100. Pfeiffer W, Ko ¨nig S, Legrand JF, Bayerl T, Richter D, Sackmann E (1993) Neutron spin echo
study of membrane undulations in lipid multibilayers. Europhys Lett 23(6):457–462
101. Takeda T, Kawabata Y, Seto H, Komura S, Ghosh SK, Nagao M, Okuhara D (1999) Neutron
spin-echo investigations of membrane undulations in complex fluids involving amphiphiles.
J Phys Chem Solids 60(8–9):1375–1377
102. Rheinsta ¨dter MC, Ha ¨ußler W, Salditt T (2006) Dispersion relation of lipid membrane shape
fluctuations by neutron spin-echo spectrometry. Phys Rev Lett 97(4):048103
103. Watson MC, Brown FLH (2010) Interpreting membrane scattering experiments at the
mesoscale: the contribution of dissipation within the bilayer. Biophys J 98(6):L09–L11
104. Bo L, Waugh RE (1989) Determination of bilayer membrane bending stiffness by tether
formation from giant, thin-walled vesicles. Biophys J 55(3):509–517
105. Cuvelier D, Dere ´nyi I, Bassereau P, Nassoy P (2005) Coalescence of membrane tethers:
experiments, theory, and applications. Biophys J 88(4):2714–2726
106. Tian A, Baumgart T (2008) Sorting of lipids and proteins in membrane curvature gradients.
Biophys J 96(7):2676–2688
107. Ayton G, Voth GA (2002) Bridging microscopic and mesoscopic simulations of lipid
bilayers. Biophys J 83(6):3357–3370
108. Farago O (2003) “Water-free” computer model for fluid bilayer membranes. J Chem Phys
119(1):596–605
109. Wang ZJ, Frenkel D (2005) Modeling flexible amphiphilic bilayers: a solvent-free off-lattice
Monte Carlo study. J Chem Phys 122:234711
110. Wang ZJ, Deserno M (2010) A systematically coarse-grained solvent-free model for quantitative phospholipid bilayer simulation. J Phys Chem B 114(34):11207–11220
111. Shiba H, Noguchi H (2011) Estimation of the bending rigidity and spontaneous curvature of
fluid membranes in simulations. Phys Rev E 84:031926
112. Watson MC, Brandt EG, Welch PM, Brown FLH (2012) Determining biomembrane bending
rigidities from simulations of modest size. Phys Rev Lett 109:028102
113. Harmandaris VA, Deserno M (2006) A novel method for measuring the bending rigidity of
model lipid membranes by simulating tethers. J Chem Phys 125(20):204905
114. Arkhipov A, Yin Y, Schulten K (2008) Four-scale description of membrane sculpting by bar
domains. Biophys J 95(6):2806–2821
115. Noguchi H (2011) Anisotropic surface tension of buckled fluid membranes. Phys Rev E
83:061919
116. Hu M, Diggins IVP, Deserno M (2013) Determining the bending modulus of a lipid
membrane by simulating buckling. J Chem Phys 138:214110. doi:10.1063/1.4808077
117. Siegel DP, Kozlov MM (2004) The Gaussian curvature elastic modulus of n-monomethylated
dioleoylphosphatidylethanolamine: relevance to membrane fusion and lipid phase behavior.
Biophys J 87(1):366–374
118. Siegel DP (2006) Determining the ratio of the Gaussian curvature and bending elastic moduli
of phospholipids from Q II phase unit cell dimensions. Biophys J 91(2):608–618
119. Siegel DP (2008) The Gaussian curvature elastic energy of intermediates in membrane
fusion. Biophys J 95(11):5200–5215
120. Templer RH, Khoo BJ, Seddon JM (1998) Gaussian curvature modulus of an amphiphile
monolayer. Langmuir 14(26):7427–7434
121. Baumgart T, Das S, Webb WW, Jenkins JT (2005) Membrane elasticity in giant vesicles with
fluid phase coexistence. Biophys J 89(2):1067–1080
122. Semrau S, Idema T, Holtzer L, Schmidt T, Storm C (2008) Accurate determination of elastic
parameters for multicomponent membranes. Phys Rev Lett 100(8):088101
123. Hu M, de Jong DH, Marrink SJ, Deserno M (2013) Gaussian curvature elasticity determined
from global shape transformations and local stress distributions: a comparative study using
the MARTINI model. Farad Discuss 161:365–382
124. Taupin C, Dvolaitzky M, Sauterey C (1975) Osmotic-pressure induced pores in phospholipid
vesicles. Biochemistry 14(21):4771–4775
Computational Studies of Biomembrane Systems: Theoretical Considerations. . .
