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Computational Studies of Biomembrane Systems: Theoretical Considerations, Simulation Models, and Applications

  • Markus DesernoEmail author
  • Kurt Kremer
  • Harald Paulsen
  • Christine Peter
  • Friederike Schmid
Chapter
Part of the Advances in Polymer Science book series (POLYMER, volume 260)

Abstract

This chapter summarizes several approaches combining theory, simulation, and experiment that aim for a better understanding of phenomena in lipid bilayers and membrane protein systems, covering topics such as lipid rafts, membrane-mediated interactions, attraction between transmembrane proteins, and aggregation in biomembranes leading to large superstructures such as the light-harvesting complex of green plants. After a general overview of theoretical considerations and continuum theory of lipid membranes we introduce different options for simulations of biomembrane systems, addressing questions such as: What can be learned from generic models? When is it expedient to go beyond them? And, what are the merits and challenges for systematic coarse graining and quasi-atomistic coarse-grained models that ensure a certain chemical specificity?

Keywords

Coarse graining Curvature elasticity Lipid bilayer Mediated interactions Multiscaling Simulation 

Notes

Acknowledgements

We would like to thank the many coworkers and colleagues who have contributed to the research reported here, in particular Ira Cooke, Jemal Guven, Vagelis Harmandaris, Gregoria Illya, Martin Müller, Benedict Reynwar, Ira Rothstein, Cem Yolcu, Frank Brown, Olaf Lenz, Sebastian Meinhardt, Peter Nielaba, Beate West, Ananya Debnath, Christoph Globisch, Christoph Junghans, Shahoua Ding, Sabine Wiegand, Sandra Ritz, and Eva Sinner.

References

  1. 1.
    Smith R, Tanford C (1972) The critical micelle concentration of Lα-dipalmitoylphosphatidylcholine in water and water/methanol solutions. J Mol Biol 67(1):75–83Google Scholar
  2. 2.
    Israelachvili JN, Mitchell DJ, Ninham BW (1976) Theory of self-assembly of hydrocarbon amphiphiles into micelles and bilayers. J Chem Soc Faraday Trans 72(2):1525–1568Google Scholar
  3. 3.
    Rawicz W, Olbrich K, McIntosh T, Needham D, Evans E (2000) Effect of chain length and unsaturation on elasticity of lipid bilayers. Biophys J 79:328–339Google Scholar
  4. 4.
    Canham PB (1970) The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. J Theoret Biol 26(1):61–81Google Scholar
  5. 5.
    Helfrich W (1973) Elastic properties of lipid bilayers—theory and possible experiments. Z Naturforsch C 28(11):693–703Google Scholar
  6. 6.
    Evans EA (1974) Bending resistance and chemically induced moments in membrane bilayers. Biophys J 14(12):923–931Google Scholar
  7. 7.
    Helfrich W (1974) The size of bilayer vesicles generated by sonication. Phys Lett A 50(2):115–116Google Scholar
  8. 8.
    Kreyszig E (1991) Differential geometry. Dover, New YorkGoogle Scholar
  9. 9.
    do Carmo M (1976) Differential geometry of curves and surfaces. Prentice Hall, Englewood CliffsGoogle Scholar
  10. 10.
    Lipowsky R, Grotehans S (1993) Hydration versus protrusion forces between lipid bilayers. Europhys Lett 23:599–604Google Scholar
  11. 11.
    Lipowsky R, Grotehans S (1993) Renormalization of hydration forces by collective protrusion modes. Biophys Chem 49:27–37Google Scholar
  12. 12.
    Goetz R, Gompper G, Lipowsky R (1999) Mobility and elasticity of self-assembled membranes. Phys Rev Lett 82:221–224Google Scholar
  13. 13.
    Brandt EG, Edholm O (2010) Stretched exponential dynamics in lipid bilayer simulations. J Chem Phys 133:115101Google Scholar
  14. 14.
    Brandt EG, Braun AR, Sachs JN, Nagle JF, Edholm O (2011) Interpretation of fluctuation spectra in lipid bilayer simulations. Biophys J 100:2104–2111Google Scholar
  15. 15.
    Lindahl E, Edholm O (2000) Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations. Biophys J 79(1):426–433Google Scholar
  16. 16.
