Configurations of fluid membranes and vesicles

References

• Alberts , B. , Bray , D. , Lewis , J. , Raff , M. , Roberts , K. and Watson , J.D. 1989 . Molecular Biology of the Cell , Second edn , New York : Garland .
   Google Scholar
• Andelman , D. , Kawakatsu , T. and Kawasaki , K. 1992 . Equilibrium shape of two-component unilamellar membranes and vesicles . Europhys. Lett. , 19 : 57 – 62 .
   Google Scholar
• Aronovitz , J.A. and Lubensky , T.C. 1988 . Fluctuations of solid membranes . Phys. Rev. Lett. , 60 : 2634 – 2637 .
   PubMed Web of Science ®Google Scholar
• Backer , J.M. and Dawidowicz , E.A. 1981 . Transmembrane movement of cholesterol in small unilamellar vesicles detected by cholesterol oxidase . J. biol. Chem. , 256 : 586 – 588 .
   PubMed Web of Science ®Google Scholar
• Bailey , S.M. , Chiruvolu , S. , Israelachvili , J.N. and Zasadzinski , J.A.N. 1990 . Measurements of forces involved in veshicle adhesion using freeze-fracture electron microscopy . Langmuir , 6 : 1326 – 1329 .
   Web of Science ®Google Scholar
• Bar-Ziv , R. , Frisch , T. and Moses , E. 1995a . Entropic expulsion in vesicles . Phys. Rev. Lett. , 75 : 3481 – 3481 .
   PubMed Web of Science ®Google Scholar
• Bar-Ziv , R. , Menes , R. , Moses , E. and Safran , S.A. 1995b . Local unbinding of pinched membranes . Phys. Rev. Lett. , 75 : 3356 – 3359 .
   PubMed Web of Science ®Google Scholar
• Bar-Ziv , R. and Moses , E. 1994 . Instability and pearling states produced in tubular membranes by competition of curvature and tension . Phys. Rev. Lett. , 73 : 1392 – 1395 .
   PubMed Web of Science ®Google Scholar
• Benvegnu , D.J. and McConnell , H.M. 1992 . Line tension between liquid domains in lipid monolayers . J. phys. Chem. , 96 : 6820 – 6824 .
   Web of Science ®Google Scholar
• Berndl , K. 1990 . Formen von Vesikeln , München : Diplomarbeit. Ludwig-Maximilians-Universität .
   Google Scholar
• Berndl , K. , Käs , J. , Lipowsky , R. , Sackmann , E. and Seifert , U. 1990 . Shape transformations of giant vesicles: extreme sensitivity to bilayer asymmetry . Europhys. Lett. , 13 : 659 – 664 .
   Google Scholar
• Beysens , D. , Boccara , N. and Forgacs , G. , eds. 1991 . Dynamical Phenomena at Interfaces, Surfaces and Membranes , New York : Nova Science .
   Google Scholar
• Billoire , A. and David , F. 1986 . Scaling properties of randomly triangulated planar random surfaces . Nucl. Phys. B , 275 : 617 – 640 .
   Web of Science ®Google Scholar
• Bivas , I. , Bivolarski , L. , Mitov , M.D. and Derzhanski , A. 1992 . Correlations between the form fluctuation modes of flaccid quasispherical lipid vesicles and their role in the calculation of the curvature elastic modulus of the vesicle membrane. Numerical results . J. Phys. II , 2 : 1423 – 1438 .
   Google Scholar
• Bivas , I. , Hanusse , P. , Bothorel , P. , Lalanne , J. and Aguerre-Chariol , O. 1987 . An application of the optical microscopy to the determination of the curvature elastic modulus of biological and model membranes . J. Phys. , 48 : 855 – 867 .
   Web of Science ®Google Scholar
• Bloom , M. 1992 . The physics of soft, natural materials . Phys. Canada , 48 : 7 – 16 .
   Google Scholar
• Bloom , M. , Evans , E. and Mouritsen , O.G. 1991 . Physical properties of the fluid lipidbilayer component of cell membranes: a perspective . Quart. Rev. Biophys. , 24 : 293 – 397 .
   PubMed Web of Science ®Google Scholar
• Bo , L. and Waugh , R.E. 1989 . Determination of bilayer membrane bending stiffness by tether formation from giant, thin-walled vesicles . Biophys. J. , 55 : 509 – 517 .
   PubMed Web of Science ®Google Scholar
• Boal , D.H. 1994 . Computer simulation of a model network for the erythrocyte cytoskeleton . Biophys. J. , 67 : 521 – 529 .
   PubMed Web of Science ®Google Scholar
• Boal , D.H. and Rao , M. 1992a . Scaling behavior of fluid membranes in three dimensions . Phys. Rev. A , 45 : 6947 – 6950 . 1992b, Topology changes in fluid membranes, Ibid., 46, 3037–3045
   Web of Science ®Google Scholar
• Boal , D.H. , Seifert , U. and Zilker , A. 1992 . Dual network model for red blood cell membranes . Phys. Rev. Lett. , 69 : 3405 – 3408 .
   PubMed Web of Science ®Google Scholar
• Boroske , E. , Elwenspoek , M. and Helfrich , W. 1981 . Osmotic shrinkage of giant egg lecithin vesicles . Biophys. J. , 34 : 95 – 109 .
   PubMed Web of Science ®Google Scholar
• Boulatov , D.V. , Kazakov , V.A. , Kostov , I.K. and Migdal , A.A. 1986 . Analytical and numerical study of a model of dynamically triangulated surfaces . Nucl. Phys. B , 275 : 641 – 686 .
   Web of Science ®Google Scholar
• Bozic , B. , Svetina , S. , Zeks , B. and Waugh , R.E. 1992 . Role of lamellar membrane structure in tether formation from bilayer vesicles . Biophys. J. , 61 : 963 – 973 .
   PubMed Web of Science ®Google Scholar
• Brakke , K.A. 1992 . The surface evolver . Exp. Math. , 1 : 141 – 165 .
   Google Scholar
• Brochard , F. and de Gennes , P.G. 1975 . Hydrodynamic properties of fluid lamellar phases of lipid/water . Pramana , 1 : 1 – 21 .
   Google Scholar
• Brochard , F. and Lennon , J.F. 1975 . Frequency spectrum of the flicker phenomenon in erythrocytes . J. Phys. (France) , 36 : 1035 – 1047 .
   Web of Science ®Google Scholar
• Bruinsma , R. 1991 . Growth instabilities of vesicles . J. Phys. II France , 1 : 995 – 1012 . 1995, Adhesion and rolling of leukocytes: a physical model, Physics of Biomaterials, NATO ASI series, Geilo, Norway
   Google Scholar
• Bruinsma , R. , Goulian , M. and Pincus , P. 1994 . Self-assembly of membrane junctions . Biophys. J. , 67 : 746 – 750 .
   PubMed Web of Science ®Google Scholar
• Bryant , G. and Wolfe , J. 1987 . Electromechanical stresses produced in the plasma membranes of suspended cells by applied electric fields . J. Membrane Biol. , 96 : 129 – 139 .
   PubMed Web of Science ®Google Scholar
• Bryant , R. 1984 . A duality theorem for Willmore surfaces . J. Differential Geom. , 20 : 23 – 53 .
   Web of Science ®Google Scholar
• Cai , W. and Lubensky , T.C. 1994 . Covariant hydrodynamics of fluid membranes . Phys. Rev. Lett. , 73 : 1186 – 1189 . 1995, Hydrodynamics and dynamic fluctuations of fluid membranes, Phys. Rev. E, 52, 4251–4266
   PubMed Web of Science ®Google Scholar
• Cai , W. , Lubensky , T.C. , Nelson , P. and Powers , T. 1994 . Measure factors, tension, and correlations of fluid membranes . J. Phys. II France , 4 : 931 – 949 .
   Google Scholar
• Camacho , C.J. and Fisher , M.E. 1990 . Tunable fractal shapes in self-avoiding polygons and planar vesicles . Phys. Rev. Lett. , 65 : 9 – 12 . 1991, Semiflexible planar polymeric loops, J. chem. Phys., 94, 5693–5700
   PubMed Web of Science ®Google Scholar
• Canham , P.B. 1970 . The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell . J. theoret. Biol. , 26 : 61 – 81 .
