125. Zhelev DV, Needham D (1993) Tension-stabilized pores in giant vesicles—determination of
pore-size and pore line tension. Biochim Biophys Acta 1147(1):89–104
126. Genco I, Gliozzi A, Relini A, Robello M, Scalas E (1993) Osmotic-pressure induced pores in
phospholipid vesicles. Biochim Biophys Acta 1149(1):10–18
127. Karatekin E, Sandre O, Guitouni H, Borghi N, Puech PH, Brochard-Wyart F (2003) Cascades
of transient pores in giant vesicles: line tension and transport. Biophys J 84(3):1734–1749
128. Tolpekina TV, den Otter WK, Briels WJ (2004) Simulations of stable pores in membranes:
system size dependence and line tension. J Chem Phys 121(16):8014–8020
129. Wohlert J, den Otter WK, Edholm O, Briels WJ (2006) Free energy of a trans-membrane pore
calculated from atomistic molecular dynamics simulations. J Chem Phys 124(15):154905
130. Jiang FY, Bouret Y, Kindt JT (2004) Molecular dynamics simulations of the lipid bilayer
edge. Biophys J 87(1):182–192
131. Wang ZJ, Deserno M (2010) Systematic implicit solvent coarse-graining of bilayer membranes: lipid and phase transferability of the force field. New J Phys 12:095004
132. Wang H, Hu D, Zhang P (2013) Measuring the spontaneous curvature of bilayer membranes
by molecular dynamics simulations. Commun Comput Phys 13:1093–1106
133. Helfrich W (1985) Effect of thermal undulations on the rigidity of fluid membranes and
interfaces. J Phys France 46(7):1263–1268
134. Peliti L, Leibler S (1985) Effects of thermal fluctuations on systems with small surface
tension. Phys Rev Lett 54:1690–1693
135. Fo ¨rster D (1986) On the scale dependence, due to thermal fluctuations, of the elastic
properties of membranes. Phys Lett A 114(3):115–120
136. Kleinert H (1986) Thermal softening of curvature elasticity in membranes. Phys Lett A
114(5):263–268
137. Schmid F (2013) Fluctuations in lipid bilayers: are they understood? Biophys Rev Lett 8:1–20
doi:10.1142/S1793048012300113
138. Nelson DR, Peliti L (1987) Fluctuations in membranes with crystalline and hexatic order.
J Phys (France) 48(1):1085–1092. doi:10.1051/jphys:019870048070108500
139. Le Doussal P, Radzihovsky L (1992) Self-consistent theory of polymerized membranes. Phys
Rev Lett 69(8):1209–1211
140. Park JM, Lubensky TC (1995) Topological defects on fluctuating surfaces: general properties
and the Kosterlitz–Thouless transition. Phys Rev E 53(3):2648–2664
141. Park JM (1996) Renormalization of fluctuating tilted hexatic membranes. Phys Rev E 56(7):
R47–R50
142. West B, Schmid F (2010) Fluctuations and elastic properties of lipid membranes in the fluid
and gel state: a coarse-grained Monte Carlo study. Soft Matter 6:1275–1280
143. Kramer L (1971) Theory of light scattering from fluctuations of membranes and monolayers.
J Chem Phys 55:2097–2105
144. Seifert U, Langer SA (1993) Viscous modes of fluid bilayer membranes. Europhys Lett
23(1):71–76
145. Zilman AG, Granek R (1996) Undulations and dynamic structure factor of membranes. Phys
Rev Lett 77:4788–4791
146. Fromherz P (1983) Lipid-vesicle structure: size control by edge-active agents. Chem Phys
Lett 94:259–266
147. van Kampen NG (2007) Stochastic processes in physics and chemistry, 3rd edn. Elsevier,