    Owicki JC, Springgate MW, McConnell HM (1978) Theoretical study of protein–lipid interactions in bilayer membranes. Proc Natl Acad Sci USA 75:1616–1619Google Scholar
  17. 17.
    Owicki JC, McConnell HM (1979) Theory of protein–lipid and protein–protein interactions in bilayer membranes. Proc Natl Acad Sci USA 76:4750–4754Google Scholar
  18. 18.
    Huang HW (1986) Deformation free energy of bilayer membrane and its effect on gramicidin channel lifetime. Biophys J 50:1061–1070Google Scholar
  19. 19.
    Sperotto MM, Mouritsen OG (1991) Monte Carlo simulation of lipid order parameter profiles near integral membrane proteins. Biophys J 59:261–270Google Scholar
  20. 20.
    Dan N, Pincus P, Safran SA (1993) Membrane-induced interactions between inclusions. Langmuir 9:2768–2771Google Scholar
  21. 21.
    Dan N, Berman A, Pincus P, Safran SA (1994) Membrane-induced interactions between inclusions. J Phys II (France) 4:1713Google Scholar
  22. 22.
    Aranda-Espinoza H, Berman A, Dan N, Pincus P, Safran S (1996) Interaction between inclusions embedded in membranes. Biophys J 71:648Google Scholar
  23. 23.
    Huang HW (1995) Elasticity of lipid bilayer interacting with amphiphilic helical peptides. J Phys II (France) 5:1427–1431Google Scholar
  24. 24.
    Nielsen C, Goulian M, Andersen OS (2000) Energetics of inclusion-induced bilayer deformations. Biophys J 74:1966–1983Google Scholar
  25. 25.
    Harroun TA, Heller WT, Weiss TM, Yang L, Huang HW (1999) Theoretical analysis of hydrophobic matching and membrane-mediated interactions in lipid bilayers containing gramicidin. Biophys J 76:3176–3185Google Scholar
  26. 26.
    Nielsen C, Andersen OS (2000) Inclusion-induced bilayer deformations: effects of monolayer equilibrium curvature. Biophys J 79:2583–2604Google Scholar
  27. 27.
    Jensen MO, Mouritsen OG (2004) Lipids do influence protein function – the hydrophobic matching hypothesis revisited. Biochim Biophys Acta 1666:205–226Google Scholar
  28. 28.
    Brannigan G, Brown F (2006) A consistent model for thermal fluctuations and protein-induced deformations in lipid bilayer. Biophys J 90:1501Google Scholar
  29. 29.
    Brannigan G, Brown FLH (2007) Contributions of Gaussian curvature and nonconstant lipid volume to protein deformation of lipid bilayers. Biophys J 92:864–876Google Scholar
  30. 30.
    West B, Brown FLH, Schmid F (2009) Membrane-protein interactions in a generic coarse-grained model for lipid bilayers. Biophys J 96:101–115Google Scholar
  31. 31.
    Fournier JB (1998) Coupling between membrane tilt-difference and dilation: a new “ripple” instability and multiple crystalline inclusions phases. Europhys Lett 43:725–730Google Scholar
  32. 32.
    Fournier JB (1999) Microscopic membrane elasticity and interactions among membrane inclusions: interplay between the shape, dilation, tilt and tilt-difference modes. Eur Phys J B 11:261–272Google Scholar
  33. 33.
    Bohinc K, Kralj-Iglic V, May S (2003) Interaction between two cylindrical inclusions in a symmetric lipid bilayer. J Chem Phys 119:7435–7444Google Scholar
  34. 34.
    May ER, Narang A, Kopelevich DI (2007) Role of molecular tilt in thermal fluctuations of lipid membranes. Phys Rev E 76:021913Google Scholar
  35. 35.
    Watson MC, Penev ES, Welch PM, Brown FLH (2011) Thermal fluctuations in shape, thickness, and molecular orientation in lipid bilayers. J Chem Phys 135:244701Google Scholar
  36. 36.
    Watson MC, Morriss-Andrews A, Welch PM, Brown FLH (2013) Thermal fluctuations in shape, thickness, and molecular orientation in lipid bilayers II: finite surface tensions. J Chem Phys 139:084706 doi: 10.1063/1.4818530Google Scholar
  37. 37.
    Neder J, West B, Nielaba P, Schmid F (2010) Coarse-grained simulations of membranes under tension. J Chem Phys 132:115101Google Scholar
  38. 38.