   PubMed Web of Science ®Google Scholar
• Cevc , G. 1995 . Structure and Dynamics of Membranes , Edited by: Lipowsky , R. and Sackmann , E. 465 – 490 . Amsterdam : Elsevier .
   Google Scholar
• Cevc , G. , Fenzl , W. and Sigl , I. 1990 . Surface induced X-ray reflection visualization of membrane orientation and fusion into multibilayers . Science , 249 : 1161 – 1163 .
   PubMed Web of Science ®Google Scholar
• Cevc , G. and Marsh , D. 1987 . Phospholipid Bilayers: Physical Principles and Models , New York : Wiley .
   Google Scholar
• Chang , D.C. , Chassy , B.M. , Saunders , J.A. and Sowers , A.E. 1992 . Guide to Electroporation and Electrofusion , San Francisco : Academic Press .
   Google Scholar
• Chen , C.-M. , Lubensky , T.C. and MacKintosh , F.C. 1995 . Phase transitions and modulated phases in lipid bilayers . Phys. Rev. E , 51 : 504 – 504 .
   Web of Science ®Google Scholar
• Chiruvolu , S. , Walker , S. , Israelachvili , J. , Schmitt , F.J. , Leckband , D. and Zasadzinski , J.A. 1994 . Higher order self-assembly of vesicles by site specific binding . Science , 264 : 1753 – 1756 .
   PubMed Web of Science ®Google Scholar
• Cook-Röder , J. and Lipowsky , R. 1992 . Adhesion and unbinding for bunches of fluid membranes . Europhys. Lett. , 18 : 433 – 438 .
   Google Scholar
• Crowley , J.M. 1973 . Electrical breakdown of bimolecular lipid membranes as an electromechanical instability . Biophys. J. , 13 : 711 – 724 .
   PubMed Web of Science ®Google Scholar
• Dan , N. , Berman , A. , Pincus , P. and Safran , S. 1994 . Membrane-induced interactions between inclusions . J. Phys. II France , 4 : 1713 – 1725 .
   Google Scholar
• David , F. , Guitter , E. and Peliti , L. 1987 . Critical properties of fluid membranes with hexatic order . J. Phys. (France) , 48 : 2059 – 2066 .
   Web of Science ®Google Scholar
• David , F. and Leibler , S. 1991 . Vanishing tension of fluctuating membranes . J. Phys. II France , 1 : 959 – 976 .
   Google Scholar
• de Gennes , P.G. and Prost , J. 1993 . The Physics of Liquid Crystals , Oxford : Clarendon Press .
   Google Scholar
• de Gennes , P.G. and Taupin , C. 1982 . Microemulsions and the flexibility of oil/water interfaces . J. chem. Phys. , 86 : 2294 – 2304 .
   Web of Science ®Google Scholar
• de Loof , H. , Harvey , S.C. , Segrest , J.P. and Pastor , R.W. 1991 . Mean field stochastic boundary molecular dynamics simulation of a phospholipid in a membrane . Biochemistry , 30 : 2099 – 2113 .
   PubMed Web of Science ®Google Scholar
• Dee , G. and Langer , J. 1983 . Propagating pattern selection . Phys. Rev. Lett. , 50 : 383 – 386 .
   Web of Science ®Google Scholar
• Deuling , H.J. and Helfrich , W. 1976 . The curvature elasticity of fluid membranes: a catalogue of vesicle shapes . J. Phys. (France) , 37 : 1335 – 1345 . 1977, A theoretical explanation for the myelin shapes of red blood cells, Blood Cells, 3, 712–720
   Web of Science ®Google Scholar
• Dimitrov , D.S. 1984 . Electric field induced breakdown of lipid bilayers and cell membranes: a thin viscoelastic film model . J. Membrane Biol. , 78 : 53 – 60 .
   PubMed Web of Science ®Google Scholar
• do Carmo , M.P. 1976 . Differential Geometry of Curves and Surfaces , New Jersey : Prentice-Hall .
   Google Scholar
• Döbereiner , H.G. 1995 . The Budding Transition of Phospholipid Vesicles: A Quantitative Study via Phase Contrast Microscopy, Ph.D. Thesis , Canada : Simon Fraser University .
   Google Scholar
• Döbereiner , H.-G. , Evans , E. , Seifert , U. and Wortis , M. 1995 . Spinodal fluctuations of budding vesicles . Phys. Rev. Lett. , 75 : 3360 – 3363 .
   PubMed Web of Science ®Google Scholar
• Döbereiner , H.G. , Käs , J. , Noppl. , D. , Sprenger , I. and Sackmann , E. 1993 . Budding and fission of vesicles . Biophys. J. , 65 : 1396 – 1403 .
   PubMed Web of Science ®Google Scholar
• Doi , M. and Edwards , S.F. 1986 . The Theory of Polymer Dynamics , Oxford : Clarendon Press .
   Google Scholar
• Duplantier , B. 1990 . Exact curvature energies of charged membranes of arbitrary shapes . Physica A , 168 : 179 – 197 .
   Web of Science ®Google Scholar
• Duplantier , B. , Goldstein , R.E. , Romero-Rochin , V. and Pesci , A.I. 1990 . Geometrical and topological aspects of electric double layers near curved surfaces . Phys. Rev. Lett. , 65 : 508 – 511 .
   PubMed Web of Science ®Google Scholar
• Duwe , H.P. 1989 . Korrelationsanalyse thermischer Formfluktuationen von Vesikel, Ph.D. Thesis , Germany : Technische Universität München .
   Google Scholar
• Duwe , H.P. , Käs , J. and Sackmann , E. 1990 . Bending elastic moduli of lipid bilayers: modulation by solutes . J. Phys. France , 51 : 945 – 962 .
   Google Scholar
• Engelhardt , H. , Duwe , H.P. and Sackmann , E. 1985 . Bilayer bending elasticity measured by Fourier analysis of thermally excited surface undulations of flaccid vesicles . J. Phys. Lett. (France) , 46 : 395 – 400 .
   Web of Science ®Google Scholar
• Engelhardt , H. and Sackmann , E. 1988 . On the measurement of shear elastic moduli and viscosities of erythrocyte plasma membranes by transient deformation in high frequency electric fields . Biophys. J. , 54 : 495 – 508 .
   PubMed Web of Science ®Google Scholar
• Evans , D.F. and Wennerström , H. 1994 . The Colloidal Domain , New York : VCH .
   Google Scholar
• Evans , E. 1974 . Bending resistance and chemically induced moments in membrane bilayers . Biophys. J. , 14 : 923 – 931 . 1980, Minimum energy analysis of membrane deformation applied to pipet aspiration and surface adhesion of red blood cells, Ibid., 30, 265–284; 1983, Bending elastic modulus of red blood cell membrane derived from buckling instability in micropipet aspiration tests, Ibid., 43, 27–30; 1985, Detailed mechanics of membrane-membrane adhesion and separation. I. Continuum of molecular cross-bridges, Ibid., 48, 175–183; 1990, Adhesion of surfactant-membrane covered droplets: special features and curvature elasticity effects, Colloids and Surfaces, 43, 327–347; 1991, Entropy driven tension in vesicle membranes and unbinding of adherent vesicles, Langmuir, 7, 1900–1908; 1995a, Structure and Dynamics of Membranes, edited by R. Lipowsky and E. Sackmann (Amsterdam: Elsevier), pp. 723–754
   PubMed Web of Science ®Google Scholar
• Evans , E. and Metcalfe , M. 1984 . Free energy potential for aggregation of mixed phosphatidylcholine/phosphatidylserin lipid vesicles in glucose polymer/dextran solutions . Biophys. J. , 45 : 715 – 720 .
   PubMed Web of Science ®Google Scholar
• Evans , E. and Needham , D. 1987 . Physical properties of surfactant bilayer membranes: thermal transitions, elasticity, rigidity, cohesion, and colloidal interactions . J. chem. Phys. , 91 : 4219 – 4228 .
   Web of Science ®Google Scholar
• Evans , E. and Rawicz , W. 1990 . Entropy-driven tension and bending elasticity in condensed-fluid membranes . Phys. Rev. Lett. , 64 : 2094 – 2097 .
