Bending Rigidities of Lipid Bilayers. Their Determination and Main Inputs in Biophysical Studies.

Advances in Planar Lipid Bilayers and Liposomes

Volumn 15, Issue , 2012, Pages 1-75

  Bouvrais, Hélène ^a  

^a UNIVERSITY OF SOUTHERN DENMARK   (Denmark)

Author keywords

Bending rigidity; Flickering technique; Giant unilamellar vesicle; Lipid bilayers; Membrane mechanics; Vesicle fluctuations analysis

Indexed keywords

EID: 84861203947     PISSN: 15544516     EISSN: None     Source Type: Book Series    
DOI: 10.1016/B978-0-12-396533-2.00006-9     Document Type: Chapter

References (164)

1. Alberts B., Bray D., Lewis J., Raff M., Roberts K., Watson J.D. Molecular Biology of the Cell 1994, Garland Publishing, New York.
2. Sackmann E. Biological membranes architecture and function. Handbook of Biological Physics 1995, vol. 1A. Elsevier Science B.V, Amsterdam, Chapter 1.
3. Heimburg T. Thermal Biophysics of Membranes 2007, Wiley-VCH, Weinheim.
4. Mouritsen O.G. Life-As a Matter of Fat: The Emerging Science of Lipodomics 2005, Springer-Verlag, Heidelberg.
5. Jamieson G.A., Robinson D.M. Mammalian Cell Membranes: Responses of Plasma Membranes 1977, Butterworths, London.
6. Gorter E., Grendel F. On bimolecular layers of lipids on the chromocytes of the blood. J. Exp. Med. 1925, 41(4):439.
7. Davson H.A., Danielli J.F. A contribution to the theory of thin films. J. Cell. Comp. Physiol. 1935, 5:495-508.
8. Robertson J.D. New observations on the ultrastructure of the membranes of frog peripheral nerve fibers. J. Cell Biol. 1957, 3(6):1043.
9. Singer S.J., Nicolson G.L. The fluid mosaic model of the structure of cell membranes. Science 1972, 175(4023):720-731.
10. Israelachvili J.N., Canberra A.C.T. The packing of lipids and proteins in membranes. Light Transducing Membranes: Structure Function and Evolution pages 1978, 91-107. Academic Press, New York. D.W. Deamer (Ed.).
11. Mouritsen O.G., Bloom M. Mattress model of lipid-protein interactions in membranes. Biophys. J. 1984, 46(2):141-153.
12. Mayor S., Rao M. Rafts: scale-dependent, active lipid organization at the cell surface. Traffic 2004, 5(4):231-240.
13. Pike L.J. Rafts defined: a report on the Keystone symposium on lipid rafts and cell function. J. Lipid Res. 2006, 47(7):1597.
14. Simons K., Ikonen E. Functional rafts in cell membranes. Nature 1997, 387(6633):569-572.
15. Sackmann E. Supported membranes: scientific and practical applications. Science 1996, 271(5245):4343.
16. Tamm L.K., McConnell H.M. Supported phospholipid bilayers. Biophys. J. 1985, 47(1):105-113.
17. Akashi K., Miyata H., Itoh H., Kinosita K. Preparation of giant liposomes in physiological conditions and their characterization under an optical microscope. Biophys. J. 1996, 71(6):3242-3250.
18. Lasic D.D. Liposomes: From Physics to Applications 1993, Elsevier Science Ltd, Amsterdam.
19. Lorin A., Flore C., Thomas A., Brasseur R. Les liposomes: description, fabrication et applications. Biotechnol. Agron. Soc. Environ. 2004, 8(3):163-176.
20. Luisi P.L., Walde P. Giant Vesicles 2000, Wiley, Chichester.
21. Menger F.M., Keiper J.S. Chemistry and physics of giant vesicles as biomembrane models. Curr. Opin. Chem. Biol. 1998, 2(6):726-732.
22. Walde P., Cosentino K., Engel H., Stano P. Giant vesicles: preparations and applications. Chembiochem 2010, 11(7):834.
23. Reeves J.P., Dowben R.M. Formation and properties of thin-walled phospholipid vesicles. J. Cell. Physiol. 1969, 73(1):49-60.