    Li J, Pastor KA, Shi AC, Schmid F, Zhou J (2013) Elastic properties and line tension of self-assembled bilayer membranes. Phys Rev E 88:012718 doi: 10.1103/PhysRevE.88.012718Google Scholar
  39. 39.
    Scott H (2002) Modeling the lipid component of membranes. Curr Opin Struct Biol 12(4):495–502Google Scholar
  40. 40.
    Saiz L, Bandyopadhyay S, Klein ML (2002) Towards an understanding of complex biological membranes from atomistic molecular dynamics simulations. Biosci Rep 22(2):151–173Google Scholar
  41. 41.
    Saiz L, Klein ML (2002) Computer simulation studies of model biological membranes. Acc Chem Res 35(6):482–489Google Scholar
  42. 42.
    Berkowitz ML (2009) Detailed molecular dynamics simulations of model biological membranes containing cholesterol. Biochim Biophys Acta Biomembr 1788(1):86–96Google Scholar
  43. 43.
    Niemelä PS, Hyvonen MT, Vattulainen I (2009) Atom-scale molecular interactions in lipid raft mixtures. Biochim Biophys Acta 1788(1):122–135Google Scholar
  44. 44.
    Gompper G, Kroll DM (1997) Network models of fluid, hexatic and polymerized membranes. J Phys Condens Matt 9(42):8795–8834Google Scholar
  45. 45.
    Gompper G, Kroll D (1998) Membranes with fluctuating topology: Monte Carlo simulations. Phys Rev Lett 81(11):2284–2287Google Scholar
  46. 46.
    Kumar PBS, Gompper G, Lipowsky R (2001) Budding dynamics of multicomponent membranes. Phys Rev Lett 86(17):3911–3914Google Scholar
  47. 47.
    Noguchi H, Gompper G (2004) Fluid vesicles with viscous membranes in shear flow. Phys Rev Lett 93(25):258102Google Scholar
  48. 48.
    Atzberger PJ, Kramer PR, Peskin CS (2007) A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales. J Comput Phys 224(2):1255–1292Google Scholar
  49. 49.
    Brown FLH (2008) Elastic Modeling of biomembranes and lipid bilayers. Ann Rev Phys Chem 59:685–712Google Scholar
  50. 50.
    Venturoli M, Sperotto MM, Kranenburg M, Smit B (2006) Mesoscopic models of biological membranes. Phys Rep 437(1–2):1–54Google Scholar
  51. 51.
    Müller M, Katsov K, Schick M (2006) Biological and synthetic membranes: what can be learned from a coarse-grained description? Phys Rep 434(5–6):113–176Google Scholar
  52. 52.
    Brannigan G, Lin L, Brown F (2006) Implicit solvent simulation models for biomembranes. Eur Biophys J 35(2):104–124Google Scholar
  53. 53.
    Marrink Siewert J, de Vries AH, Tieleman DP (2009) Lipids on the move: simulations of membrane pores, domains, stalks and curves. Biochim Biophys Acta Biomembr 1788(1):149–168Google Scholar
  54. 54.
    Bennun SV, Hoopes MI, Xing C, Faller R (2009) Coarse-grained modeling of lipids. Chem Phys Lipids 159(2):59–66Google Scholar
  55. 55.
    Deserno M (2009) Mesoscopic membrane physics: concepts, simulations, and selected applications. Macromol Rapid Comm 30(9–10):752–771Google Scholar
  56. 56.
    Noguchi H (2009) Membrane simulation models from nanometer to micrometer scale. J Phys Soc Jpn 78(4):041007Google Scholar
  57. 57.
    Schmid F (2009) Toy amphiphiles on the computer: What can we learn from generic models? Macromol Rapid Comm 30:741–751Google Scholar
  58. 58.
    Müller-Plathe F (2002) Coarse-graining in polymer simulation: from the atomistic to the mesoscopic scale and back. Chem Phys Chem 3(9):754–769Google Scholar
  59. 59.
    Izvekov S, Both GA (2005) Multiscale coarse graining of liquid-state systems. J Chem Phys 123(13):134105Google Scholar
  60. 60.
    Praprotnik M, Delle Site L, Kremer K (2005) Adaptive resolution molecular-dynamics simulation: changing the degrees of freedom on the fly. J Chem Phys 123(22):224106Google Scholar
  61. 61.
