. Seddon, R.H. Templer, in Structure and Dynamics of Membranes, edited by R. Lipowsky, E. Sackmann, Vol. 1, section 3, second edition (Elsevier, Amsterdam, 1995) pp. 98-160.Google Scholar
  2. 2.
    V. Luzzati, in Biological Membranes, edited by D. Chapman (Academic Press, New York, 1968) pp. 71-123.Google Scholar
  3. 3.
    R. Lipowsky, E. Sackmann (Editors), Structure and Dynamics of Membranes (Elsevier, Amsterdam, 1995).Google Scholar
  4. 4.
    M. Bessis, Living Blood Cells and Their Ultrastructure (Springer, Berlin, 1973).Google Scholar
  5. 5.
    L.V. Chernomordik, M.M. Kozlov, Annu. Rev. Biochem. 72, 175 (2003).CrossRefGoogle Scholar
  6. 6.
    J.M. Park, T.C. Lubensky, J. Phys. (Paris) 6, 1217 (1996).CrossRefGoogle Scholar
  7. 7.
    N. Dan, P. Pincus, S.A. Safran, Langmuir 9, 2768 (1993).Google Scholar
  8. 8.
    R.R. Netz, P. Pincus, Phys. Rev. E 52, 4114 (1995).CrossRefGoogle Scholar
  9. 9.
    H. Aranda-Espinoza, A. Berman, N. Dan, P. Pincus, S.A. Safran, Biophys. J.71, 648 (1996).Google Scholar
  10. 10.
    J.B. Fournier, Eur. Phys. J. E11, 261 (1999).Google Scholar
  11. 11.
    M. Goulian, Curr. Opin. Colloid Interface Sci.1, 358 (1996).Google Scholar
  12. 12.
    T.R. Weikl, M.M. Kozlov, W. Helfrich, Phys. Rev. E57, 6988 (1998).Google Scholar
  13. 13.
    S. May, A. Ben-Shaul, Phys. Chem. Chem. Phys.2, 4494 (2000).Google Scholar
  14. 14.
    D.D. Lasic, Liposomes in Gene Delivery (CRC Press, Boca Raton, 1997).Google Scholar
  15. 15.
    J.W. Gibbs, On the Equilibrium of Heterogeneous Substances. 1876/1878, in The Collected Works of J. Willard Gibbs, Vol. 1 (Yale University Press, New Haven, 1948).Google Scholar
  16. 16.
    W. Helfrich, Z. Naturforsch.28, 693 (1973).Google Scholar
  17. 17.
    E. Evans, R. Skalak, Mechanics and Thermodynamics of Biomembranes (CRC Press, Boca Raton, 1980).Google Scholar
  18. 18.
    M. Hamm, M.M. Kozlov, Eur. Phys. J. B6, 519 (1998).Google Scholar
  19. 19.
    R.P. Rand, N.L. Fuller, Biophys J.66, 2127 (1994).Google Scholar
  20. 20.
    N. Dan, S.A. Safran, Biophys. J.75, 1410 (1998).Google Scholar
  21. 21.
    S. May, A. Ben-Shaul, Biophys. J.76, 751 (1999).Google Scholar
  22. 22.
    M.M. Kozlov, V.S. Markin Biofizika28, 242 (1983).Google Scholar
  23. 23.
    D.P. Siegel, Biophys. J.65, 2124 (1993).Google Scholar
  24. 24.
    Y. Kozlovsky, M.M. Kozlov, Biophys J.85, 85 (2003).Google Scholar
  25. 25.
    S. May, Eur. Phys. J. E3, 37 (2000).Google Scholar
  26. 26.
    J.B. Fournier, Europhys. Lett.43, 725 (1998).Google Scholar
  27. 27.
    R.M. Epand, R.F. Epand, Biochem. Biophys. Res. Comm.202, 1420 (1994).Google Scholar
  28. 28.
    Y. Kozlovsky, J. Zimmerberg, M.M. Kozlov, to be published in Biophys. J. (2004).Google Scholar
  29. 29.
    W. Helfrich, J. Prost, Phys. Rev. A38, 3065 (1988).Google Scholar
  30. 30.
    F.C. MacKintosh, T.C. Lubensky, Phys. Rev. Lett.67, 1169 (1991).Google Scholar
  31. 31.
    J.V. Selinger, J.M. Schnur, Phys. Rev. Lett.71, 4091 (1993).Google Scholar
  32. 32.
    P.-G. de Gennes, The Physics of Liquid Crystals (Oxford University Press, 1987).Google Scholar
  33. 33.
    Y. Kozlovsky, M.M. Kozlov, Biophys. J.82, 882 (2002).Google Scholar
  34. 34.
    M. Hamm, M.M. Kozlov, Eur. Phys. J. E3, 323 (2000).Google Scholar
  35. 35.
    F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, 1965).Google Scholar
  36. 36.
    L.D. Landau, E.M. Lifshitz, Statistical Physics (Nauka, Moskva, 1976).Google Scholar
  37. 37.
    S. May, Eur. Biophys. J.29, 17 (2000).Google Scholar
  38. 38.
    K. Bohinc, V. Kralj-Iglič, S. May, J. Chem. Phys.119, 7435 (2003).Google Scholar
  39. 39.
    A. Ben-Shaul, in Structure and Dynamics of Membranes edited by R. Lipowsky, E. Sackmann, Vol. 1, section 7 (Elsevier, Amsterdam, 1995) pp. 359-402.Google Scholar
  40. 40.
    J.N. Israelachvili, Intermolecular and Surface Forces, second edition (Academic Press, 1992).Google Scholar
  41. 41.
    P.J. Flory, Statistical Mechanics of Chain Molecules (Wiley-Interscience, New York, 1969).Google Scholar
  42. 42.
    I. Szleifer, A. Benshaul, W.M. Gelbart, J. Chem. Phys.83, 3612 (1985).Google Scholar
  43. 43.
    V.A. Parsegian, R.P. Rand, in Structure and Dynamics of Membranes, edited by R. Lipowsky, E. Sackmann, number 1B (Elsevier, Amsterdam, 1995) pp. 643-690.Google Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  • S. May
    • 1
  • Y. Kozlovsky
    • 2
  • A. Ben-Shaul
    • 3
  • M. M. Kozlov
    • 2
  1. 1.Junior Research Group “Lipid Membranes”Friedrich-Schiller-Universität JenaJenaGermany
  2. 2.Department of Physiology and Pharmacology, Sackler Faculty of MedicineTel-Aviv UniversityTel AvivIsrael
  3. 3.Department of Physical Chemistry and the Fritz Haber Research CenterThe Hebrew UniversityJerusalemIsrael

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