Skip to main content
Log in

Equilibrium Shape Equation and Geometrically Permissible Condition for Two-Component Lipid Bilayer Vesicles

  • Published:
Journal of Biological Physics Aims and scope Submit manuscript

Abstract

Equilibrium shapes of vesicles composed of a mixture of partially miscible amphiphiles are investigated. To take into account the influences of the composition, a simple phenomenological coupling between the co mposition and the curvatures, including the mean curvature and the Gauss curvature of the membrane surface, is suggested. By minimizing the potential functional, the general shape equation is obtained and solved analytically for vesicles with simple shapes. Besides, the geometrical constraint equation and geometrically permissible condition for the two-component lipid vesicles are put forward. The influences of physical parameters on the geometrically permissible phase diagrams are predicted. The close relations between the predictions and existing experimental phenomena published recently are shown.

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

  • Canham, P.B.: The Minimum Energy of Bending as a Possible Explanation of the Biconcave Shape of the Human Red Blood Cell, J. Theor. Biol. 26 (1970), 61–81.

    PubMed  Google Scholar 

  • Helfrich, W.: Elastic Properties of Lipid Bilayers: Theory and Possible Experiments, Z. Naturforsch.C. 28 (1973), 693–703.

    PubMed  Google Scholar 

  • Deuling, H.J. and Helfrich, W.: The Curvature Elasticity of Fluid Membranes: A Catalogue of Vesicle Shapes, J. Phys. France. 37 (1976), 1335–1345.

    Google Scholar 

  • Seifert, U., Berndl, K. and Lipowsky, R.: Shape Transformations of Vesicles: Phase Diagrams for Spontaneous Curvature and Bilayer-Coupling Models, Phys. Rev. A. 44 (1991), 1182–1202.

    Article  PubMed  Google Scholar 

  • Leibler, S.: Curvature Instability in Membranes, J. Phys. France. 47 (1986), 507–516.

    Google Scholar 

  • Seifert, U.: Configurations of Fluid Membranes and Vesicles, Adv. Phys. 46 (1997), 13–137.

    Google Scholar 

  • Taniguchi, T., Kawasaki, K., Andlman, D. and Kawakatsu, T.: Equilibrium Shape Deformations of Two-Component Vesicles, J. Phys. II. France. 4 (1994), 1333–1362.

    Article  Google Scholar 

  • Chen, C.-M., Higgs, P.G. and Mackintosh, F.C.: Theory of Fission for Two-Component Lipid Vesicles, Phys. Rev. Lett. 79 (1997), 1579–1582.

    Article  Google Scholar 

  • Deuling, H.J. and Helfrich, W.: Red Blood Cell Shapes as Explained on the Basis of Curvature Elasticity, Biophys. J. 16 (1976), 861–868.

    PubMed  Google Scholar 

  • Brochard, F., DE Gennes, P.G. and Pfeuty, P.: Surface Tension and Deformations of Membrane Structures: Relation to Two-Dimensional Phase Transitions, J. Physique 37 (1976), 1099–1104.

    Google Scholar 

  • Iglič, A.: A Possible Mechanism Determining the Stability of Spiculated Red Blood Cells, J. Biomech. 30 (1997), 35–40.

    Article  PubMed  Google Scholar 

  • Evans, E. and Rawicz, W.: Entropy-Driven Tension and Bending Elasticity in Condensed-Fluid Membranes, Phys. Rev. Lett. 64 (1990), 2094–2097.

    Article  PubMed  Google Scholar 

  • Fourcade, B., Miao, L., Rao, M. and Wortis, M.: Scaling Analysis of Narrow Necks in Curvature Models of Fluid Lipid-Bilayer Vesicles, Phys. Rev. E. 49 (1994), 5276–5286.

    Article  Google Scholar 

  • Mutz, M. and Bensimon, D.: Observation of Toroidal Vesicles, Phys. Rev. A. 43 (1991), 4525–4527.

    Article  PubMed  Google Scholar 

  • Yin, Y., Chen, Y., Ni, D., Shi, H. and Fan, Q.: Shape Equations and Curvature Bifurcations Induced by Inhomogeneous Rigidities in Cell Membranes, J. Biomech (2004), in press.

  • Ou-Yang, Z.-C. and Helfrich, W.: Instability and Deformation of a Spherical Vesicle by Pressure, Phys. Rev. Lett. 59 (1987), 2486–2488.

    Article  PubMed  Google Scholar 

  • Ou-Yang, Z.-C. and Helfrich, W.: Bending Energy of Vesicle Membranes: General Expressions for the First, Second and Third Variation of the Shape Energy and Applications to Spheres and Cylinders, Phys. Rev. A. 39 (1989), 5280–5288.

    Article  PubMed  Google Scholar 

  • Yin, Y.: Integral Theorems Based on A New Gradient Operator Derived from Biomembranes (Part II): Deduced Transformations and Applications, Tsinghua Science & Technology, 10(3) (2005), in press.

  • Yin, Y. and Yin, J.: Geometrical Constraint Equations and Geometrically Permissible Phase Diagrams for Vesicles or Biomembranes, Chin. Phys. Lett. 21 (2004), 2057–2058.

    Article  Google Scholar 

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

    Google Scholar 

  • Saitoh, A., Takiguchi, K., Tanaka, Y. and Hotani, H.: Opening-up of Liposomal Membranes by Talin, Proc. Natl. Acad. Sci. U.S.A. 95 (1998), 1026–1031.

    Google Scholar 

  • Yin, Y.: Integral Theorems Based on a New Gradient Operator Derived from Biomembranes (Part II), Tsinghua Science & Technology, 10(3) (2005), in press.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yin Yajun.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dong, N., Yajun, Y. & Huiji, S. Equilibrium Shape Equation and Geometrically Permissible Condition for Two-Component Lipid Bilayer Vesicles. J Biol Phys 31, 135–143 (2005). https://doi.org/10.1007/s10867-005-4307-1

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10867-005-4307-1

Keywords

Navigation