    Praprotnik M, Delle Site L, Kremer K (2007) A macromolecule in a solvent: adaptive resolution molecular dynamics simulation. J Chem Phys 126(13):134902Google Scholar
  62. 62.
    Praprotnik M, Site LD, Kremer K (2008) Multiscale simulation of soft matter: from scale bridging to adaptive resolution. Ann Rev Phys Chem 59(1):545–571Google Scholar
  63. 63.
    Delgado-Buscalioni R, Kremer K, Praprotnik M (2008) Concurrent triple-scale simulation of molecular liquids. J Chem Phys 128(11):114110Google Scholar
  64. 64.
    Noid WG, Chu JW, Ayton GS, Krishna V, Izvekov S, Voth GA, Das A, Andersen HC (2008) The multiscale coarse-graining method. I. A rigorous bridge between atomistic and coarse-grained models. J Chem Phys 128(24):244114Google Scholar
  65. 65.
    Noid WG, Liu P, Wang Y, Chu JW, Ayton GS, Izvekov S, Andersen HC, Voth GA (2008) The multiscale coarse-graining method. II. Numerical implementation for coarse-grained molecular models. J Chem Phys 128(24):244115Google Scholar
  66. 66.
    Das A, Andersen HC (2009) The multiscale coarse-graining method. III. A test of pairwise additivity of the coarse-grained potential and of new basis functions for the variational calculation. J Chem Phys 131(3):034102Google Scholar
  67. 67.
    Delgado-Buscalioni R, Kremer K, Praprotnik M (2009) Coupling atomistic and continuum hydrodynamics through a mesoscopic model: application to liquid water. J Chem Phys 131(24):244107Google Scholar
  68. 68.
    Peter C, Kremer K (2009) Multiscale simulation of soft matter systems – from the atomistic to the coarse-grained level and back. Soft Matter 5:4357–4366Google Scholar
  69. 69.
    Poblete S, Praprotnik M, Kremer K, Delle Site L (2010) Coupling different levels of resolution in molecular simulations. J Chem Phys 132(11):114101Google Scholar
  70. 70.
    Voth GA (ed) (2008) Coarse-graining of condensed phase and biomolecular systems, 1st edn. CRC, Boca RatonGoogle Scholar
  71. 71.
    Rühle V, Junghans C, Lukyanov A, Kremer K, Andrienko D (2009) Versatile object-oriented toolkit for coarse-graining applications. J Chem Theory Comput 5(12):3211–3223Google Scholar
  72. 72.
    Lu L, Voth GA (2012) The multiscale coarse-graining method. In: Rice SA, Dinner AR (eds) Advances in chemical physics, vol 149. Wiley, Hoboken, pp 47–81 doi: 10.1002/9781118180396.ch2Google Scholar
  73. 73.
    Cooke IR, Kremer K, Deserno M (2005) Tunable generic model for fluid bilayer membranes. Phys Rev E 72(1):011506Google Scholar
  74. 74.
    Cooke IR, Deserno M (2005) Solvent-free model for self-assembling fluid bilayer membranes: stabilization of the fluid phase based on broad attractive tail potentials. J Chem Phys 123(22):224710Google Scholar
  75. 75.
    Cooke IR, Deserno M (2006) Coupling between lipid shape and membrane curvature. Biophys J 91(2):487–495Google Scholar
  76. 76.
    Hu M, Briguglio JJ, Deserno M (2012) Determining the Gaussian curvature modulus of lipid membranes in simulations. Biophys J 102(6):1403–1410Google Scholar
  77. 77.
    Schmid F, Düchs D, Lenz O, West B (2007) A generic model for lipid monolayers, bilayers, and membranes. Comp Phys Comm 177(1–2):168Google Scholar
  78. 78.
    Düchs D, Schmid F (2001) Phase behavior of amphiphilic monolayers: theory and simulations. J Phys Cond Matt 13:4853Google Scholar
  79. 79.
    Lenz O, Schmid F (2005) A simple computer model for liquid lipid bilayers. J Mol Liquid 117(1–3):147–152Google Scholar
  80. 80.
    Lenz O, Schmid F (2007) Structure of symmetric and asymmetric ripple phases in lipid bilayers. Phys Rev Lett 98:058104Google Scholar
  81. 81.