   PubMed Web of Science ®Google Scholar
• Evans , E. and Yeung , A. 1994 . Hidden dynamics in rapid changes of bilayer shape . Chem. Phys. Lipids , 73 : 39 – 56 .
   Web of Science ®Google Scholar
• Evans , E. , Yeung , A. , Waugh , R. and Song , J. 1992 . “ The Structure and Conformation of Amphiphilic Membranes ” . In Springer Proceedings in Physics , Edited by: Lipowsky , R. , Richter , D. and Kremer , K. Vol. 66 , 148 – 153 . Berlin : Springer .
   Google Scholar
• Evans , R.M.L. 1995b . Phase diagrams for deformable toroidal and spherical surfaces with intrinsic orientational order . J. Phys. II France , 5 : 507 – 530 .
   Google Scholar
• Farge , E. and Devaux , P.F. 1992 . Shape changes of giant liposomes induced by an asymmetric transmembrane distribution of phospholipids . Biophys. J. , 61 : 347 – 357 .
   PubMed Web of Science ®Google Scholar
• Faucon , J.F. , Mitov , M.D. , Meleard , P. , Bivas , I. and Bothorel , P. 1989 . Bending elasticity and thermal fluctuations of lipid membranes. Theoretical and experimental requirements . J. Phys. (France) , 50 : 2389 – 2414 .
   Web of Science ®Google Scholar
• Fenzl , W. , Sigl , L. , Richardsen , H. and Cevc , G. 1995 . The surface-confined structures of dimyristoylphosphatidylcholine bilayers in contact with the vesicle suspension as studied by means of X-ray reflectivity . Colloids and Surfaces A , 102 : 247 – 256 .
   Web of Science ®Google Scholar
• Fischer , T.M. 1993 . Bending stiffness of lipid bilayers. V. Comparison of two formulations . J. Phys. II France , 3 : 1795 – 1805 . 1994, Mechanisms for determining the time scales in vesicle budding, Phys. Rev. E, 50, 4156–4166
   Google Scholar
• Foltin , G. 1994 . Dynamics of incompressible fluid membranes . Phys. Rev. E , 49 : 5243 – 5248 .
   Web of Science ®Google Scholar
• Förster , D. 1986 . On the scale dependence, due to thermal fluctuations, of the elastic properties of membranes . Phys. Lett. A , 114 : 115 – 120 .
   Web of Science ®Google Scholar
• Fourcade , B. 1992 . Theoretical results of toroidal vesicles . J. Phys. II France , 2 : 1705 – 1724 .
   Google Scholar
• Fourcade , B. , Miao , L. , Rao , M. , Wortis , M. and Zia , R.K.P. 1994 . Scaling analysis of narrow necks in curvature models of fluid lipid-bilayer vesicles . Phys. Rev. E , 49 : 5276 – 5286 .
   Web of Science ®Google Scholar
• Fourcade , B. , Mutz , M. and Bensimon , D. 1992 . Experimental and theoretical study of toroidal vesicles . Phys. Rev. Lett. , 68 : 2551 – 2554 .
   PubMed Web of Science ®Google Scholar
• Frey , E. and Nelson , D.R. 1991 . Dynamics of flat membranes and flickering in red blood cells . J. Phys. I France , 1 : 1715 – 1757 .
   Google Scholar
• Fromherz , P. 1983 . Lipid-vesicle structure: size control by edge-active agents . Chem. Phys. Lett. , 94 : 259 – 266 .
   Web of Science ®Google Scholar
• Gebhardt , C. , Gruler , H. and Sackmann , E. 1977 . On domain structure and local curvature in lipid bilayers and biological membranes . Z. Naturforsch., C , 32 : 581 – 596 .
   PubMed Web of Science ®Google Scholar
• Goldstein , R.E. , Nelson , P. , Powers , T. and Seifert , U. 1996 . Front propagation in the pearling instability of tubular vesicles . J. Phys. II France , 6 : 767 – 796 .
   Google Scholar
• Gompper , G. and Kroll , D.M. 1989 . Steric interactions in multimembrane systems: a Monte Carlo study . Europhys. Lett. , 9 : 59 – 64 . 1992a, Inflated vesicles: a new phase of fluid membranes, Ibid., 19, 581–586; 1992b, Shape of inflated vesicles, Phys. Rev. A, 46, 7466; 1993, Floppy fluid vesicles in elongational flow, Phys. Rev. Lett., 71, 1111–1114; 1994, Phase diagram of fluid vesicles, Ibid., 73, 2139–2142; 1995a, Driven transport of fluid vesicles through narrow pores, Phys. Rev. E, 52, 4198–4208; 1995b, Phase diagram and scaling behavior of fluid vesicles, Ibid., 51, 512–525
   Google Scholar
• Gompper , G. and Schick , M. 1994 . “ Self assembling amphiphilic systems ” . In Phase Transition and Critical Phenomena , Edited by: Domb , C. and Lebowitz , J. London : Academic .
   Google Scholar
• Goos , J. and Gompper , G. 1993 . Topological defects in lamellar phases: passages, and their fluctuations . J. Phys. I France , 3 : 1551 – 1567 .
   Google Scholar
• Goulian , M. , Bruinsma , R. and Pincus , P. 1993 . Long-range forces in heterogeneous fluid membranes . Europhys. Lett. , 22 : 145 – 150 .
   Google Scholar
• Granek , R. and Olami , Z. 1995 . Dynamics of Rayleigh-like instability induced by laser tweezers in tubular vesicles of self-assembled membranes . J. Phys. II France , 5 : 1349 – 1370 .
   Google Scholar
• Gruler , H. 1975 . Chemoelastic effects of membranes . Z. Naturforsch. C , 30 : 608 – 614 .
   PubMed Web of Science ®Google Scholar
• Haeckl , W. , Seifert , U. and Sackmann , E. 1995 . Effects of fully and partially solubilized amphiphiles on bilayers bending stiffness and temperature dependence of the effective tension of giant vesicles (preprint)
   Google Scholar
• Heinrich , V. , Brumen , M. , Heinrich , R. , Svetina , S. and Zeks , B. 1992 . Nearly spherical vesicle shapes calculated by use of spherical harmonics: axisymmetric and nonaxisymmetric shapes and their stability . J. Phys. II France , 2 : 1081 – 1108 .
   Google Scholar
• Heinrich , V. , Svetina , S. and Zeks , B. 1993 . Nonaxisymmetric vesicle shapes in a generalized bilayer-couple model and the transition between oblate and prolate axisymmetric shapes . Phys. Rev. E , 48 : 3112 – 3123 .
   Web of Science ®Google Scholar
• Helfrich , W. 1973 . Elastic properties of lipid bilayers: theory and possible experiments . Z. Naturforsch. C , 28 : 693 – 703 . 1974a, Blocked lipid exchanges in bilayers and its possible influence on the shape of vesicles, Ibid., 29, 510–515; 1974b, The size of bilayer vesicles generated by sonication, Phys. Lett. A, 50, 115–116; 1978, Steric interaction of fluid membranes in multilayer systems, Z. Naturforsch., 33, 305–315; 1985, Effect of thermal undulations on the rigidity of fluid membranes and interfaces, J. Phys. (France), 46, 1263–1268; 1986, Size distributions of vesicles: the role of the effective rigidity of membranes, Ibid., 47, 321–329; 1987, Measures of integration in calculating the effective rigidity of fluid surfaces, Ibid., 48, 285–289; 1989, Hats and saddles in liquid membranes, Liq. Crystals, 5, 1647–1658; 1993, Mean field theory of n-layer unbinding, J. Phys. II France, 3, 385–393; 1994, Lyotropic lamellar phases, J. Phys.: condens. Matter, 6, A79–A92; 1995, Structure and Dynamics of Membranes, edited by R. Lipowsky and E. Sackmann (Amsterdam: Elsevier), pp. 691–722
   PubMed Web of Science ®Google Scholar
• Helfrich , W. and Klösgen , B. 1992 . Dynamical Phenomena at Interfaces, and Surfaces and Membranes , Edited by: Beysens , D. , Boccara , N. and Forgacz , G. 211 – 220 . New York : Nova .
   Google Scholar
• Helfrich , W. and Kozlov , M.M. 1994 . Flexibility and roughness of mixed and partially polymerized bilayers in terms of the hat model and local bending frustration . J. Phys. II France , 4 : 1427 – 1438 .
