Entropic part of the boundary energy in a lipid membrane

  • B. B. Kheyfets
  • S. I. Mukhin


Two-phase lipid membrane is modeled with lipids of different bending rigidity of hydrophobic tails: domains consist of “rigid” lipid liquid condensed phase and are surrounded by the “flexible” lipid liquid expanded phase. Within the framework of the earlier proposed model of flexible strings, entropic contribution not including mismatch energy is calculated analytically. “Entropic” line tension is found to be weakly dependent on the domain radius. According to the model, it is shown that merely “entropic mismatch” is not enough for the domain formation. In the paper it is assumed that lipids at the boundary, on the average, have larger area than the ones in the volume. This leads to an increase of energy of boundary lipids. Cases of lipids with nearly the same bending rigidities and with strongly different ones are considered. Free energy is calculated using Taylor expansion on the difference of area of lipids at the domain’s boundary and in the volume. Based on the calculated boundary energy domain stability in the finite system is estimated.


lipid membrane raft line tension flexible string model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Edidin M. 2003. The state of lipid rafts: From model membranes to cells. Annu. Rev Biophys. Biomol. Struct. 32, 257–283.PubMedCrossRefGoogle Scholar
  2. 2.
    Yethiraj A., Weisshaar J. 2007. Why are lipid rafts not observed in vivo? Biophys. J. 93, 3113–3119.PubMedCrossRefGoogle Scholar
  3. 3.
    Fan J., Sammalkorpi M., Haataja M. 2010. Formation and regulation of lipid microdomains in cell membranes: Theory, modeling, and speculation. FEBS Let. 584, 1678–1684.CrossRefGoogle Scholar
  4. 4.
    Frolov V.A., Chizmadzhev Y.A., Cohen F.S., Zimmerberg J. 2006. “Entropic traps” in the kinetics of phase separation in multicomponent membranes stabilize nanodomains. Biophys. J. 91, 189–205.PubMedCrossRefGoogle Scholar
  5. 5.
    Mukhin S.I., Baoukina S. 2005. Analytical derivation of lateral pressure profile from microscopic model of lipid bilayer. Phys. Rev. E. 88, 061918–6.CrossRefGoogle Scholar
  6. 6.
    Mukhin S.I., Kheyfets B.B. 2010. Analytical approach to thermodynamics of bolalipid membrane. Phys. Rev. E. 82, 051901–9.CrossRefGoogle Scholar
  7. 7.
    Akimov S.A., Kuzmin P.I., Zimmerberg J., Cohen F.S. 2007. Lateral tension increases the line tension between two domains in a lipid bilayer membrane. Phys. Rev. E. 75, 011919-1–011919-8.CrossRefGoogle Scholar
  8. 8.
    Landau L.D., Lifshitz E.M., 1970. Theoretical Physics, Vol. VII. Theory of elasticity. Pergamon, Oxford.Google Scholar
  9. 9.
    Nelson D. 2002. Defects and Geometry in Condensed Matter Physics. Cambridge, U.K.: Cambridge University Press.Google Scholar
  10. 10.
    Israelachvili J.N. 1992. Intermolecular and Surface Forces. 2nd ed. London: Academic Press.Google Scholar
  11. 11.
    Lipid Rafts and Caveolae — From Membrane Biophysics to Cell Biology. 2006. Ed. Fielding C.J. Wiley-VCH.Google Scholar
  12. 12.
    Stein W.A., Jones E., Oliphant T., et al. Sage Mathematics Software. Vol. 4.6.2. The Sage Development Team.

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  1. 1.National University of Science and Technology “MISIS”MoscowRussia

Personalised recommendations