    Meinhardt S, Vink R, Schmid F (2013) Monolayer curvature stabilizes nanoscale raft domains in mixed lipid bilayers. Proc Natl Acad Sci USA 12:4476–4481Google Scholar
  82. 82.
    Pike L (2006) Rafts defined: a report on the keystone symposium on lipid rafts and cell function. J Lipid Res 47:1597–1598Google Scholar
  83. 83.
    Marrink SJ, de Vries AH, Mark AE (2004) Coarse grained model for semiquantitative lipid simulations. J Phys Chem B 108(2):750–760Google Scholar
  84. 84.
    Marrink SJ, Risselada HJ, Yefimov S, Tieleman DP, de Vries AH (2007) The MARTINI force field: coarse grained model for biomolecular simulations. J Phys Chem B 111:7812–7824Google Scholar
  85. 85.
    Monticelli L, Kandasamy SK, Periole X, Larson RG, Tieleman DP, Marrink SJ (2008) The MARTINI coarse-grained force field: extension to proteins. J Chem Theory Comput 4(5):819–834Google Scholar
  86. 86.
    López CA, Rzepiela AJ, de Vries AH, Dijkhuizen L, Huenenberger PH, Marrink SJ (2009) Martini coarse-grained force field: extension to carbohydrates. J Chem Theory Comput 5(12):3195–3210Google Scholar
  87. 87.
    López EA, Sovova Z, van Eerden FJ, de Vries AH, Marrink SJ (2013) MARTINI force field parameters for glycolipids. J Chem Theory Comput 9(3):1694–1708Google Scholar
  88. 88.
    Lee S (1962) Spiderman, Amazing fantasy # 15. Marvel Comics, New YorkGoogle Scholar
  89. 89.
    Brochard F, Lennon JF (1975) Frequency spectrum of flicker phenomenon in erythrocytes. J Phys (France) 36(11):1035–1047Google Scholar
  90. 90.
    Brochard F, De Gennes PG, Pfeuty P (1976) Surface tension and deformations of membrane structures: relation to two-dimensional phase transitions. J Phys (France) 37:1099Google Scholar
  91. 91.
    Schneider MB, Jenkins JT, Webb WW (1984) Thermal fluctuations of large cylindrical phospholipid-vesicles. Biophys J 45(5):891–899Google Scholar
  92. 92.
    Schneider MB, Jenkins JT, Webb WW (1984) Thermal fluctuations of large quasi-spherical bimolecular phospholipid-vesicles. Biophys J 45(9):1457–1472Google Scholar
  93. 93.
    Faucon JF, Mitov MD, Méléard P, Bivas I, Bothorel P (1989) Bending elasticity and thermal fluctuations of lipid-membranes—theoretical and experimental requirements. J Phys (France) 50(17):2389–2414Google Scholar
  94. 94.
    Henriksen J, Rowat AC, Ipsen JH (2004) Vesicle fluctuation analysis of the effects of sterols on membrane bending rigidity. Eur Biophys J 33(8):732–741Google Scholar
  95. 95.
    Evans E, Rawicz W (1990) Entropy-driven tension and bending elasticity in condensed-fluid membranes. Phys Rev Lett 64(17):2094–2097Google Scholar
  96. 96.
    Liu YF, Nagle JF (2004) Diffuse scattering provides material parameters and electron density profiles of biomembranes. Phys Rev E 69(4):040901Google Scholar
  97. 97.
    Chu N, Kučerka N, Liu YF, Tristram-Nagle S, Nagle JF (2005) Anomalous swelling of lipid bilayer stacks is caused by softening of the bending modulus. Phys Rev E 71(4):041904Google Scholar
  98. 98.
    Tristram-Nagle S, Nagle JF (2007) HIV-1 fusion peptide decreases bending energy and promotes curved fusion intermediates. Biophys J 93(6):2048–2055Google Scholar
  99. 99.
    Pan J, Tristram-Nagle S, Kučerka N, Nagle JF (2008) Temperature dependence of structure, bending rigidity, and bilayer interactions of dioleoylphosphatidylcholine bilayers. Biophys J 94(1):117–124Google Scholar
  100. 100.
