153. Diamant H (2011) Model-free thermodynamics of fluid vesicles. Phys Rev E 84(6):0611203
154. Capovilla R, Guven J (2002) Stresses in lipid membranes. J Phys A Math Gen 35:6233–6247
155. Capovilla R, Guven J (2004) Stress and geometry of lipid vesicles. J Phys Condens Matter 16:
S2187–S2191
156. Farago O, Pincus P (2004) Statistical mechanics of bilayer membrane with a fixed projected
area. J Chem Phys 120:2934–2950
157. Guven J (2004) Membrane geometry with auxiliary variables and quadratic constraints.
J Phys A Math Gen 37:L313–L319
158. Mu ¨ller MM, Deserno M, Guven J (2005) Geometry of surface-mediated interactions.
Europhys Lett 69:482–488
159. Mu ¨ller MM, Deserno M, Guven J (2005) Interface-mediated interactions between particles: a
geometrical approach. Phys Rev E 72:061407
160. Mu ¨ller MM, Deserno M, Guven J (2007) Balancing torques in membrane-mediated interactions: exact results and numerical illustrations. Phys Rev E 76:011921. doi:10.1103/
PhysRevE.76.011921
161. Deserno M, Mu ¨ller MM, Guven J (2007) Contact lines for fluid surface adhesion. Phys Rev E
76:011605. doi:10.1103/PhysRevE.76.011605
162. Schmid F (2011) Are stress-free membranes really “tensionless”? Europhys Lett 95:28008
163. Deuling H, Helfrich W (1976) The curvature elasticity of fluid membranes: a catalogue of
vesicle shapes. J Phys (France) 37:1335–1345
164. David F, Leibler S (1991) Vanishing tension of fluctuating membranes. J Phys II (France)
1:959–976
165. Cai W, Lubensky TC, Nelson P, Powers T (1994) Measure factors, tension, and correlations
of fluid membranes. J Phys II (France) 4:931–949
166. Ja ¨hnig F (1996) What is the surface tension of a lipid bilayer membrane? Biophys J
71:1348–1349
167. Marsh D (1997) Renormalization of the tension and area expansion modulus in fluid
membranes. Biophys J 73:865–869
168. Farago O, Pincus P (2003) The effect of thermal fluctuations on Schulman area elasticity. Eur
Phys J E 11:399–408
169. Imparato A (2006) Surface tension in bilayer membranes with fixed projected area. J Chem
Phys 124:154714
170. Stecki J (2008) Balance of forces in simulated bilayers. J Phys Chem B 112(14):4246–4252
171. Fournier JB, Barbetta C (2008) Direct calculation from the stress tensor of the lateral surface
tension of fluctuating fluid membranes. Phys Rev Lett 100:078103
172. Fournier JB (2012) Comment on “are stress-free membranes really ‘tensionless’?” by Schmid
F. Europhys Lett 97:18001
173. Schmid F (2012) Reply to Comment on “are stress-free membranes really ‘tensionless’?”.
Europhys Lett 97:18002
174. Farago O (2011) Mechanical surface tension governs membrane thermal fluctuations. Phys
Rev E 84:051944
175. Marrink SJ, Mark AE (2001) Effect of undulations on surface tension in simulated bilayers.
J Phys Chem B 105:6122–6127
176. Loison C, Mareschal M, Kremer K, Schmid F (2003) Thermal fluctuations in a lamellar phase
of a binary amphiphile-solvent mixture: a molecular-dynamics study. J Chem Phys 119(13):
138–13148
177. Ahmed SN, Brown DA, London E (1997) On the origin of sphingolipid/cholesterol-rich
detergent-insoluble cell membranes: Physiological concentrations of cholesterol and
sphingolipid induce formation of a detergent-insoluble, liquid-ordered lipid phase in model
membranes. Biochemistry 36(36):10944–10953
178. Simons K, Ikonen E (1997) Functional rafts in cell membranes. Nature 387:569–572
179. Brown DA, London E (1998) Structure and origin of ordered lipid domains in biological
membranes. J Membr Biol 164(2):103–114
Computational Studies of Biomembrane Systems: Theoretical Considerations. . .