   Google Scholar
• Helfrich , W. and Prost , J. 1988 . Intrinsic bending force in anisotropic membranes made of chiral molecules . Phys. Rev. A , 38 : 3065 – 3068 .
   PubMed Web of Science ®Google Scholar
• Helfrich , W. and Servuss , R.M. 1984 . Undulations, steric interaction and cohesion of fluid membranes . Il Nuovo Cimento, D , 3 : 137 – 151 .
   Google Scholar
• Ho , J.S. and Baumgärtner , A. 1990 . Simulation of fluid self-avoiding membranes . Europhys. Lett. , 12 : 295 – 300 .
   Google Scholar
• Hoffmanm , H. , Thunig , C. , Munkert , U. , Meyer , H.W. and Richter , W. 1992 . From vesicles to the L 3 (sponge) phase in alkyldimenthylamine oxide/heptanol systems . Langmuir , 8 : 2629 – 2638 .
   Web of Science ®Google Scholar
• Homan , R. and Pownall , H.J. 1988 . Transbilayer diffusion of phospholipids: dependence on headgroup structure and acyl chain length . Biochim. Biophys. Acta , 938 : 155 – 166 .
   PubMed Web of Science ®Google Scholar
• Hotani , H. 1984 . Transformation pathways of liposomes . J. molec. Biol. , 178 : 113 – 120 .
   PubMed Web of Science ®Google Scholar
• Hsu , L. , Kusner , R. and Sullivan , J. 1992 . Minimizing the squared mean curvature integral for surfaces in space forms . Exp. Math. , 1 : 191 – 207 .
   Google Scholar
• Hu , J.-G. and Ou-Yang , Z.-C. 1993 . Shape equations of the axisymmetric vesicles . Phys. Rev. E , 47 : 461 – 467 .
   Web of Science ®Google Scholar
• Hyuga , H. , Kinosita , K. Jr and Wakabayashi , N. 1991a . Deformation of vesicles under the influence of strong electric fields . Jap. J. appl. Phys. , 30 : 1141 – 1148 . 1991b, Deformation of vesicles under the influence of strong electric fields. II, Ibid., 30, 1333–1335
   Web of Science ®Google Scholar
• Israelachvili , J.N. 1991 . Intermolecular and Surface Forces , second edn , London : Academic Press .
   Google Scholar
• Israelachvili , J.N. and Wennerström , H. 1990 . Hydration or steric forces between amphiphilic surfaces? . Langmuir , 6 : 873 – 876 .
   Web of Science ®Google Scholar
• Janiak , M.J. , Small , D.M. and Shipley , G.G. 1979 . Temperature and compositional dependence of the structure of hydrated dimyristoyl lecithin . J. biol. Chem. , 254 : 6068 – 6078 .
   PubMed Web of Science ®Google Scholar
• Janke , W. and Kleinert , H. 1987 . Fluctuation pressure of a stack of membranes . Phys. Rev. Lett. , 58 : 144 – 147 .
   PubMed Web of Science ®Google Scholar
• Jaric , M. , Seifert , U. , Wintz , W. and Wortis , M. 1995 . Vesicular instabilities: the prolate-to-oblate transition and other shape instabilities of fluid bilayer membranes . Phys. Rev. E , 52 : 6623 – 6623 .
   Web of Science ®Google Scholar
• Jenkins , J.T. 1977 . static equilibrium configurations of a model red blood cell . J. math. Biol. , 4 : 149 – 169 .
   PubMed Web of Science ®Google Scholar
• Jülicher , F. 1993 . Die Morphologie von Vesikeln, Ph.D. Thesis , Germany : Universität zu Köln .
   Google Scholar
• Jülicher , F. and Lipowsky , R. 1993 . Domain induced budding of vesicles . Phys. Rev. Lett. , 70 : 2964 – 2967 .
   PubMed Web of Science ®Google Scholar
• Jülicher , F. and Seifert , U. 1994 . Shape equations for axisymmetric vesicles: a clarification . Phys. Rev. E , 49 : 4728 – 4731 .
   Web of Science ®Google Scholar
• Jülicher , F. , Seifert , U. and Lipowsky , R. 1993a . Conformal degeneracy and conformal diffusion of vesicles . Phys. Rev. Lett. , 71 : 452 – 455 . 1993b, Phase diagrams and shape transformations of toroidal vesicles, J. Phys. II France, 3, 1681–1705
   PubMed Web of Science ®Google Scholar
• Kaler , E.W. , Herrington , K.L. , Murthy , A.K. and Zasadzinski , J.A.N. 1992 . Phase behavior and structures of mixtures of anionic and cationic surfactants . J. phys. Chem. , 96 : 6698 – 6707 .
   Web of Science ®Google Scholar
• Kaler , E.W. , Murthy , A.K. , Rodriguez , B.E. and Zasadzinski , J.A.N. 1989 . Spontaneous vesicle formation in aqueous mixtures of single-tailed surfactants . Science , 245 : 1371 – 1374 .
   PubMed Web of Science ®Google Scholar
• Karcher , H. , Pinkall , U. and Sterling , I. 1988 . New minimal surfaces in S 3 . J. Differential Geom. , 28 : 169 – 185 .
   Web of Science ®Google Scholar
• Käs , J. and Sackmann , E. 1991 . Shape transitions and shape stability of giant phospholipid vesicles in pure water induced by area-to-volume changes . Biophys. J. , 60 : 825 – 844 .
   PubMed Web of Science ®Google Scholar
• Käs , J. , Sackmann , E. , Podgornik , R. , Svetina , S. and Zeks , B. 1993 . Thermally induced budding of phospholipid vesicles—a discontinuous process . J. Phys. II France , 3 : 631 – 645 .
   Google Scholar
• Kawakatsu , T. , Andelman , D. , Kawasaki , K. and Taniguchi , K. 1993 . Phase transitions and shape of two component membranes and vesicles. I: Strong segregation limit . J. Phys. II France , 3 : 971 – 997 .
   Google Scholar
• Kleinert , H. 1986 . Thermal softening of curvature elasticity in membranes . Phys. Lett., A , 114 : 263 – 268 .
   Web of Science ®Google Scholar
• Komura , S. and Lipowsky , R. 1992 . Fluctuations and stability of polymerized vesicles . J. Phys. II France , 3 : 1563 – 1575 .
   Google Scholar
• Kramer , L. 1971 . Theory of light scattering from fluctuations of membranes and monolayers . J. chem. Phys. , 55 : 2097 – 2105 .
   Web of Science ®Google Scholar
• Kraus , M. and Seifert , U. 1994 . Relaxation modes of an adhering bilayer membrane . J. Phys. II France , 4 : 1117 – 1134 .
   Google Scholar
• Kraus , M. , Seifert , U. and Lipowsky , R. 1995 . Gravity-induced shape transformations of vesicles . Europhys. Lett. , 32 : 431 – 436 .
   Google Scholar
• Kroll , D.M. and Gompper , G. 1992 . The conformation of fluid membranes: Monte Carlo simulations . Science , 255 : 968 – 971 . 1993, Floppy tethered networks, J. Phys. I France, 3, 1131–1140
   PubMed Web of Science ®Google Scholar
• Kummrow , M. and Helfrich , W. 1991 . Deformation of giant lipid vesicles by electric fields . Phys. Rev. A , 44 : 8356 – 8360 .
   PubMed Web of Science ®Google Scholar
• Kusner , R. 1989 . Comparison surfaces of the Willmore problem . Pacific J. Math. , 138 : 317 – 345 .
   Web of Science ®Google Scholar
• Kusner , R. 1994 . Private communication
   Google Scholar
• Lammert , P.E. , Prost , J. and Bruinsma , R. 1996 . Ion drive for vesicles and cells . J. theoret. Biol. , 178 : 387 – 391 .
   Web of Science ®Google Scholar
• Landau , L.D. and Lifshitz , E.M. 1989 . Elastizitätstheorie , Berlin : Akademie-Verlag .
   Google Scholar
• Langer , J. and Singer , D. 1984 . Curves in the hyperbolic plane and mean curvature of tori and R 3 and S 3 . Bull. London Math. Soc. , 16 : 531 – 534 .