24. Ambroggio E.E., Separovic F., Bowie J.H., Fidelio G.D., Bagatolli L.A. Direct visualization of membrane leakage induced by the antibiotic peptides: maculatin, citropin, and aurein. Biophys. J. 2005, 89(3):1874-1881.
25. Bagatolli L.A., Sanchez S.A., Hazlett T., Gratton E. Giant vesicles, laurdan, and two-photon fluorescence microscopy: evidence of lipid lateral separation in bilayers. Methods Enzymol. 2003, 360:481-500.
26. Baumgart T., Hess S.T., Webb W.W. Imaging coexisting fluid domains in biomembrane models coupling curvature and line tension. Nature 2003, 425(6960):821-824.
27. Dimova R., Aranda S., Bezlyepkina N., Nikolov V., Riske K.A., Lipowsky R. A practical guide to giant vesicles. Probing the membrane nanoregime via optical microscopy. J. Phys. Condens. Matter 2006, 18:S1151-S1176.
28. Fischer A., Oberholzer T., Luisi P.L. Giant vesicles as models to study the interactions between membranes and proteins. Biochim. Biophys. Acta Biomembr. 2000, 1467(1):177-188.
29. Korlach J., Reichle C., Müller T., Schnelle T., Webb W.W. Trapping, deformation, and rotation of giant unilamellar vesicles in octode dielectrophoretic field cages. Biophys. J. 2005, 89(1):554-562.
30. Staneva G., Seigneuret M., Koumanov K., Trugnan G., Angelova M.I. Detergents induce raft-like domains budding and fission from giant unilamellar heterogeneous vesicles: a direct microscopy observation. Chem. Phys. Lipids 2005, 136(1):55-66.
31. Wesołowska O., Michalak K., Maniewska J., Hendrich A.B. Giant unilamellar vesicles-a perfect tool to visualize phase separation and lipid rafts in model systems. Acta Biochim. Pol. 2009, 56(1):33-39.
32. Angelova M.I., Dimitrov D.S. Liposome electroformation. Faraday Discuss. Chem. Soc. 1986, 81:303-311.
33. Angelova M.I., Soleau S., Méléard P., Faucon J.F., Bothorel P. Preparation of giant vesicles by external AC electric fields. Kinetics and applications. Progr. Colloid Polym. Sci. 1992, 89:127-131.
34. Bagatolli L.A., Gratton E., Khan T.K., Chong P.L.G. Two-photon fluorescence microscopy studies of bipolar tetraether giant liposomes from thermoacidophilic archaebacteria Sulfolobus acidocaldarius. Biophys. J. 2000, 79(1):416-425.
35. Bernardino de la Serna J., Perez-Gil J., Simonsen A.C., Bagatolli L.A. Cholesterol rules: direct observation of the coexistence of two fluid phases in native pulmonary surfactant membranes at physiological temperatures. J. Biol. Chem. 2004, 279:40715-40722.
36. Dietrich C., Bagatolli L.A., Volovyk Z.N., Thompson N.L., Levi M., Jacobson K., et al. Lipid rafts reconstituted in model membranes. Biophys. J. 2001, 80(3):1417-1428.
37. Nag K., Pao J.S., Harbottle R.R., Possmayer F., Petersen N.O., Bagatolli L.A. Segregation of saturated chain lipids in pulmonary surfactant films and bilayers. Biophys. J. 2002, 82(4):2041-2051.
38. Baumgart T., Hammond A.T., Sengupta P., Hess S.T., Holowka D.A., Baird B.A., et al. Large-scale fluid/fluid phase separation of proteins and lipids in giant plasma membrane vesicles. Proc. Natl. Acad. Sci. USA 2007, 104(9):3165.
39. Montes L.R., Alonso A., Goñi F.M., Bagatolli L.A. Giant unilamellar vesicles electroformed from native membranes and organic lipid mixtures under physiological conditions. Biophys. J. 2007, 93(10):3548-3554.
40. Ruan Q., Cheng M.A., Levi M., Gratton E., Mantulin W.W. Spatial-temporal studies of membrane dynamics: scanning fluorescence correlation spectroscopy (SFCS). Biophys. J. 2004, 87(2):1260-1267.