275
study of membrane undulations in lipid multibilayers. Europhys Lett 23(6):457–462
101. Takeda T, Kawabata Y, Seto H, Komura S, Ghosh SK, Nagao M, Okuhara D (1999) Neutron
spin-echo investigations of membrane undulations in complex fluids involving amphiphiles.
J Phys Chem Solids 60(8–9):1375–1377
102. Rheinsta ¨dter MC, Ha ¨ußler W, Salditt T (2006) Dispersion relation of lipid membrane shape
fluctuations by neutron spin-echo spectrometry. Phys Rev Lett 97(4):048103
103. Watson MC, Brown FLH (2010) Interpreting membrane scattering experiments at the
mesoscale: the contribution of dissipation within the bilayer. Biophys J 98(6):L09–L11
104. Bo L, Waugh RE (1989) Determination of bilayer membrane bending stiffness by tether
formation from giant, thin-walled vesicles. Biophys J 55(3):509–517
105. Cuvelier D, Dere ´nyi I, Bassereau P, Nassoy P (2005) Coalescence of membrane tethers:
experiments, theory, and applications. Biophys J 88(4):2714–2726
106. Tian A, Baumgart T (2008) Sorting of lipids and proteins in membrane curvature gradients.
Biophys J 96(7):2676–2688
107. Ayton G, Voth GA (2002) Bridging microscopic and mesoscopic simulations of lipid
bilayers. Biophys J 83(6):3357–3370
108. Farago O (2003) “Water-free” computer model for fluid bilayer membranes. J Chem Phys
119(1):596–605
109. Wang ZJ, Frenkel D (2005) Modeling flexible amphiphilic bilayers: a solvent-free off-lattice
Monte Carlo study. J Chem Phys 122:234711
110. Wang ZJ, Deserno M (2010) A systematically coarse-grained solvent-free model for quantitative phospholipid bilayer simulation. J Phys Chem B 114(34):11207–11220
111. Shiba H, Noguchi H (2011) Estimation of the bending rigidity and spontaneous curvature of
fluid membranes in simulations. Phys Rev E 84:031926
112. Watson MC, Brandt EG, Welch PM, Brown FLH (2012) Determining biomembrane bending
rigidities from simulations of modest size. Phys Rev Lett 109:028102
113. Harmandaris VA, Deserno M (2006) A novel method for measuring the bending rigidity of
model lipid membranes by simulating tethers. J Chem Phys 125(20):204905
114. Arkhipov A, Yin Y, Schulten K (2008) Four-scale description of membrane sculpting by bar
domains. Biophys J 95(6):2806–2821
115. Noguchi H (2011) Anisotropic surface tension of buckled fluid membranes. Phys Rev E
83:061919
116. Hu M, Diggins IVP, Deserno M (2013) Determining the bending modulus of a lipid
membrane by simulating buckling. J Chem Phys 138:214110. doi:10.1063/1.4808077
117. Siegel DP, Kozlov MM (2004) The Gaussian curvature elastic modulus of n-monomethylated
dioleoylphosphatidylethanolamine: relevance to membrane fusion and lipid phase behavior.
Biophys J 87(1):366–374
118. Siegel DP (2006) Determining the ratio of the Gaussian curvature and bending elastic moduli
of phospholipids from Q II phase unit cell dimensions. Biophys J 91(2):608–618
119. Siegel DP (2008) The Gaussian curvature elastic energy of intermediates in membrane
fusion. Biophys J 95(11):5200–5215
120. Templer RH, Khoo BJ, Seddon JM (1998) Gaussian curvature modulus of an amphiphile
monolayer. Langmuir 14(26):7427–7434
121. Baumgart T, Das S, Webb WW, Jenkins JT (2005) Membrane elasticity in giant vesicles with
fluid phase coexistence. Biophys J 89(2):1067–1080
122. Semrau S, Idema T, Holtzer L, Schmidt T, Storm C (2008) Accurate determination of elastic
parameters for multicomponent membranes. Phys Rev Lett 100(8):088101
123. Hu M, de Jong DH, Marrink SJ, Deserno M (2013) Gaussian curvature elasticity determined
from global shape transformations and local stress distributions: a comparative study using
the MARTINI model. Farad Discuss 161:365–382
124. Taupin C, Dvolaitzky M, Sauterey C (1975) Osmotic-pressure induced pores in phospholipid
vesicles. Biochemistry 14(21):4771–4775
Computational Studies of Biomembrane Systems: Theoretical Considerations. . .
275