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Numéro
J. Phys. II France
Volume 1, Numéro 8, August 1991
Page(s) 995 - 1012
DOI https://doi.org/10.1051/jp2:1991122
References of J. Phys. II France 1 995-1012
  1. For a general reference see : Statistical Mechanics of Membranes and Surfaces, Eds D Nelson, T. Piran and S Weinberg (World Scientific, New Jersey, 1988)
  2. Canham P B , J Theor B$\imath$ol 26 (1970) 61 , Helfrich W , Z Naturforsch 28c (1973) 693, Deuling H J and Helfrich W., J Phys France 37 (1976) 1335 [CrossRef] [EDP Sciences] , Evans E A , B$\imath$ophys J 30 (1980) 265 , Jenkins J T , J Math B$\imath$ology 4 (1977) 149 , Peterson M A , Mol Cryst L$\imath$q Cryst 127 (1985) 257 and J Math Phys 26 (1985) 711 We dropped the Gaussian curvature term as it is independent of the vesicle shape
  3. Sackmann E , Duwe H P and Engelhardt H , Faraday Discuss Chem Soc 81 (1986) , Evans E. and Rawicz W , Phys Rev Lett. 64 (1990) 2094 [CrossRef] [PubMed] , Berndl K., KAs J., Lipovsky R., Sackmann E and Seiffert U , submitted to Europhys Lett
  4. Evans E , in abstract of Self-Assembling Molecular Materials Conference, Princeton, May 1990 This experiment provided the original motivation for investigating the van der Waals interaction
  5. Miao L , Fourcade B , Rao M., Wortis M and Zia R K. P , preprint
  6. Seifert U , Berndl K and Lipovsky R., preprint
  7. Svetina S and Zeks B , J Eur. B$\imath$ophys 17 (1989) 101
  8. For reviews see Israelachvilli J N., Intermolecular and Surface Forces (Academic, Orlando, 1985) and Mahanty J and Ninham B W., Dispersion Forces (Academic, London, 1971)
  9. Lis L J , McAlister M , Fuller N , Rand R P. and Parsegian V A , J. B$\imath$ophys 37 (1982) 657 , Harbich W and Helfrich W., Chem. Phys L$\imath$p$\imath$ds 36 (1984) 39
  10. Cowley A C , Fuller N L , Rand R P and Parsegian V A , B$\imath$ochem 17 (1978) 3163
  11. Parsegian V A , Fuller N and Rand R P , Proc Natl Acad Sc$\imath$ 76 (1979) 2750
  12. Helfrich W., Z Naturforsch. 33a (1978) 305
  13. This is estimated from the current-density across a membrane J($\sigma$) = P $\Delta c$ ($\sigma$) where P is the permeability and $\Delta c$ ($\sigma$) the concentration difference across the membrane at the point $\sigma$ on the membrane surface The solvent current I at time t is then $I(t) \,=\,P\,\,\int\,{{\textrm{d}}^{2} \sigma\,\Delta c(\sigma, t)}$ with the integral extending over the surface The change in vesicle volume $\Delta V(t)$ is $\Delta V(t)\, =\,\int^{1}_{0}\,{\Omega I(t^{\prime})\,{\textrm{d}}t^{\prime}}$ with $\Omega$ the solvent atomic volume The mean square of the volume fluctuations is $\langle \Delta V^{2}(t) \rangle \, =\,St(\Omega P)^{2}\,\int\,{{\textrm{d}}^{2}... ...ty}_{0}\,{{\textrm{d}}t\,\langle \Delta c(\sigma,\,t)\,\Delta c(0,\,0) \rangle}$ with S the vesicle area If the concentration fluctuations have a correlation length $\xi$ and a correlation time $\tau$ then $\langle \Delta V^{2}(t) \rangle \,\sim\,(\Omega P)^{2}\,St \xi^{2}\,\tau\,\langle\Delta c^{2} \rangle$ Our estimate for the time t when $\langle \Delta V^{2}(t) \rangle\,\sim \,V^{2}$ follows if we choose for $\xi \,\sim \,1$ Å, $\tau \,\sim \,10^{-11}\,{\textrm{s}}$, $\Omega\,\sim \,1$ Å3, ${\langle \Delta c^{2} \rangle}^{1/2}\,\sim$ 1/Å3 (typical microscopic values). For the vesicle we choose $S\,\sim \,1\, \mu^{2}$ and $V\,\sim \,1\,\mu^{3}$ and for the permeability $P\,\sim \,10^{-2}$ cm/s (see Stryer L., Biochemistry (W H Freeman, New York, 1988) p. 291)
  14. Landau L D and Lifshitz E M , Fluid Mechanics (Pergamon Press, New York, 1975) p 242
  15. De Gennes P G , Rev Mod Phys 57 (3) (1985) 827 We are borrowing a method described in this article
  16. Lord Rayleigh, Proc London Math. Soc 10 (1878) 4
  17. Helfrich W and Harbich W , Chem$\imath$ca Scr$\imath$pta 25 (1985) 32
  18. Berndl K., Kas J , Lipovsky R , Sackmann E. and Seiffert U , submitted to Europhys Lett
  19. Evans E and Shalah R., Mechanics and Thermodynamics of Biomembranes (Crc Press, Boca Raton, Fla, 1980)
  20. Lipowsky R and Leibler S , Phys. Rev Lett. 56 (1986) 2541 [CrossRef] [PubMed] , Erratum 59 (1987) ; Lipowsky R and Fisher M E , Phys. Rev Lett 57 (1986) 2711
  21. Johnny J F and De Gennes P G , J Phys France 47 (1986) 121 [CrossRef] [EDP Sciences]