41. Girard P., Pécréaux J., Lenoir G., Falson P., Rigaud J.L., Bassereau P. A new method for the reconstitution of membrane proteins into giant unilamellar vesicles. Biophys. J. 2004, 87(1):419-429.
42. Kahya N., Pécheur E.I., de Boeij W.P., Wiersma D.A., Hoekstra D. Reconstitution of membrane proteins into giant unilamellar vesicles via peptide-induced fusion. Biophys. J. 2001, 81(3):1464-1474.
43. Moscho A., Orwar O., Chiu D.T., Modi B.P., Zare R.N. Rapid preparation of giant unilamellar vesicles. Proc. Natl. Acad. Sci. USA 1996, 93(21):11443.
44. Pott T., Bouvrais H., Méléard P. Giant unilamellar vesicle formation under physiologically relevant conditions. Chem. Phys. Lipids 2008, 154(2):115-119.
45. MacDonald R.C., MacDonald R.I., Menco B.P.M., Takeshita K., Subbarao N.K., Hu L. Small-volume extrusion apparatus for preparation of large, unilamellar vesicles. Biochim. Biophys. Acta Biomembr. 1991, 1061(2):297-303.
46. Mayer L.D., Hope M.J., Cullis P.R. Vesicles of variable sizes produced by a rapid extrusion procedure. Biochim. Biophys. Acta Biomembr. 1986, 858(1):161-168.
47. Mui B., Chow L., Hope M.J. Extrusion technique to generate liposomes of defined size. Methods Enzymol. 2003, 367:3.
48. Szoka F., Papahadjopoulos D. Procedure for preparation of liposomes with large internal aqueous space and high capture by reverse-phase evaporation. Proc. Natl. Acad. Sci. USA 1978, 75(9):4194.
49. Huang C.H. Phosphatidylcholine vesicles. Formation and physical characteristics. Biochemistry 1969, 8(1):344-352.
50. Papahadjopoulos D., Miller N. Phospholipid model membranes. I. Structural characteristics of hydrated liquid crystals. Biochim. Biophys. Acta Biomembr. 1967, 135(4):624-638.
51. Sheetz M.P., Chan S.I. Effect of sonication on the structure of lecithin bilayers. Biochemistry 1972, 11(24):4573-4581.
52. Rigaud J.L., Levy D. Reconstitution of membrane proteins into liposomes. Methods Enzymol. 2003, 372:65.
53. Evans E., Rawicz W. Entropy-driven tension and bending elasticity in condensed-fluid membranes. Phys. Rev. Lett. 1990, 64(17):2094-2097.
54. Helfrich W. Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. 1973, 28c(11):693-703.
55. Sackmann E. Membrane bending energy concept of vesicle-and cell-shapes and shape-transitions. FEBS Lett. 1994, 346(1):3-16.
56. Deuling H.J., Helfrich W. Red blood cell shapes as explained on the basis of curvature elasticity. Biophys. J. 1976, 16(8):861-868.
57. Deuling H.J., Helfrich W. The curvature elasticity of fluid membranes: a catalogue of vesicle shapes. J. Phys. 1976, 37(11):1335-1345.
58. Brochard F., Lennon J.F. Frequency spectrum of the flicker phenomenon in erythrocytes. J. Phys. (Paris) 1975, 36:1035-1047.
59. Browicz T. Further observation of motion phenomena on red blood cells in pathological states. Zbl. med. Wissen 1890, 28:625-627.
60. Beblik G., Servuss R.M., Helfrich W. Bilayer bending rigidity of some synthetic lecithins. J. Phys. (Paris) 1985, 46(10):1773-1778.
61. Schneider M.B., Jenkins J.T., Webb W.W. Thermal fluctuations of large cylindrical phospholipid vesicles. Biophys. J. 1984, 45(5):891-899.
62. Servuss R.M., Harbich W., Helfrich W. Measurement of the curvature-elastic modulus of egg lecithin bilayers. Biochim. Biophys. Acta 1976, 436(4):900-903.