   Web of Science ®Google Scholar
• Langer , S.A. and Seifert , U. 1996 . in preparation
   Google Scholar
• Langevin , D. 1992 . Light Scattering by Liquid Surfaces and Complementary Techniques , New York : Marcel Dekker .
   Google Scholar
• Lasic , D.D. 1995 . Structure and Dynamics of Membranes , Edited by: Lipowsky , R. and Sackmann , E. 491 – 520 . Amsterdam : Elsevier .
   Google Scholar
• Lawson , H.B. 1970 . Ann. Math. , 92 : 335 – 374 .
   Web of Science ®Google Scholar
• Le Doussal , P. and Radzihovsky , L. 1992 . Self-consistent theory of polymerized membranes . Phys. Rev. Lett. , 69 : 1209 – 1212 .
   PubMed Web of Science ®Google Scholar
• Leibler , S. 1986 . Curvature instability in membranes . J. Phys. (France) , 47 : 507 – 516 .
   Web of Science ®Google Scholar
• Leibler , S. and Andelman , D. 1987 . Ordered and curved meso-structures in membranes and amphiphilic films . J. Phys. , 48 : 2013 – 2018 .
   Web of Science ®Google Scholar
• Leibler , S. , Singh , R.R.P. and Fisher , M.E. 1987 . Thermodynamic behavior of two-dimensional vesicles . Phys. Rev. Lett. , 59 : 1989 – 1992 .
   PubMed Web of Science ®Google Scholar
• Lipowsky , R. 1990 . Fundamental Problems in Statistical Mechanics VII , Edited by: van Beijeren , H. 139 – 170 . Amsterdam : Elsevier . 1991, The conformation of membranes, Nature, 349, 475–481; 1992, Budding of membranes induced by intramembrane domains, J. Phys. II France, 2, 1825–1840; 1993, Domain-induced budding of fluid membranes, Biophys. J., 64, 1133–1138; 1995, Structure and Dynamics of Membranes, edited by R. Lipowsky and E. Sackmann (Amsterdam: Elsevier), pp. 521–602
   Google Scholar
• Lipowsky , R. and Girardet , M. 1990 . Shape fluctuations of polymerized or solidlike membranes . Phys. Rev. Lett. , 65 : 2893 – 2896 .
   PubMed Web of Science ®Google Scholar
• Lipowsky , R. and Grotehans , S. 1993 . Hydration versus protrusion forces between lipid bilayers . Europhys. Lett. , 23 : 599 – 604 .
   Google Scholar
• Lipowsky , R. and Leibler , S. 1986 . Unbinding transitions of interacting membranes . Phys. Rev. Lett. , 56 : 2541 – 2544 .
   PubMed Web of Science ®Google Scholar
• Lipowsky , R. , Richter , D. and Kremer , K. , eds. 1992 . The Structure and Conformation of Amphiphilic Membranes, Springer Proceedings in Physics , Vol. 66 , Berlin : Springer .
   Google Scholar
• Lipowsky , R. and Sackmann , E. 1995 . Structure and Dynamics of Membranes , Amsterdam : Elsevier .
   Google Scholar
• Lipowsky , R. and Seifert , U. 1991a . Adhesion of membranes: a theoretical perspective . Langmuir , 7 : 1867 – 1873 . 1991b, Adhesion of vesicles and membranes, Molec. Crystals, Liq. Crystals, 202, 17–25
   Web of Science ®Google Scholar
• Lipowsky , R. and Zielinska , B. 1989 . Binding and unbinding of lipid membranes: a Monte Carlo study . Phys. Rev. Lett. , 62 : 1572 – 1575 .
   PubMed Web of Science ®Google Scholar
• Lubensky , T.C. and MacKintosh , F.C. 1993 . Theory of ripple phases of lipid bilayers . Phys. Rev. Lett. , 71 : 1565 – 1568 .
   PubMed Web of Science ®Google Scholar
• Lubensky , T.C. and Prost , J. 1992 . Orientational order and vesicle shape . J. Phys. II France , 2 : 371 – 382 .
   Google Scholar
• Luke , J.C. 1982 . A method for the calculation of vesicle shapes . SIAM J. appl. Math. , 42 : 333 – 345 .
   Web of Science ®Google Scholar
• Luke , J.C. and Kaplan , J.I. 1979 . On theoretical shapes of bilayer lipid vesicles under conditions of increasing membrane area . Biophys. J. , 25 : 107 – 111 .
   PubMed Web of Science ®Google Scholar
• MacKintosh , F.C. and Lubensky , T.C. 1991 . Orientational order, topology, and vesicle shapes . Phys. Rev. Lett. , 67 : 1169 – 1172 .
   PubMed Web of Science ®Google Scholar
• Maggs , A.C. and Leibler , S. 1990 . Adsorption and fluctuations of two-dimensional vesicles . Europhys. Lett. , 12 : 19 – 24 .
   Google Scholar
• Maggs , A.C. , Leibler , S. , Fisher , M.E. and Camacho , C.J. 1990 . Size of an inflated vesicle in two dimensions . Phys. Rev. A , 42 : 691 – 695 .
   PubMed Web of Science ®Google Scholar
• Marathe , Y. and Ramaswamy , S. 1989 . Frequency-dependent viscosity of membrane solution . Europhys. Lett. , 8 : 581 – 585 .
   Google Scholar
• Markin , V.S. 1981 . Lateral organization of membranes and cell shapes . Biophys. J. , 36 : 1 – 19 .
   PubMed Web of Science ®Google Scholar
• Marra , J. and Israelachvili , J.N. 1985 . Direct measurements of forces between phosphatidylcholine and phosphatidylethanolamine bilayers in aqueous electrolyte solutions . Biochemistry , 24 : 4608 – 4618 .
   PubMed Web of Science ®Google Scholar
• Marsh , D. 1990 . Handbook of Lipid Bilayers , Boca Raton, Florida : CRC Press .
   Google Scholar
• Mecke , K.R. 1995 . Bending rigidity of fluctuating membranes . Z. Phys. B , 97 : 379 – 387 .
   Google Scholar
• Meleard , P. , Faucon , J.F. , Mitov , M.D. and Botherel , P. 1992 . Pulsed-light microscopy applied to the measurement of the bending elasticity of giant liposomes . Europhys. Lett. , 19 : 267 – 271 .
   Google Scholar
• Menger , F.M. and Gabrielson , K.D. 1995 . Die cytomimetische organische Chemie—ein erster Bericht . Angew. Chem. , 107 : 2260 – 2278 .
   Google Scholar
• Merkel , R. , Sackmann , E. and Evans , E. 1989 . Molecular friction and epitactic coupling between monolayers in supported bilayers . J. Phys. (France) , 50 : 1535 – 1555 .
   Web of Science ®Google Scholar
• Mermin , N.D. and Wagner , H. 1966 . Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models . Phys. Rev. Lett. , 17 : 1133 – 1136 .
   Web of Science ®Google Scholar
• Meunier , J. , Langevin , D. and Boccara , N. 1987 . Physics of Amphiphilic Layers , Berlin : Springer-Verlag .
   Google Scholar
• Miao , L. 1992 . “ Equilibrium shapes and shape transitions of fluid lipid-bilayer vesicles ” . In Ph.D. Thesis , Simon Fraser University .
   Google Scholar
• Miao , L. , Fourcade , B. , Rao , M. , Wortis , M. and Zia , R.K.P. 1991 . Equilibrium budding and vesiculation in the curvature model of fluid lipid vesicles . Phys. Rev. A , 43 : 6843 – 6856 .
   PubMed Web of Science ®Google Scholar
• Miao , L. , Seifert , U. , Wortis , M. and Döbereiner , H.G. 1994 . Budding transitions of fluid-bilayer vesicles: the effect of area difference elasticity . Phys. Rev. E , 49 : 5389 – 5407 .
   Web of Science ®Google Scholar
• Michalet , X. 1994 . “ Etude expérimentale de vésicule phospholipidiques de genre topologique non sphérique ” . In Ph.D. Thesis , France : l'Université de Paris, VII .
   Google Scholar
• Michalet , X. and Bensimon , D. 1995a . Vesicles of toroidal topology: observed morphology and shape transformations . J. Phys. II France , 5 : 263 – 287 . 1995b, Observation of stable shapes and conformal diffusion in genus 2 vesicles, Science, 269, 666
   Google Scholar
• Michalet , X. , Bensimon , D. and Fourcade , B. 1994a . Fluctuation vesicles of nonspherical topology . Phys. Rev. Lett. , 72 : 168 – 171 .