Amsterdam
148. Helfrich W (1981) Physics of defects. North Holland, Amsterdam
149. Helfrich W (1994) Lyotropic lamellar phases. J Phys Condens Matter 6:A79–A92
150. Szleifer I, Kramer D, Ben-Shaul A, Gelbart WM, Safran SA (1990) Molecular theory of
curvature elasticity in surfactant films. J Chem Phys 92:6800–6817
151. Rowlinson JS, Widom B (2002) Molecular theory of capillarity, 1st edn. Dover, New York
152. Gompper G, Klein S (1992) Ginzburg-Landau theory of aqueous surfactant solutions. J Phys
II (France) 2:1725–1744
276
M. Deserno et al.
pore-size and pore line tension. Biochim Biophys Acta 1147(1):89–104
126. Genco I, Gliozzi A, Relini A, Robello M, Scalas E (1993) Osmotic-pressure induced pores in
phospholipid vesicles. Biochim Biophys Acta 1149(1):10–18
127. Karatekin E, Sandre O, Guitouni H, Borghi N, Puech PH, Brochard-Wyart F (2003) Cascades
of transient pores in giant vesicles: line tension and transport. Biophys J 84(3):1734–1749
128. Tolpekina TV, den Otter WK, Briels WJ (2004) Simulations of stable pores in membranes:
system size dependence and line tension. J Chem Phys 121(16):8014–8020
129. Wohlert J, den Otter WK, Edholm O, Briels WJ (2006) Free energy of a trans-membrane pore
calculated from atomistic molecular dynamics simulations. J Chem Phys 124(15):154905
130. Jiang FY, Bouret Y, Kindt JT (2004) Molecular dynamics simulations of the lipid bilayer
edge. Biophys J 87(1):182–192
131. Wang ZJ, Deserno M (2010) Systematic implicit solvent coarse-graining of bilayer membranes: lipid and phase transferability of the force field. New J Phys 12:095004
132. Wang H, Hu D, Zhang P (2013) Measuring the spontaneous curvature of bilayer membranes
by molecular dynamics simulations. Commun Comput Phys 13:1093–1106
133. Helfrich W (1985) Effect of thermal undulations on the rigidity of fluid membranes and
interfaces. J Phys France 46(7):1263–1268
134. Peliti L, Leibler S (1985) Effects of thermal fluctuations on systems with small surface
tension. Phys Rev Lett 54:1690–1693
135. Fo ¨rster D (1986) On the scale dependence, due to thermal fluctuations, of the elastic
properties of membranes. Phys Lett A 114(3):115–120
136. Kleinert H (1986) Thermal softening of curvature elasticity in membranes. Phys Lett A
114(5):263–268
137. Schmid F (2013) Fluctuations in lipid bilayers: are they understood? Biophys Rev Lett 8:1–20
doi:10.1142/S1793048012300113
138. Nelson DR, Peliti L (1987) Fluctuations in membranes with crystalline and hexatic order.
J Phys (France) 48(1):1085–1092. doi:10.1051/jphys:019870048070108500
139. Le Doussal P, Radzihovsky L (1992) Self-consistent theory of polymerized membranes. Phys
Rev Lett 69(8):1209–1211
140. Park JM, Lubensky TC (1995) Topological defects on fluctuating surfaces: general properties
and the Kosterlitz–Thouless transition. Phys Rev E 53(3):2648–2664
141. Park JM (1996) Renormalization of fluctuating tilted hexatic membranes. Phys Rev E 56(7):
R47–R50
142. West B, Schmid F (2010) Fluctuations and elastic properties of lipid membranes in the fluid
and gel state: a coarse-grained Monte Carlo study. Soft Matter 6:1275–1280
143. Kramer L (1971) Theory of light scattering from fluctuations of membranes and monolayers.
J Chem Phys 55:2097–2105
144. Seifert U, Langer SA (1993) Viscous modes of fluid bilayer membranes. Europhys Lett
23(1):71–76
145. Zilman AG, Granek R (1996) Undulations and dynamic structure factor of membranes. Phys
Rev Lett 77:4788–4791
146. Fromherz P (1983) Lipid-vesicle structure: size control by edge-active agents. Chem Phys
Lett 94:259–266
147. van Kampen NG (2007) Stochastic processes in physics and chemistry, 3rd edn. Elsevier,
Amsterdam
148. Helfrich W (1981) Physics of defects. North Holland, Amsterdam
149. Helfrich W (1994) Lyotropic lamellar phases. J Phys Condens Matter 6:A79–A92
150. Szleifer I, Kramer D, Ben-Shaul A, Gelbart WM, Safran SA (1990) Molecular theory of
curvature elasticity in surfactant films. J Chem Phys 92:6800–6817
151. Rowlinson JS, Widom B (2002) Molecular theory of capillarity, 1st edn. Dover, New York
152. Gompper G, Klein S (1992) Ginzburg-Landau theory of aqueous surfactant solutions. J Phys
II (France) 2:1725–1744
276
M. Deserno et al.