63. Mutz M., Helfrich W. Bending rigidities of some biological model membranes as obtained from the Fourier analysis of contour sections. J. Phys. (Paris) 1990, 51(10):991-1001.
64. Bivas I., Hanusse P., Bothorel P., Lalanne J., Aguerre-Chariol O. An application of the optical microscopy to the determination of the curvature elastic modulus of biological and model membranes. J. Phys. (Paris) 1987, 48(5):855-867.
65. Bouvrais H., Méléard P., Pott T., Ipsen J.H. Anion specificity of sodium salts on the bending rigidity of POPC lipid bilayer 2012, in preparation.
66. Bouvrais H., Méléard P., Pott T., Jensen K.J., Brask J., Ipsen J.H. Softening of POPC membranes by magainin. Biophys. Chem. 2008, 137(1):7-12.
67. Bouvrais H., Pott T., Bagatolli L.A., Ipsen J.H., Méléard P. Impact of membrane-anchored fluorescent probes on the mechanical properties of lipid bilayers. Biochim. Biophys. Acta Biomembr. 2010, 1798(7):1333-1337.
68. Duwe H.P., Kaes J., Sackmann E. Bending elastic moduli of lipid bilayers: modulation by solutes. J. Phys. (Paris) 1990, 51(10):945-961.
69. Engelhardt H., Duwe H.P., Sackmann E. Bilayer bending elasticity measured by Fourier analysis of thermally excited surface undulations of flaccid vesicles. J. Phys. Lett. 1985, 46(8):395-400.
70. Faucon J.F., Mitov M.D., Méléard P., Bivas I., Bothorel P. Bending elasticity and thermal fluctuations of lipid membranes. Theoretical and experimental requirements. J. Phys. (France) 1989, 50:2389-2414.
71. Fernandez-Puente L., Bivas I., Mitov M.D., Méléard P. Temperature and chain length effects on bending elasticity of phosphatidylcholine bilayers. Europhys. Lett. 1994, 28(3):181-186.
72. Genova J., Vitkova V., Aladgem L., Méléard P., Mitov M.D. Using stroboscopic illumination to improve the precision of the bending modulus measurement. Bulg. J. Phys. 2004, 31(1-2):68-75.
73. Genova J., Vitkova V., Aladjem L., Méléard P., Mitov M.D. Stroboscopic illumination gives new opportunities and improves the precision of bending elastic modulus measurements. J. Optoelectron. Adv. Mater. 2005, 7(1):257-260.
74. Genova J., Zheliaskova A., Mitov M.D. Monosaccharides (fructose, glucose) and disaccharides (sucrose, trehalose) influence the elasticity of SOPC membranes. J. Optoelectron. Adv. Mater. 2007, 9(2):427-430.
75. Genova J., Zheliaskova A., Mitov M.D. Does maltose influence on the elasticity of SOPC membrane?. J. Phys. Conf. Ser. 2010, 253:012063.
76. Gracià R.S., Bezlyepkina N., Knorr R.L., Lipowsky R., Dimova R. Effect of cholesterol on the rigidity of saturated and unsaturated membranes: fluctuation and electrodeformation analysis of giant vesicles. Soft Matter 2010, 6(7):1472-1482.
77. Henriksen J.R., Andresen T.L., Feldborg L.N., Duelund L., Ipsen J.H. Understanding detergent effects on lipid membranes: a model study of lysolipids. Biophys. J. 2010, 98(10):2199.
78. Henriksen J.R., Rowat A.C., Ipsen J.H. Vesicle fluctuation analysis of the effects of sterols on membrane bending rigidity. Eur. Biophys. J. 2004, 33(8):732-741.
79. Méléard P., Faucon J.F., Mitov M.D., Bothorel P. Pulsed-light microscopy applied to the measurement of the bending elasticity of giant liposomes. Europhys. Lett. 1992, 19(4):267-271.
80. Méléard P., Gerbeaud C., Bardusco P., Jeandaine N., Mitov M.D., Fernandez-Puente L. Mechanical properties of model membranes studied from shape transformations of giant vesicles. Biochimie 1998, 80(5-6):401-413.