   PubMed Web of Science ®Google Scholar
• Michalet , X. , Jülicher , F. , Fourcade , B. , Seifert , U. and Bensimon , D. 1994b . La physique des liposomes . La Recherche , 25 : 1012 – 1018 .
   Google Scholar
• Milner , S.T. and Roux , D. 1992 . Flory theory of the unbinding transition . J. Phys. I France , 2 : 1741 – 1754 .
   Google Scholar
• Milner , S.T. and Safran , S.A. 1987 . Dynamical fluctuations of droplet microemulsions and vesicles . Phys. Rev. A , 36 : 4371 – 4379 .
   Web of Science ®Google Scholar
• Morse , D.C. and Milner , S.T. 1994 . Fluctuation and phase behavior of fluid membrane vesicles . Europhys. Lett. , 26 : 565 – 570 . 1995, Statistical mechanics of closed fluid membranes, Phys. Rev. E, 52, 5918
   Google Scholar
• Moy , V.T. , Florin , E.-L. and Gaub , H.E. 1994 . Intermolecular forces and energies between ligands and receptors . Science , 266 : 257 – 259 .
   PubMed Web of Science ®Google Scholar
• Mui , B.L.-S. , Döbereiner , H.-G. , Madden , T.D. and Cullis , P.R. 1995 . Influence of transbilayer area asymmetry on the morphology of large unilamellar vesicles . Biophys. J. , 69 : 930 – 941 .
   PubMed Web of Science ®Google Scholar
• Mutz , M. and Bensimon , D. 1991 . Observation of toroidal vesicles . Phys. Rev. A , 43 : 4525 – 4527 .
   PubMed Web of Science ®Google Scholar
• Mutz , M. and Helfrich , W. 1989 . Unbinding transition of a biological model membrane . Phys. Rev. Lett. , 62 : 2881 – 2884 . 1990, Bending rigidities of some biological model membranes as obtained from the Fourier analysis of contour sections, J. Phys. (France), 51, 991–1002
   PubMed Web of Science ®Google Scholar
• Naito , H. , Okuda , M. and Zhong-can , O.Y. 1993 . Counterexample to some shape equations for axisymmetric vesicles . Phys. Rev. E , 48 : 2304 – 2307 . 1995, New solutions to the Helfrich variational problem for the shapes of lipid bilayer vesicles: beyond Delaunay surfaces, Phys. Rev. Lett., 74, 4345–4348
   Web of Science ®Google Scholar
• Needham , D. and Hochmuth , R.M. 1989 . Electro-mechanical permeabilization of lipid vesicles . Biophys. J. , 55 : 1001 – 1009 .
   PubMed Web of Science ®Google Scholar
• Needham , D. , McIntosh , T.J. and Evans , E. 1988 . Thermomechanical and transition properties of dimyristoylphosphatidycholine/cholesterol bilayers . Biochemistry , 27 : 4668 – 4673 .
   PubMed Web of Science ®Google Scholar
• Nelson , D. 1988 . Random Fluctuations and Pattern Growth Edited by: Stanley , H.E. and Ostrowsky , N. 193 – 215 .
   Google Scholar
• Nelson , D. , Piran , T. and Weinberg , S. , eds. 1989 . Statistical Mechanics of Membranes and Surfaces , Singapore : World Scientific .
   Google Scholar
• Nelson , D.R. and Peliti , L. 1987 . Fluctuation in membranes with crystalline and hexatic order . J. Phys. France , 48 : 1085 – 1092 .
   Google Scholar
• Nelson , P. and Powers , T. 1992 . Rigid chiral membranes . Phys. Rev. Lett. , 69 : 3409 – 3412 . 1993, Renormalization of chiral couplings in tilted bilayer membranes, J. Phys. II France, 3, 1535–1569
   PubMed Web of Science ®Google Scholar
• Nelson , P. , Powers , T. and Seifert , U. 1995 . Dynamical theory of the pearling instability in cylindrical vesicles . Phys. Rev. Lett. , 74 : 3384 – 3384 .
   PubMed Web of Science ®Google Scholar
• Netz , R.R. 1995 . Complete unbinding of fluid membranes in the presence of short-range forces . Phys. Rev. E , 51 : 2286 – 2294 .
   PubMed Web of Science ®Google Scholar
• Netz , R.R. and Lipowsky , R. 1993 . Unbinding of symmetric and asymmetric stacks of membranes . Phys. Rev. Lett. , 71 : 3596 – 3599 . 1995, Stacks of fluid membranes under pressure and tension, Europhys. Lett., 29, 345–350
   PubMed Web of Science ®Google Scholar
• Neumann , E. , Sowers , A.E. and Jordan , C.A. , eds. 1989 . Electroporation and Electrofusion in Cell Biology , New York : Plenum Press .
   Google Scholar
• Nezil , F.A. and Bloom , M. 1992 . Combined influence of cholesterol and synthetic amphiphilic peptides upon bilayer thickness in model membranes . Biophys. J. , 61 : 1176 – 1183 .
   PubMed Web of Science ®Google Scholar
• Niggemann , G. , Kummrow , M. and Helfrich , W. 1995 . The bending rigidity of phosphatidylcholine bilayers: dependence on experimental method, sample cell sealing and temperature . J. Phys. II France , 5 : 413 – 425 .
   Google Scholar
• Ou-Yang , Z.C. 1990 . Anchor ring-vesicle membranes . Phys. Rev. A , 41 : 4517 – 4520 .
   PubMed Web of Science ®Google Scholar
• Ou-Yang , Z.C. and Helfrich , W. 1987 . Instability and deformation of a spherical vesicle by pressure . Phys. Rev. Lett. , 59 : 2486 – 2488 . 1989, 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, 5280–5288
   PubMed Web of Science ®Google Scholar
• Palmer , K.M. , Goulian , M. and Pincus , P. 1994 . Fluctuation-induced forces in stacked fluid membranes . J. Phys. II France , 4 : 805 – 817 .
   Google Scholar
• Park , J. , Lubensky , T.C. and MacKintosh , F.C. 1992 . n-atic order and continuous shape changes of deformable surfaces of the genus zero . Europhys. Lett. , 20 : 279 – 284 .
   Google Scholar
• Parsegian , V.A. , Fuller , N. and Rand , R.P. 1979 . Measured work of deformation and repulsion of lecithin bilayers . Natl Acad. Sci. USA , 76 : 2750 – 2854 .
   PubMed Web of Science ®Google Scholar
• Parsegian , V.A. and Rand , R.P. 1995 . Structure and Dynamics of Membranes , Edited by: Lipowsky , R. and Sackmann , E. 643 – 690 . Amsterdam : Elsevier .
   Google Scholar
• Peliti , L. 1991 . Biologically Inspired Physics , New York and London : Plenum Press .
   Google Scholar
• Peliti , L. and Leibler , S. 1995 . Effects of thermal fluctuations on systems with small surface tension . Phys. Rev. Lett. , 54 : 1690 – 1693 .
   Web of Science ®Google Scholar
• Peliti , L. and Prost , J. 1989 . Fluctuations in membranes with reduced symmetry . J. Phys. France , 50 : 1557 – 1571 .
   Google Scholar
• Peterson , M.A. 1985a . Geometrical methods for the elasticity theory of membranes . J. math. Phys. , 26 : 711 – 717 . 1985b, An instability of the red blood cell shape, J. appl. Phys., 57, 1739–1742; 1985c, Shape fluctuations of red blood cells, Molec. Crystals, Liq. Crystals., 127, 159–186; 1988, Comment on ‘Instability and deformation of a spherical vesicle by pressure’, Phys. Rev. Lett., 61, 1325; 1989, Deformation energy of vesicles at fixed volume and surface area in the spherical limit, Phys. Rev. A, 39, 2643–2645; 1992, Linear response of the human erythrocyte to mechanical stress, Phys. Rev. A, 45, 4116–4131
   Web of Science ®Google Scholar
• Peterson , M.A. , Strey , H. and Sackmann , E. 1992 . Theoretical and phase contrast microscopic eigenmode analysis of erythrocyte flicker: amplitudes . J. Phys. II France, , 2 : 1273 – 1285 .