    Pfeiffer W, König S, Legrand JF, Bayerl T, Richter D, Sackmann E (1993) Neutron spin echo study of membrane undulations in lipid multibilayers. Europhys Lett 23(6):457–462Google Scholar
  101. 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):1375–1377Google Scholar
  102. 102.
    Rheinstädter MC, Häußler W, Salditt T (2006) Dispersion relation of lipid membrane shape fluctuations by neutron spin-echo spectrometry. Phys Rev Lett 97(4):048103Google Scholar
  103. 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–L11Google Scholar
  104. 104.
    Bo L, Waugh RE (1989) Determination of bilayer membrane bending stiffness by tether formation from giant, thin-walled vesicles. Biophys J 55(3):509–517Google Scholar
  105. 105.
    Cuvelier D, Derényi I, Bassereau P, Nassoy P (2005) Coalescence of membrane tethers: experiments, theory, and applications. Biophys J 88(4):2714–2726Google Scholar
  106. 106.
    Tian A, Baumgart T (2008) Sorting of lipids and proteins in membrane curvature gradients. Biophys J 96(7):2676–2688Google Scholar
  107. 107.
    Ayton G, Voth GA (2002) Bridging microscopic and mesoscopic simulations of lipid bilayers. Biophys J 83(6):3357–3370Google Scholar
  108. 108.
    Farago O (2003) “Water-free” computer model for fluid bilayer membranes. J Chem Phys 119(1):596–605Google Scholar
  109. 109.
    Wang ZJ, Frenkel D (2005) Modeling flexible amphiphilic bilayers: a solvent-free off-lattice Monte Carlo study. J Chem Phys 122:234711Google Scholar
  110. 110.
    Wang ZJ, Deserno M (2010) A systematically coarse-grained solvent-free model for quantitative phospholipid bilayer simulation. J Phys Chem B 114(34):11207–11220Google Scholar
  111. 111.
    Shiba H, Noguchi H (2011) Estimation of the bending rigidity and spontaneous curvature of fluid membranes in simulations. Phys Rev E 84:031926Google Scholar
  112. 112.
    Watson MC, Brandt EG, Welch PM, Brown FLH (2012) Determining biomembrane bending rigidities from simulations of modest size. Phys Rev Lett 109:028102Google Scholar
  113. 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):204905Google Scholar
  114. 114.
    Arkhipov A, Yin Y, Schulten K (2008) Four-scale description of membrane sculpting by bar domains. Biophys J 95(6):2806–2821Google Scholar
  115. 115.
    Noguchi H (2011) Anisotropic surface tension of buckled fluid membranes. Phys Rev E 83:061919Google Scholar
  116. 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 Google Scholar
  117. 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):366–374Google Scholar
  118. 118.
    Siegel DP (2006) Determining the ratio of the Gaussian curvature and bending elastic moduli of phospholipids from QII phase unit cell dimensions. Biophys J 91(2):608–618Google Scholar
  119. 119.
    Siegel DP (2008) The Gaussian curvature elastic energy of intermediates in membrane fusion. Biophys J 95(11):5200–5215Google Scholar
  120. 120.
    Templer RH, Khoo BJ, Seddon JM (1998) Gaussian curvature modulus of an amphiphile monolayer. Langmuir 14(26):7427–7434Google Scholar
  121. 121.
    Baumgart T, Das S, Webb WW, Jenkins JT (2005) Membrane elasticity in giant vesicles with fluid phase coexistence. Biophys J 89(2):1067–1080Google Scholar
  122. 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):088101Google Scholar
  123. 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 161:365–382Google Scholar
  124. 124.
    Taupin C, Dvolaitzky M, Sauterey C (1975) Osmotic-pressure induced pores in phospholipid vesicles. Biochemistry 14(21):4771–4775Google Scholar
  125. 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):89–104Google Scholar
  126. 126.
    Genco I, Gliozzi A, Relini A, Robello M, Scalas E (1993) Osmotic-pressure induced pores in phospholipid vesicles. Biochim Biophys Acta 1149(1):10–18Google Scholar
  127. 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):1734–1749Google Scholar
  128. 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):8014–8020Google Scholar
  129. 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):154905Google Scholar
  130. 130.
    Jiang FY, Bouret Y, Kindt JT (2004) Molecular dynamics simulations of the lipid bilayer edge. Biophys J 87(1):182–192Google Scholar
  131. 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 12:095004Google Scholar
  132. 132.