81. Méléard P., Gerbeaud C., Pott T., Fernandez-Puente L., Bivas I., Mitov M.D., et al. Bending elasticities of model membranes: influences of temperature and sterol content. Biophys. J. 1997, 72(6):2616-2629.
82. Pakkanen K.I., Duelund L., Qvortrup K., Pedersen J.S., Ipsen J.H. Mechanics and dynamics of triglyceride-phospholipid model membranes: implications for cellular properties and function. Biochim. Biophys. Acta Biomembr. 2011, 1808:1947-1956.
83. Pavlič J.I., Genova J., Zheliaskova A., Iglič A., Mitov M.D. Bending elasticity of lipid membranes in presence of beta 2 glycoprotein I in the surrounding solution. J. Phys. Conf. Ser. 2010, 253:012064.
84. Pécréaux J., Döbereiner H.G., Prost J., Joanny J.F., Bassereau P. Refined contour analysis of giant unilamellar vesicles. Eur. Phys. J. E 2004, 13(3):277-290.
85. Sackmann E., Duwe H.P., Engelhardt H. Membrane bending elasticity and its role for shape fluctuations and shape transformations of cells and vesicles. Faraday Discuss. Chem. Soc. 1986, 81:281-290.
86. Schneider M.B., Jenkins J.T., Webb W.W. Thermal fluctuations of large quasi-spherical bimolecular phospholipid vesicles. J. Phys. (Paris) 1984, 45(9):1457-1472.
87. Vitkova V., Méléard P., Pott T., Bivas I. Alamethicin influence on the membrane bending elasticity. Eur. Biophys. J. 2006, 35(3):281-286.
88. Mitov M.D., Faucon J.F., Méléard P., Bivas I., Bothorel P. Thermal fluctuations of membranes. Advances in Supramolecular Chemistry 1992, vol. 2:93-139. Jai Press, Greenwich.
89. Angelova M.I., Soleau S., Méléard P., Faucon J.F., Bothorel P. AC field controlled formation of giant fluctuating vesicles and bending elasticity measurements. Springer Proc. Phys. 1992, 66:178-182.
90. Hønger T., Mortensen K., Ipsen J.H., Lemmich J., Bauer R., Mouritsen O.G. Anomalous swelling of multilamellar lipid bilayers in the transition region by renormalization of curvature elasticity. Phys. Rev. Lett. 1994, 72(24):3911-3914.
91. Henriksen J.R., Ipsen J.H. Thermal undulations of quasi-spherical vesicles stabilized by gravity. Eur. Phys. J. E 2002, 9(4):365-374.
92. Gerbeaud C. Effet de l'insertion de protéines et de peptides membranaires sur les propriétés mécaniques et les changements morphologiques de vésicules géantes 1998, Université de Bordeaux I, Ph.D. Thesis.
93. Häckl W., Seifert U., Sackmann E. Effects of fully and partially solubilized amphiphiles on bilayer bending stiffness and temperature dependence of the effective tension of giant vesicles. J. Phys. II, France 1997, 7:1141-1157.
94. Bouvrais H. Mechanical properties of giant vesicle membranes investigated by flickering technique 2011, University of Southern Denmark, Ph.D. Thesis.
95. Méléard P., Pott T., Bouvrais H., Ipsen J.H. Statistical analysis of giant vesicle thermal fluctuations for bending elasticity measurements. Eur. Phys. J. E 2011, 34(11):1-6.
96. Evans E. Bending elastic modulus of red blood cell membrane derived from buckling instability in micropipet aspiration tests. Biophys. J. 1983, 43(1):27.
97. Evans E., Needham D. Physical properties of surfactant bilayer membranes: thermal transitions, elasticity, rigidity, cohesion and colloidal interactions. J. Phys. Chem. 1987, 91(16):4219-4228.
98. Henriksen J.R., Ipsen J.H. Measurement of membrane elasticity by micro-pipette aspiration. Eur. Phys. J. E Soft Matter 2004, 14(2):149-167.
99. Rawicz W., Olbrich K.C., McIntosh T., Needham D., Evans E. Effect of chain length and unsaturation on elasticity of lipid bilayers. Biophys. J. 2000, 79(1):328-339.