   Google Scholar
• Pfeiffer , W. , König , S. , Legrand , J.F. , Bayerl , T. , Richter , D. and Sackmann , E. 1993 . Neutron spin echo study of membrane undulations in lipid multibilayers . Europhys. Lett. , 23 : 457 – 462 .
   Google Scholar
• Pincus , P. 1976 . Excluded volume effects and stretched polymer chains . Macromolecules , 9 : 386 – 388 .
   Web of Science ®Google Scholar
• Pinkall , U. 1985 . Hopf tori in S 3 . Invent. Math. , 81 : 379 – 386 .
   Web of Science ®Google Scholar
• Pinkall , U. and Sterling , I. 1987 . Willmore surfaces . Math. Intelligencer , 9 : 38 – 43 .
   Web of Science ®Google Scholar
• Podgornik , R. , Svetina , S. and Zeks , B. 1995 . Parametrization invariance and shape equations of elastic axisymmetric vesicles . Phys. Rev. E , 51 : 544 – 544 .
   Web of Science ®Google Scholar
• Polyakov , A.M. 1987 . Gauge Fields and Strings , Cambridge, MA : Harvard Academic Publishers .
   Google Scholar
• Porte , G. 1992 . Lamellar phases and disordered phase of fluid bilayer membranes . J. Phys.: condens. Matter , 4 : 8649 – 8670 .
   Web of Science ®Google Scholar
• Powers , T. and Nelson , P. 1995 . Fluctuating membranes with tilt order . J. Phys. II France , 5 : 1671 – 1678 .
   Google Scholar
• Prost , J. and Bruinsma , R. 1996 . Shape fluctuation of active membranes . Europhys. Lett. , 33 : 321 – 326 .
   Google Scholar
• Rädler , J. 1993 . Über Wechselwirkung fluider Phospholipid-Membranen mit Festkörperoberflächen, Ph.D. Thesis , Germany : TU-Münche .
   Google Scholar
• Rädler , J. and Sackmann , E. 1992 . The Structure and Conformation of Amphiphilic Membranes , Edited by: Lipowsky , R. , Richter , D. and Kremer , K. 158 – 161 . Berlin : Springer .
   Google Scholar
• Rädler , J.O. , Feder , T.J. , Strey , H.H. and Sackmann , E. 1995 . Fluctuation analysis of tension controlled undulation forces between giant vesicles and solid substrates . Phys. Rev. E , 51 : 4526 – 4536 .
   Web of Science ®Google Scholar
• Rand , R.P. and Parsegian , V.A. 1989 . Hydration forces between phospholipid bilayers . Biochim. Biophys. Acta , 988 : 351 – 376 .
   Web of Science ®Google Scholar
• Roux , D. , Coulon , C. and Cates , M.E. 1992 . Sponge phases in surfactant solutions . J. phys. Chem. , 96 : 4174 – 4187 .
   Web of Science ®Google Scholar
• Sackmann , E. 1994 . Membrane bending energy concept of vesicle- and cell-shapes and shape-transitions . FEBS Letters , 346 : 3 – 16 .
   PubMed Web of Science ®Google Scholar
• Safran , S. 1994 . Statistical Thermodynamics of Surfaces, Interfaces, and Membranes , Reading, , UK : Addison-Wesley .
   Google Scholar
• Safran , S.A. , Pincus , P. and Andelman , D. 1990 . Theory of spontaneous vesicle formation in surfactant mixtures . Science , 248 : 354 – 356 .
   PubMed Web of Science ®Google Scholar
• Safran , S.A. , Pincus , P.A. , Andelman , D. and MacKintosh , F.C. 1991 . Stability and phase behavior of mixed surfactant vesicles . Phys. Rev. A , 43 : 1071 – 1078 .
   PubMed Web of Science ®Google Scholar
• Schmidt , C.F. , Svoboda , K. , Lei , N. , Petsche , I.B. , Berman , L.E. , Safinya , C.R. and Grest , G.S. 1993 . Existence of a flat phase in red cell membrane skeletons . Science , 259 : 952 – 955 .
   PubMed Web of Science ®Google Scholar
• Schneider , M.B. , Jenkins , J.R. and Webb , W.W. 1984a . Thermal fluctuations of large cylindrical phospholipid vesicles . Biophys. J. , 45 : 891 – 899 . 1984b, Thermal fluctuations of large quasi-spherical bimolecular phospholipid vesicles, J. Phys. France, 45, 1457–1472
   PubMed Web of Science ®Google Scholar
• Schnitzler , W. 1993 . Simulation und Analyse dreidimensionaler Vesikel- und Erythrozytenformen , Germany : Diplomarbeit RWTH Aachen .
   Google Scholar
• Seifert , U. 1990 . Shape transformation and free, toroidal and bound vesicles . J. de Physique, Colloque , 51 ( C7 ) : 339 – 344 . 1991a, Adhesion of vesicles in two dimensions, Phys. Rev. A, 43, 6803–6814; 1991b, Conformal transformations of vesicle shapes, J. Phys. (A), 24, L573–578; 1991c, Vesicles of toroidal topology, Phys. Rev. Lett., 66, 2404–2407; 1993, Curvature-induced lateral phase segregation in two component vesicles, Ibid., 70, 1335–1338; 1994, Dynamics of a bound membrane, Phys. Rev. E, 49, 3124–3127; 1995a, The concept of effective tension for fluctuating vesicles, Z. Physik B, 97, 299–309; 1995b, Fluid membranes—theory of vesicle conformations, Habilitation Thesis, Juel-Bericht 2997, Forschungszentrum Jülich; 1995c, Interplay of Genetic and Physical Processes in the Development of Biological Form, Les Houches Series, edited by D. Felix, M. A. Beysens, F. Gaill and G. Forgacs (Singapore: World Scientific), pp. 38–44; 1995d, Self-consistent theory of bound vesicles, Phys. Rev. Lett., 74, 5060–5063
   Google Scholar
• Seifert , U. , Berndl , K. and Lipowsky , R. 1991 . Shape transformations of vesicles: phase diagrams for spontaneous curvature and bilayer-coupling models . Phys. Rev. A , 44 : 1182 – 1202 .
   PubMed Web of Science ®Google Scholar
• Seifert , U. and Langer , S.A. 1993 . Viscous modes of fluid bilayer membranes . Europhys. Lett. , 23 : 71 – 76 . 1994, Hydrodynamics of membranes: the bilayer aspect and adhesion, Biophys. Chem., 49, 13–22
   Google Scholar
• Seifert , U. and Lipowsky , R. 1990 . Adhesion of vesicles . Phys. Rev. A , 42 : 4768 – 4771 . 1993, Dynamical Phenomena at Interfaces, Surfaces and Membranes, edited by D. Beysens, N. Boccara and G. Forgacs (New York: Nova), pp. 295–304
   PubMed Web of Science ®Google Scholar
• Seifert , U. , Miao , L. , Döbereiner , H.G. and Wortis , M. 1992 . “ The Structure and Conformation of Amphiphilic Membranes ” . In Springer Proceedings in Physics , Edited by: Lipowsky , R. , Richter , D. and Kremer , K. Vol. 66 , 93 – 96 . Berlin : Springer .
   Google Scholar
• Selinger , J.V. and Schnur , J.M. 1993 . Theory of chiral lipid tubules . Phys. Rev. Lett. , 71 : 4091 – 4094 .
   PubMed Web of Science ®Google Scholar
• Servuss , R.M. , Harbich , W. and Helfrich , W. 1976 . Measurements of the curvature elastic modulus of egg lecithin bilayers . Biochim. Biophys. Acta , 436 : 900 – 903 .
   PubMed Web of Science ®Google Scholar
• Servuss , R.M. and Helfrich , W. 1989 . Mutual adhesion of lecithin membranes at ultralow tensions . J. Phys. (France) , 50 : 809 – 827 .
   Web of Science ®Google Scholar
• Seung , H.S. and Nelson , D.R. 1988 . Defects in flexible membranes with crystalline order . Phys. Rev. A , 38 : 1005 – 1018 .