277
154. Capovilla R, Guven J (2002) Stresses in lipid membranes. J Phys A Math Gen 35:6233–6247
155. Capovilla R, Guven J (2004) Stress and geometry of lipid vesicles. J Phys Condens Matter 16:
S2187–S2191
156. Farago O, Pincus P (2004) Statistical mechanics of bilayer membrane with a fixed projected
area. J Chem Phys 120:2934–2950
157. Guven J (2004) Membrane geometry with auxiliary variables and quadratic constraints.
J Phys A Math Gen 37:L313–L319
158. Mu ¨ller MM, Deserno M, Guven J (2005) Geometry of surface-mediated interactions.
Europhys Lett 69:482–488
159. Mu ¨ller MM, Deserno M, Guven J (2005) Interface-mediated interactions between particles: a
geometrical approach. Phys Rev E 72:061407
160. Mu ¨ller MM, Deserno M, Guven J (2007) Balancing torques in membrane-mediated interactions: exact results and numerical illustrations. Phys Rev E 76:011921. doi:10.1103/
PhysRevE.76.011921
161. Deserno M, Mu ¨ller MM, Guven J (2007) Contact lines for fluid surface adhesion. Phys Rev E
76:011605. doi:10.1103/PhysRevE.76.011605
162. Schmid F (2011) Are stress-free membranes really “tensionless”? Europhys Lett 95:28008
163. Deuling H, Helfrich W (1976) The curvature elasticity of fluid membranes: a catalogue of
vesicle shapes. J Phys (France) 37:1335–1345
164. David F, Leibler S (1991) Vanishing tension of fluctuating membranes. J Phys II (France)
1:959–976
165. Cai W, Lubensky TC, Nelson P, Powers T (1994) Measure factors, tension, and correlations
of fluid membranes. J Phys II (France) 4:931–949
166. Ja ¨hnig F (1996) What is the surface tension of a lipid bilayer membrane? Biophys J
71:1348–1349
167. Marsh D (1997) Renormalization of the tension and area expansion modulus in fluid
membranes. Biophys J 73:865–869
168. Farago O, Pincus P (2003) The effect of thermal fluctuations on Schulman area elasticity. Eur
Phys J E 11:399–408
169. Imparato A (2006) Surface tension in bilayer membranes with fixed projected area. J Chem
Phys 124:154714
170. Stecki J (2008) Balance of forces in simulated bilayers. J Phys Chem B 112(14):4246–4252
171. Fournier JB, Barbetta C (2008) Direct calculation from the stress tensor of the lateral surface
tension of fluctuating fluid membranes. Phys Rev Lett 100:078103
172. Fournier JB (2012) Comment on “are stress-free membranes really ‘tensionless’?” by Schmid
F. Europhys Lett 97:18001
173. Schmid F (2012) Reply to Comment on “are stress-free membranes really ‘tensionless’?”.
Europhys Lett 97:18002
174. Farago O (2011) Mechanical surface tension governs membrane thermal fluctuations. Phys
Rev E 84:051944
175. Marrink SJ, Mark AE (2001) Effect of undulations on surface tension in simulated bilayers.
J Phys Chem B 105:6122–6127
176. Loison C, Mareschal M, Kremer K, Schmid F (2003) Thermal fluctuations in a lamellar phase
of a binary amphiphile-solvent mixture: a molecular-dynamics study. J Chem Phys 119(13):
138–13148
177. Ahmed SN, Brown DA, London E (1997) On the origin of sphingolipid/cholesterol-rich
detergent-insoluble cell membranes: Physiological concentrations of cholesterol and
sphingolipid induce formation of a detergent-insoluble, liquid-ordered lipid phase in model
membranes. Biochemistry 36(36):10944–10953
178. Simons K, Ikonen E (1997) Functional rafts in cell membranes. Nature 387:569–572
179. Brown DA, London E (1998) Structure and origin of ordered lipid domains in biological
membranes. J Membr Biol 164(2):103–114
Computational Studies of Biomembrane Systems: Theoretical Considerations. . .
277