100. Bo L., Waugh R.E. Determination of bilayer membrane bending stiffness by tether formation from giant, thin-walled vesicles. Biophys. J. 1989, 55(3):509-517.
101. Cuvelier D., Derényi I., Bassereau P., Nassoy P. Coalescence of membrane tethers: experiments, theory, and applications. Biophys. J. 2005, 88(4):2714-2726.
102. Heinrich V., Waugh R.E. A piconewton force transducer and its application to measurement of the bending stiffness of phospholipid membranes. Ann. Biomed. Eng. 1996, 24(5):595-605.
103. Settles E.I., Loftus A.F., McKeown A.N., Parthasarathy R. The vesicle trafficking protein sar1 lowers lipid membrane rigidity. Biophys. J. 2010, 99(5):1539-1545.
104. Song J., Waugh R.E. Bending rigidity of SOPC membranes containing cholesterol. Biophys. J. 1993, 64(6):1967-1970.
105. Waugh R.E., Hochmuth R.M. Mechanical equilibrium of thick, hollow, liquid membrane cylinders. Biophys. J. 1987, 52(3):391.
106. Kummrow M., Helfrich W. Deformation of giant lipid vesicles by electric fields. Phys. Rev. A 1991, 44(12):8356-8360.
107. Dimova R., Pouligny B., Dietrich C. Pretransitional effects in dimyristoylphosphatidylcholine vesicle membranes: optical dynamometry study. Biophys. J. 2000, 79(1):340-356.
108. Lee C.H., Lin W.C., Wang J. Measuring the bending rigidity of giant unilamellar liposomes with differential confocal microscopy. Lasers Electro Optics 2000, 592-593.
109. Lee C.H., Lin W.C., Wang J. All-optical measurements of the bending rigidity of lipid-vesicle membranes across structural phase transitions. Phys. Rev. E 2001, 64(2):020901.
110. Lee C.H., Wang J. Noninterferometric differential confocal microscopy with 2-nm depth resolution. Opt. Commun. 1997, 135(4-6):233-237.
111. Lewis R.N.A.H., Mak N., McElhaney R.N. A differential scanning calorimetric study of the thermotropic phase behavior of model membranes composed of phosphatidylcholines containing linear saturated fatty acyl chains. Biochemistry 1987, 26(19):6118-6126.
112. Arriaga L.R., López-Montero I., Monroy F., Orts-Gil G., Farago B., Hellweg T. Stiffening effect of cholesterol on disordered lipid phases: a combined neutron spin echo + dynamic light scattering analysis of the bending elasticity of large unilamellar vesicles. Biophys. J. 2009, 96(9):3629-3637.
113. Arriaga L.R., López-Montero I., Orts-Gil G., Farago B., Hellweg T., Monroy F. Fluctuation dynamics of spherical vesicles: frustration of regular bulk dissipation into subdiffusive relaxation. Phys. Rev. E 2009, 80(3):031908.
114. Chu N., Kučerka N., Liu Y., Tristram-Nagle S., Nagle J.F. Anomalous swelling of lipid bilayer stacks is caused by softening of the bending modulus. Phys. Rev. E 2005, 71(4):41904.
115. Kučerka N., Liu Y., Chu N., Petrache H.I., Tristram-Nagle S., Nagle J.F. Structure of fully hydrated fluid phase DMPC and DLPC lipid bilayers using X-Ray scattering from oriented multilamellar arrays and from unilamellar vesicles. Biophys. J. 2005, 88(4):2626-2637.
116. Kučerka N., Tristram-Nagle S., Nagle J.F. Structure of fully hydrated fluid phase lipid bilayers with monounsaturated chains. J. Membr. Biol. 2006, 208(3):193-202.
117. Liu Y., Nagle J.F. Diffuse scattering provides material parameters and electron density profiles of biomembranes. Phys. Rev. E 2004, 69(4):40901.
118. Lyatskaya Y., Liu Y., Tristram-Nagle S., Katsaras J., Nagle J.F. Method for obtaining structure and interactions from oriented lipid bilayers. Phys. Rev. E 2000, 63(1):11907.