   Web of Science ®Google Scholar
• Sheet , M.P. and Singer , S.J. 1974 . Biological membranes as bilayer couples. A molecular mechanism of drug-erythrocyte interactions . Proc. Natl. Acad. Sci. (USA) , 71 : 4457 – 4461 .
   PubMed Web of Science ®Google Scholar
• Song , J. and Waugh , R.E. 1993 . Bending rigidity of SOPC membranes containing cholesterol . Biophys. J. , 64 : 1967 – 1970 .
   PubMed Web of Science ®Google Scholar
• Spector , M.S. , Naranjo , E. , Chiruvolu , S. and Zasadzinski , J.A. 1994 . Conformations of a tethered membrane: crumpling in graphite oxide? . Phys. Rev. Lett. , 73 : 2867 – 2867 .
   PubMed Web of Science ®Google Scholar
• Steck , T.L. 1989 . Cell Shape Determinants, Regulations, and Regulatory Role , Edited by: Stein , W. and Bronner , F. 205 – 246 . New York : Academic Press .
   Google Scholar
• Stokke , B.T. , Mikkelsen , A. and Elgsaeter , A. 1986a . The human erythrocyte membrane skeleton may be an ionic gel. I. Membrane mechanochemical properties . Eur. Biophys. J. , 13 : 203 – 218 . 1986b, The human erythrocyte membrane skeleton may be an ionic gel. II. Numerical analyses of cell shapes and shape transformations, Ibid., 13, 219–233
   PubMed Web of Science ®Google Scholar
• Strey , H. , Peterson , M. and Sackmann , E. 1995 . Measurement of erythrocyte membrane elasticity by flicker eigenmode decomposition . Biophys. J. , 69 : 478 – 488 .
   PubMed Web of Science ®Google Scholar
• Svetina , S. , Ottova-Leitmanova , A. and Glaser , R. 1982 . Membrane bending energy in relation to bilayer couples concept of red blood cell shape transformations . J. theoret. Biol. , 94 : 13 – 23 .
   PubMed Web of Science ®Google Scholar
• Svetina , S. and Zeks , B. 1983 . Bilayer couple hypothesis of red cell shape transformations and osmotic hemolysis . Biochem. Biophys. Acta , 42 : 86 – 90 . 1989, Membrane bending energy and shape determination of phospholipid vesicles and red blood cells, Eur. Biophys. J., 17, 101–111; 1992, The elastic deformability of closed multilayered membranes is the same as that of a bilayer membrane, Ibid., 21, 251–255
   Google Scholar
• Svoboda , K. , Schmidt , C.F. , Branton , D. and Block , S.M. 1992 . Conformation and elasticity of the isolated red blood cell membrane skeleton . Biophys. J. , 63 : 784 – 793 .
   PubMed Web of Science ®Google Scholar
• Taniguchi , T. , Kawasaki , K. , Andelman , D. and Kawakatsu , T. 1994 . Equilibrium shape deformations of two-component vesicles . J. Phys. II France , 4 : 1333 – 1362 .
   Google Scholar
• Tersoff , J. 1992 . Energies of fullerenes . Phys. Rev. B , 46 : 15546 – 15549 .
   Web of Science ®Google Scholar
• Thomsen , G. 1924 . Grundlagen der konformen Flächentheorie . Abh. Math. Sem. Univ. Hamburg , 3 : 31 – 56 .
   Google Scholar
• van Saarloos , W. 1988 . Front propagation into unstable shapes . Phys. Rev. A , 37 : 211 – 229 .
   Web of Science ®Google Scholar
• Vist , M.R. and Davis , J.H. 1990 . Phase equilibria of cholesterol/dipalmitoylphosphatidlycholine mixtures. 2H nuclear magnetic resonance and differential scanning calorimetry . Biochemistry , 29 : 451 – 464 .
   PubMed Web of Science ®Google Scholar
• Waugh , R. and Evans , E.A. 1979 . Thermoelasticity of red blood cell membrane . Biophys. J. , 26 : 115 – 132 .
   PubMed Web of Science ®Google Scholar
• Waugh , R.E. , Song , J. , Svetina , S. and Zeks , B. 1992 . Local and nonlocal curvature elasticity in bilayer membranes by tether formation from lecithin vesicles . Biophys. J. , 61 : 974 – 982 .
   PubMed Web of Science ®Google Scholar
• Wheater , J.F. 1994 . Random surfaces: from polymer membranes to strings . J. Phys. A , 27 : 3323 – 3353 .
   Google Scholar
• Wiese , W. , Harbich , W. and Helfrich , W. 1992 . Budding of lipid bilayer vesicles and flat membranes . J. Phys.: condens, Matter , 4 : 1647 – 1657 .
   Web of Science ®Google Scholar
• Willmore , T.J. 1965 . Note on embedded surfaces . Anal. Scient. ale Univ. Iasi (Sect. Ia) , 11 : 493 – 496 . 1982, Total Curvature in Riemannian Geometry (Chichester, UK: Ellis Horwood)
   Google Scholar
• Winterhalter , M. and Helfrich , W. 1986 . Effect of voltage on pores in membranes . Phys. Rev. A , 36 : 5874 – 5876 . 1992, Bending elasticity of electrically charged bilayers: coupled monolayers, neutral surfaces, and balancing stresses, J. phys. Chem., 96, 327
   Web of Science ®Google Scholar
• Wintz , W. , Döbereiner , H.-H. and Seifert , U. 1996 . Starfish vesicles . Europhys. Lett. , 33 : 403 – 408 .
   Google Scholar
• Witten , T.A. and Li , H. 1983 . Asymptotic shape of a fullerene ball . Europhys. Lett. , 23 : 51 – 55 .
   Google Scholar
• Wortis , M. , Seifert , U. , Berndl , K. , Fourcade , B. , Miao , L. , Rao , M. and Zia , R.K.P. 1993 . Dynamical Phenomena at Interfaces, Surfaces and Membranes , Edited by: Beysens , D. , Boccara , N. and Forgacs , G. 221 – 236 . New York : Nova .
   Google Scholar
• Wu , S.H.W. and McConnell , H.M. 1975 . Phase separations in phospholipid membranes . Biochemistry , 14 : 847 – 854 .
   PubMed Web of Science ®Google Scholar
• Yeung , A. and Evans , E. 1995 . Unexpected dynamics in shape fluctuations of bilayer vesicles . J. Phys. II France , 5 : 1501 – 1523 .
   Google Scholar
• Yeung , A.K.C. 1994 . Mechanics of Inter-Monolayer Coupling in Fluid Surfactant Bilayers, Ph.D. Thesis , Canada : University of British Columbia .
   Google Scholar
• Zhang , Z. , Davis , H.T. and Kroll , D.M. 1993 . Scaling behavior of self-avoiding tethered vesicles . Phys. Rev. E , 48 : R651 – R654 .
   Web of Science ®Google Scholar
• Zhang , Z. , Davis , H.T. , Maier , R.S. and Kroll , D.M. 1995 . The asymptotic shape of elastic networks . Phys. Rev. E , 52 : 5404 – 5413 .
   Web of Science ®Google Scholar
• Zheng , W.M. and Liu , J. 1993 . Helfrich shape equation for axisymmetric vesicles as a first integral . Phys. Rev. E , 48 : 2856 – 2860 .
   Web of Science ®Google Scholar
• Zilker , A. , Engelhardt , H. and Sackmann , E. 1987 . Dynamic reflection interference contrast (RIC-) microscopy: a new method to study surface excitations of cells and to measure membrane bending elastic moduli . J. Phys. (France) , 48 : 2138 – 2151 .
   Google Scholar
• Zilker , A. , Ziegler , M. and Sackmann , E. 1992 . Spectral analysis of erythrocyte flickering in the 0.3–4 μm-1 regime by microinterferometry combined with fast image processing . Phys. Rev. A , 46 : 7998 – 8001 .
   PubMed Web of Science ®Google Scholar
• Zimmermann , U. 1992 . Electric field-mediated fusion and related electrical phenomena . Biochem. Biophys. Acta , 694 : 227 – 277 .
   Google Scholar
• Zuckerman , D. and Bruinsma , R. 1995 . Statistical mechanics of membrane adhesion by reversible molecular bonds . Phys. Rev. Lett. , 74 : 3900 – 3903 .
   PubMed Web of Science ®Google Scholar