Skip to main content
Log in

Two-phase vesicles: a study on evolutionary and stationary models

  • Original Article
  • Published:
European Biophysics Journal Aims and scope Submit manuscript

Abstract

In the current article, the dynamic evolution of two-phase vesicles is presented as an extension to a previous stationary model and based on an equilibrium of local forces. In the simplified model, ignoring the effects of membrane inertia, a dynamic equilibrium between the membrane bending potential and local fluid friction is considered in each phase. The equilibrium equations at the domain borders are completed by extended introduction of membrane section reactions. We show that in some cases, the results of stationary and evolutionary models are in agreement with each other and also with experimental observations, while in others the two models differ markedly. The value of our approach is that we can account for unresponsive points of uncertainty using our equations with the local velocity of the lipid membranes and calculating the intermediate states (shapes) in the consequent evolutionary, or response, path.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Experimental vesicle is redrawn from (García-Sáez et al. 2007)

Fig. 5

Fusion-budding process is redrawn from experiment by Riske et al. (2006)

Fig. 6

Experimental vesicle is redrawn from Dimova et al. (2006)

Fig. 7
Fig. 8

Similar content being viewed by others

Abbreviations

V:

Volume

v:

Reduced volume

v :

Membrane local velocity vector

v :

Membrane normal velocity (scalar)

References

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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Bonito A, Nochetto RH, Pauletti MS (2010) Parametric FEM for geometric biomembranes. J Comput Phys 229:3171–3188

    Article  CAS  Google Scholar 

  • Campelo F, Hernandez-Machado A (2006) Dynamic model and stationary shapes of fluid vesicles. Eur Phys J E 20:37–45

    Article  CAS  PubMed  Google Scholar 

  • Campelo F, Hernández-Machado A (2007) Model for curvature-driven pearling instability in membranes. Phys Rev Lett 99:088101

    Article  CAS  PubMed  Google Scholar 

  • Cox G, Lowengrub J (2015) The effect of spontaneous curvature on a two-phase vesicle. Nonlinearity 28:773

    Article  PubMed  PubMed Central  Google Scholar 

  • Dimova R, Aranda S, Bezlyepkina N, Nikolov V, Riske KA, Lipowsky R (2006) A practical guide to giant vesicles. Probing the membrane nano regime via optical microscopy. J Phys Condens Matter 18:S1151

    Article  CAS  PubMed  Google Scholar 

  • García-Sáez AJ, Chiantia S, Schwille P (2007) Effect of line tension on the lateral organization of lipid membranes. J Biol Chem 282:33537–33544

    Article  PubMed  Google Scholar 

  • Givli S, Giang H, Bhattacharya K (2012) Stability of multicomponent biological membranes. SIAM J Appl Math 72:489–511

    Article  CAS  Google Scholar 

  • Haluska CK, Riske KA, Marchi-Artzner V, Lehn J-M, Lipowsky R, Dimova R (2006) Time scales of membrane fusion revealed by direct imaging of vesicle fusion with high temporal resolution. Proc Natl Acad Sci 103:15841–15846

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Haußer F, Li S, Lowengrub J, Marth W, Rätz A, Voigt A (2013) Thermodynamically consistent models for two-component vesicles. IJBB 2:19–48

    Google Scholar 

  • Hess ST, Gudheti MV, Mlodzianoski M, Baumgart T (2007) Shape analysis of giant vesicles with fluid phase coexistence by laser scanning microscopy to determine curvature, bending elasticity, and line tension Methods in membrane lipids. Springer, Berlin, pp 367–387

    Google Scholar 

  • Ikonen E (2001) Roles of lipid rafts in membrane transport. Curr Opin Cell Biol 13:470–477

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • Jülicher F, Lipowsky R (1996) Shape transformations of vesicles with intramembrane domains. Phys Rev E 53:2670

    Article  Google Scholar 

  • Knorr RL, Dimova R, Lipowsky R (2012) Curvature of double-membrane organelles generated by changes in membrane size and composition. PloS One 7:e32753

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Kuwert E, Schatzle R (2002) Gradient flow for the Willmore functional. Commun Anal Geom 10:307–339

    Article  Google Scholar 

  • Link F (2013) Gradient Flow for the Willmore functional in Riemannian manifolds of bounded geometry. arXiv preprint arXiv:13086055

  • Lipowsky R (1993) Domain-induced budding of fluid membranes. Biophys J 64:1133

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Perko L (2013) Differential equations and dynamical systems, vol 7. Springer Science & Business Media, Berlin

    Google Scholar 

  • Rahimi M, Arroyo M (2012) Shape dynamics, lipid hydrodynamics, and the complex viscoelasticity of bilayer membranes. Phys Rev E 86:011932

    Article  Google Scholar 

  • Riske K, Bezlyepkina N, Lipowsky R, Dimova R (2006) Electrofusion of model lipid membranes viewed with high temporal resolution. Biophys Rev Lett 1:387–400

    Article  CAS  Google Scholar 

  • Simons K, Ikonen E (1997) Functional rafts in cell membranes. Nature 387:569–572

    Article  CAS  PubMed  Google Scholar 

  • Simons K, Vaz WL (2004) Model systems, lipid rafts, and cell membranes 1. Annu Rev Biophys Biomol Struct 33:269–295

    Article  CAS  PubMed  Google Scholar 

  • Sohn JS, Tseng Y-H, Li S, Voigt A, Lowengrub JS (2010) Dynamics of multicomponent vesicles in a viscous fluid. J Comput Phys 229:119–144

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Streets J (2012) The gradient flow of the L 2 curvature functional with small initial energy. J Geom Anal 22:691–725

    Article  Google Scholar 

  • Vequi-Suplicy CC, Riske KA, Knorr RL, Dimova R (2010) Vesicles with charged domains. Biochim et Biophys Acta (BBA) Biomembr 1798:1338–1347

    Article  CAS  Google Scholar 

  • Wang X, Du Q (2008) Modelling and simulations of multi-component lipid membranes and open membranes via diffuse interface approaches. J Math Biol 56:347–371

    Article  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to MohammadMahdi Sahebifard.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (DOCX 35 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sahebifard, M., Shahidi, A. & Ziaei-Rad, S. Two-phase vesicles: a study on evolutionary and stationary models. Eur Biophys J 46, 343–350 (2017). https://doi.org/10.1007/s00249-016-1177-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00249-016-1177-3

Keywords

Navigation