119. Pan J., Mills T.T., Tristram-Nagle S., Nagle J.F. Cholesterol perturbs lipid bilayers nonuniversally. Phys. Rev. Lett. 2008, 100(19):198103.
120. Pan J., Tristram-Nagle S., Nagle J.F. Effect of cholesterol on structural and mechanical properties of membranes depends on lipid chain saturation. Phys. Rev. E 2009, 80(2):21931.
121. Petrache H.I., Tristram-Nagle S., Harries D., Kučerka N., Nagle J.F., Parsegian V.A. Swelling of phospholipids by monovalent salt. J. Lipid Res. 2006, 47:302-309.
122. Zilker A., Engelhardt H., Sackmann E. 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) 1987, 48:2139-2151.
123. -1 regime by microinterferometry combined with fast image processing. Phys. Rev. A 1992, 46(12):7998.
124. Caillé A. Remarques sur la diffusion des rayons x dans les smectiques. C. R. Acad. Sci. Paris Ser. B 1972, 274:891-893.
125. Tristram-Nagle S., Zhang R., Suter R.M., Worthington C.R., Sun W.J., Nagle J.F. Measurement of chain tilt angle in fully hydrated bilayers of gel phase lecithins. Biophys. J. 1993, 64(4):1097.
126. Pan J., Tristram-Nagle S., Kučerka N., Nagle J.F. Temperature dependence of structure, bending rigidity, and bilayer interactions of Dioleoylphosphatidylcholine bilayers. Biophys. J. 2008, 94(1):117.
127. Zilman A.G., Granek R. Undulations and dynamic structure factor of membranes. Phys. Rev. Lett. 1996, 77(23):4788-4791.
128. Groot R.D., Warren P.B. Dissipative particle dynamics: bridging the gap between atomistic and mesoscopic simulation. J. Chem. Phys. 1997, 107(11):4423.
129. Goetz R., Gompper G., Lipowsky R. Mobility and elasticity of self-assembled membranes. Phys. Rev. Lett. 1999, 82(1):221-224.
130. Ayton G., Voth G.A. Bridging microscopic and mesoscopic simulations of lipid bilayers. Biophys. J. 2002, 83(6):3357-3370.
131. Marrink S.J., de Vries A.H., Mark A.E. Coarse grained model for semiquantitative lipid simulations. J. Phys. Chem. B 2004, 108(2):750-760.
132. May E.R., Narang A., Kopelevich D.I. Role of molecular tilt in thermal fluctuations of lipid membranes. Phys. Rev. E 2007, 76(2):21913.
133. Stevens M.J. Coarse-grained simulations of lipid bilayers. J. Chem. Phys. 2004, 121:11942.
134. Imparato A., Shillcock J.C., Lipowsky R. Shape fluctuations and elastic properties of two-component bilayer membranes. Europhys. Lett. 2005, 69:650.
135. Boek E.S., Padding J.T., den Otter W.K., Briels W.J. Mechanical properties of surfactant bilayer membranes from atomistic and coarse-grained molecular dynamics simulations. J. Phys. Chem. B 2005, 109(42):19851-19858.
136. Brannigan G., Brown F.L.H. A consistent model for thermal fluctuations and protein-induced deformations in lipid bilayers. Biophys. J. 2006, 90(5):1501-1520.
137. Cooke I.R., Deserno M. Solvent-free model for self-assembling fluid bilayer membranes: stabilization of the fluid phase based on broad attractive tail potentials. J. Chem. Phys. 2005, 123:224710.
138. Farago O. Water-free computer model for fluid bilayer membranes. J. Chem. Phys. 2003, 119:596.
139. Lindahl E., Edholm O. Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations. Biophys. J. 2000, 79(1):426-433.
140. Marrink S.J., Mark A.E. Effect of undulations on surface tension in simulated bilayers. J. Phys. Chem. B 2001, 105(26):6122-6127.
141. Chiu S.W., Vasudevan S., Jakobsson E., Mashl R.J., Scott H.L. Structure of sphingomyelin bilayers: a simulation study. Biophys. J. 2003, 85(6):3624-3635.
142. den Otter W.K., Briels W.J. The bending rigidity of an amphiphilic bilayer from equilibrium and nonequilibrium molecular dynamics. J. Chem. Phys. 2003, 118:4712.
