Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T06:36:55.052Z Has data issue: false hasContentIssue false
  • English
  • Français

A higher-order boundary layer analysis for lipid vesicles with two fluid domains

Published online by Cambridge University Press:  01 February 2008

SOVAN L. DAS  and
JAMES T. JENKINS
SOVAN L. DAS
Affiliation:
Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA
JAMES T. JENKINS
Affiliation:
Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

We obtain approximate solutions to the equations that govern the shape of giant unilamellar vesicles (GUVs) with two fluid phases. The equations involve a dimensionless small parameter related to the resistance to changes in its local mean curvature. Asymptotic solutions for the shape are obtained up to and including terms of first order in the small parameter. At this order, we determine a relationship between the tangent angle at the interface and the difference in the Gaussian curvature stiffnesses of the co-existing phases. This relationship demonstrates that a difference in the Gaussian curvature stiffnesses moves the phase boundary away from the neck, as determined in previous numerical studies. The analytical expression for the tangent angle obtained here can be used to determine elastic parameters for the membranes from experimental data. Use of the analytical expression will eliminate the need for the repeated generation of numerical solutions in the estimation of the material parameters. Our analytical solution also reduces the number of measurements needed as inputs for an existing boundary layer analysis.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 597 , 25 February 2008 , pp. 429 - 448
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Akimov, S. A., Kuzmin, P. I., Zimmerberg, J., Cohen, F. S. & Chizmadzhev, Y. A. 2004 An elastic theory for line tension at a boundary separating two lipid monolayer regions of different thickness. J. Electroanal. Chem. 564, 13–18.CrossRefGoogle Scholar
Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K. & Walter, P. 2002 Molecular Biology of The Cell, 4th edn. Garland Science, NY.Google Scholar
Allain, J.-M. & BenAmar, M. 2006 Budding and fission of a multiphase vesicle. Eur. Phys. J. E 20, 409–420.Google ScholarPubMed
Almeida, R. F. M., Fedorov, A. & Prieto, M. 2003 Sphingomyelin/phosphatidylcholine/cholesterol phase diagram: boundaries and composition of lipid rafts. Biophys. J. 85, 2406–2416.CrossRefGoogle ScholarPubMed
Baumgart, T., Das, S. L., Webb, W. W. & Jenkins, J. T. 2005 Membrane elasticity in giant vesicles with fluid phase coexistence. Biophys. J. 89, 1067–1080.CrossRefGoogle ScholarPubMed
Baumgart, T., Hess, S. T. & Webb, W. W. 2003 Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension. Nature 425, 821–824.CrossRefGoogle ScholarPubMed
Bender, C. M. & Orszag, S. A. 1999 Advanced Mathematical Methods for Scientists and Engineers. Springer.CrossRefGoogle Scholar
Calladine, C. R. & Greenwood, J. A. 2002 Mechanics of tether formation in liposomes. ASME J. Biomech. Engng 124, 576–585.CrossRefGoogle ScholarPubMed
Das, S. L. 2007 Studies of axisymmetric lipid bilayer vesicles: parameter estimation, micropipette aspiration, and phase transition. PhD Thesis, Cornell University.Google Scholar
Duwe, H. P., Käs, J. & Sackmann, E. 1990 Bending elastic moduli of lipid bilayers: Modulation by solutes. J. Phys. (Paris) 51, 945–961.CrossRefGoogle Scholar
Evans, E. A. 1980 Minimum energy analysis of membrane deformation applied to pipet aspiration and surface adhesion of red blood cells. Biophys. J. 30, 265–284.CrossRefGoogle ScholarPubMed
Evans, E. & Yeung, A. 1994 Hidden dynamics in rapid changes of bilayer shape. Chem. Phys. Lipids 73, 39–56.CrossRefGoogle Scholar
Helfrich, W. 1973 Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. 28c, 693–703.CrossRefGoogle Scholar
Hinch, E. J. 1991 Perturbation Methods. Cambridge University Press.CrossRefGoogle Scholar
Israelachvili, J. N. 1992 Intermolecular and Surface Forces: With Applications to Colloidal and Biological Systems, 2nd edn. Academic.Google Scholar
Jenkins, J. T. 1976 Static equilibrium configurations of a model red blood cell. J. Math. Biol. 4, 149–169.CrossRefGoogle Scholar
Jenkins, J. T. 1977 The equations of mechanical equilibrium of a model membrane. SIAM J. Appl. Math. 32, 755–764.CrossRefGoogle Scholar
Jülicher, F. & Lipowsky, R. 1996 Shape transformations of vesicles with intramembrane domains. Phys. Rev. E 53, 2670–2683.Google ScholarPubMed
Leibler, S. 2004 Equilibrium statistical mechanics of fluctuating flims and membranes. In Statistical Mechanics of Membranes and Surfaces, 2nd edn (ed. Nelson, D., Piran, T. & Weinberg, S.). Springer.Google Scholar
Lipowsky, R., Brinkmann, M., Dimova, R., Haluska, C., Kierfeld, J. & Shillcock, J. 2005 Wetting, budding, and fusion—morphological transitions of soft surfaces. J. Phys.: Cond. Mat. 17, S2885–S2902.Google Scholar
Lipowsky, R. & Sackmann, E., ed. 1995 Structure and Dynamics of Membranes, Handbook of Biological Physics Vol. 1. Elsevier.Google Scholar
OŃeil, B. 1966 Elementary Differential Geometry. Academic.Google Scholar
Powers, T. R., Huber, G. & Goldstein, R. E. 2002 Fluid-membrane tethers: minimal surfaces and elastic boundary layers. Phys. Rev. E 65, 041901–1-041908.CrossRefGoogle ScholarPubMed
Seifert, U. 1997 Configurations of fluid membranes and vesicles. Adv. Phys. 46, 13–137.CrossRefGoogle Scholar
Semrau, S., Idema, T., Holtzer, L., Schmidt, T. & Storm, C. 2007 Accurate determination of elastic parameters for multi-component membranes. arXiv:cond-mat/0612554v3.CrossRefGoogle Scholar
Veatch, S. L. & Keller, S. L. 2003 Separation of liquid mixtures in giant vesicles of ternary mixtures of phospholipids and cholesterol. Biophys. J. 85, 3074–3083.CrossRefGoogle Scholar
Veatch, S. L. & Keller, S. L. 2005 Seeing spots: complex phase behavior in simple membranes. Biochim. Biophys. Acta 1746, 172–185.CrossRefGoogle ScholarPubMed
Waugh, R. & Evans, E. A. 1979 Thermoelasticity of red blood cell membrane. Biophys. J. 26, 115–132.CrossRefGoogle ScholarPubMed
Widom, B. 1999 Structure and tension of interfaces. Molecular Phys. 96, 1019–1026.CrossRefGoogle Scholar