Abstract
The theory of fluid surfaces with elastic resistance to bending is applied to coexistent phase equilibria in biomembranes composed of lipid bilayers. A simplified version of the model is used to simulate the necking and budding of closed vesicles.
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Ericksen, J.L.: Theory of Cosserat surfaces and its applications to shells, interfaces and cell membranes. In: Glockner, P.G., Epstein, M., Malcolm, D.J. (eds.) Proc. Int. Symp. on Recent Developments in the Theory and Application of Generalized and Oriented Media, pp. 27–39. Calgary, Canada (1979)
Jenkins, J.T.: The equations of mechanical equilibrium of a model membrane. SIAM J. Appl. Math. 32, 755–764 (1977)
Jenkins, J.T.: Static equilibrium configurations of a model red blood cell. J. Math. Biol. 4, 149–169 (1977)
Helfrich, W.: Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. 28c, 693–703 (1973)
Rosso, R., Virga, E.G.: Adhesive borders of lipid membranes. Proc. R. Soc. Lond. A 455, 4145–4168 (1999)
Steigmann, D.J.: Fluid films with curvature elasticity. Arch. Ration. Mech. Anal. 150, 127–152 (1999)
Nitsche, J.C.C.: Boundary value problems for variational integrals involving surface curvatures. Quart. Appl. Math. 51, 363–387 (1993)
Steigmann, D.J.: On the relationship between the Cosserat and Kirchhoff-Love theories of elastic shells. Math. Mech. Solids 4, 275–288 (1999)
Murdoch, A.I., Cohen, H.: Symmetry considerations for material surfaces. Arch. Ration. Mech. Anal. 72, 61–89 (1979)
Ou-Yang, Z.-C., Liu, J.-X., Xie, Y.-Z.: Geometric Methods in the Elastic Theory of Membranes in Liquid Crystal Phases. World Scientific, Singapore (1999)
McMahon, H.T., Gallop, J.L.: Membrane curvature and mechanisms of dynamic cell membrane remodelling. Nature 438, 590–596 (2005)
Baumgart, T., Hess, S.T., Webb, W.W.: Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension. Nature 425, 821–824 (2003)
Baumgart, T., Das, S., Webb, W.W., Jenkins, J.T.: Membrane elasticity in giant vesicles with fluid phase coexistence. Biophys. J. 89, 1067–1080 (2005)
Ericksen, J.L.: Equilibrium of bars. J. Elast. 5, 191–202 (1975)
Hilgers, M.G., Pipkin, A.C.: Energy-minimizing deformations of elastic sheets with bending stiffness. J. Elast. 31, 125–139 (1993)
Eremeyev, V.A., Pietraszkiewicz, W.: The nonlinear theory of elastic shells with phase transitions. J. Elast. 74, 67–86 (2004)
Todhunter, I., Pearson, K.: A History of the Theory of Elasticity and of the Strength of Materials. Dover, New York (1960)
Steigmann, D.J.: Irreducible function bases for simple fluids and liquid crystal films. Z. Angew. Math. Phys. 54, 462–477 (2003)
Zheng, Q.-S.: Irreducible function bases for simple fluids and liquid crystal films: A new derivation. Z. Angew. Math. Phys. 54, 478–483 (2003)
Steigmann, D.J., Baesu, E., Rudd, R.E., Belak, J., McElfresh, M.: On the variational theory of cell-membrane equilibria. Interfaces Free Bound. 5, 357–366 (2003)
Gelfand, I.M., Fomin, S.V.: Calculus of Variations. Prentice-Hall, New York (1963)
Graves, L.M.: The Weierstrass condition for multiple integral variation problems. Duke Math. J. 5, 656–660 (1939)
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Agrawal, A., Steigmann, D.J. Coexistent Fluid-Phase Equilibria in Biomembranes with Bending Elasticity. J Elasticity 93, 63–80 (2008). https://doi.org/10.1007/s10659-008-9165-1
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DOI: https://doi.org/10.1007/s10659-008-9165-1