143. Farago O., Pincus P. Statistical mechanics of bilayer membrane with a fixed projected area. J. Chem. Phys. 2004, 120:2934.
144. Harmandaris V.A., Deserno M. A novel method for measuring the bending rigidity of model lipid membranes by simulating tethers. J. Chem. Phys. 2006, 125:204905.
145. Baoukina S., Monticelli L., Risselada H.J., Marrink S.J., Tieleman D.P. The molecular mechanism of lipid monolayer collapse. Proc. Natl. Acad. Sci. USA 2008, 105(31):10803.
146. Wong-Ekkabut J., Baoukina S., Triampo W., Tang I.M., Tieleman D.P., Monticelli L. Computer simulation study of fullerene translocation through lipid membranes. Nat. Nanotechnol. 2008, 3(6):363-368.
147. Döbereiner H.G., Gompper G., Haluska C.K., Kroll D.M., Petrov P.G., Riske K.A. Advanced flicker spectroscopy of fluid membranes. Phys. Rev. Lett. 2003, 91(4):48301.
148. Fa N. Micro-rhéologie de vésicules géantes 2003, Université de Strasbourg, Ph.D. Thesis.
149. Girard P. Membranes hors d'équilibre: échanges et transport actif 2004, Université de Paris, Ph.D. Thesis, 7.
150. Niggemann G., Kummrow M., Helfrich W. The bending rigidity of phosphatidylcholine bilayers: dependences on experimental method, sample cell sealing and temperature. J. Phys. II 1995, 5(3):413-425.
151. Chaikin P.M., Lubensky T.C. Principles of Condensed Matter Physics 2000, Cambridge University Press, Cambridge, UK.
152. Canham P.B. The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. J. Theor. Biol. 1970, 26(1):61-81.
153. Evans E.A. Bending resistance and chemically induced moments in membrane bilayers. Biophys. J. 1974, 14(12):923-931.
154. Méléard P. Elasticité de courbure de la bicouche lipidique: analyses statistique et dynamique des fluctuations thermiques de vésicules géantes 1990, Université de Bordeaux I, Ph.D. Thesis.
155. Milner S.T., Safran S.A. Dynamical fluctuations of droplet microemulsions and vesicles. Phys. Rev. A 1987, 36(9):4371-4379.
156. Rowat A.C., Hansen P.L., Ipsen J.H. Experimental evidence of the electrostatic contribution to membrane bending rigidity. Europhys. Lett. 2004, 67:144-149.
157. Arfken G.B., Weber H.J. Mathematical Methods for Physicists 2001, Academic press, New York.
158. Petrov A.G., Bivas I. Elastic and flexoelectric aspects of out-of-plane fluctuations in biological and model membranes. Prog. Surface Sci. 1984, 16(4):389-511.
159. Szleifer I., Kramer D., Ben-Shaul A., Gelbart W.M., Safran S.A. Molecular theory of curvature elasticity in surfactant films. J. Chem. Phys. 1990, 92:6800.
160. Szleifer I., Kramer D., Ben-Shaul A., Roux D., Gelbart W.M. Curvature elasticity of pure and mixed surfactant films. Phys. Rev. Lett. 1988, 60(19):1966-1969.
161. Henriksen J.R., Rowat A.C., Brief E., Hsueh Y.W., Thewalt J.L., Zuckermann M.J., et al. Universal behavior of membranes with sterols. Biophys. J. 2006, 90(5):1639-1649.
162. Song J., Waugh R.E. Bilayer membrane bending stiffness by tether formation from mixed PC-PS lipid vesicles. J. Biomech. Eng. 1990, 112:235.
163. Andelmann E. Electrostatics properties of membranes: the Poisson-Boltzmann theory. Handbook of Biological Physics 1995, vol. 1A. Elsevier Science B.V, Amsterdam, Chapter 12.
164. Fogden A., Ninham B.W. Electrostatics of curved fluid membranes: the interplay of direct interactions and fluctuations in charged lamellar phases. Adv. Colloid Interface Sci. 1999, 83(1-3):85-110.