    Wang H, Hu D, Zhang P (2013) Measuring the spontaneous curvature of bilayer membranes by molecular dynamics simulations. Commun Comput Phys 13:1093–1106Google Scholar
  133. 133.
    Helfrich W (1985) Effect of thermal undulations on the rigidity of fluid membranes and interfaces. J Phys France 46(7):1263–1268Google Scholar
  134. 134.
    Peliti L, Leibler S (1985) Effects of thermal fluctuations on systems with small surface tension. Phys Rev Lett 54:1690–1693Google Scholar
  135. 135.
    Förster D (1986) On the scale dependence, due to thermal fluctuations, of the elastic properties of membranes. Phys Lett A 114(3):115–120Google Scholar
  136. 136.
    Kleinert H (1986) Thermal softening of curvature elasticity in membranes. Phys Lett A 114(5):263–268Google Scholar
  137. 137.
    Schmid F (2013) Fluctuations in lipid bilayers: are they understood? Biophys Rev Lett 8:1–20 doi:10.1142/S1793048012300113Google Scholar
  138. 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 Google Scholar
  139. 139.
    Le Doussal P, Radzihovsky L (1992) Self-consistent theory of polymerized membranes. Phys Rev Lett 69(8):1209–1211Google Scholar
  140. 140.
    Park JM, Lubensky TC (1995) Topological defects on fluctuating surfaces: general properties and the Kosterlitz–Thouless transition. Phys Rev E 53(3):2648–2664Google Scholar
  141. 141.
    Park JM (1996) Renormalization of fluctuating tilted hexatic membranes. Phys Rev E 56(7):R47–R50Google Scholar
  142. 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 6:1275–1280Google Scholar
  143. 143.
    Kramer L (1971) Theory of light scattering from fluctuations of membranes and monolayers. J Chem Phys 55:2097–2105Google Scholar
  144. 144.
    Seifert U, Langer SA (1993) Viscous modes of fluid bilayer membranes. Europhys Lett 23(1):71–76Google Scholar
  145. 145.
    Zilman AG, Granek R (1996) Undulations and dynamic structure factor of membranes. Phys Rev Lett 77:4788–4791Google Scholar
  146. 146.
    Fromherz P (1983) Lipid-vesicle structure: size control by edge-active agents. Chem Phys Lett 94:259–266Google Scholar
  147. 147.
    van Kampen NG (2007) Stochastic processes in physics and chemistry, 3rd edn. Elsevier, AmsterdamGoogle Scholar
  148. 148.
    Helfrich W (1981) Physics of defects. North Holland, AmsterdamGoogle Scholar
  149. 149.
    Helfrich W (1994) Lyotropic lamellar phases. J Phys Condens Matter 6:A79–A92Google Scholar
  150. 150.
    Szleifer I, Kramer D, Ben-Shaul A, Gelbart WM, Safran SA (1990) Molecular theory of curvature elasticity in surfactant films. J Chem Phys 92:6800–6817Google Scholar
  151. 151.
    Rowlinson JS, Widom B (2002) Molecular theory of capillarity, 1st edn. Dover, New YorkGoogle Scholar
  152. 152.
    Gompper G, Klein S (1992) Ginzburg-Landau theory of aqueous surfactant solutions. J Phys II (France) 2:1725–1744Google Scholar
  153. 153.
    Diamant H (2011) Model-free thermodynamics of fluid vesicles. Phys Rev E 84(6):0611203Google Scholar
  154. 154.
    Capovilla R, Guven J (2002) Stresses in lipid membranes. J Phys A Math Gen 35:6233–6247Google Scholar
  155. 155.
    Capovilla R, Guven J (2004) Stress and geometry of lipid vesicles. J Phys Condens Matter 16:S2187–S2191Google Scholar
  156. 156.
    Farago O, Pincus P (2004) Statistical mechanics of bilayer membrane with a fixed projected area. J Chem Phys 120:2934–2950Google Scholar
  157. 157.
    Guven J (2004) Membrane geometry with auxiliary variables and quadratic constraints. J Phys A Math Gen 37:L313–L319Google Scholar
  158. 158.
    Müller MM, Deserno M, Guven J (2005) Geometry of surface-mediated interactions. Europhys Lett 69:482–488Google Scholar
  159. 159.
    Müller MM, Deserno M, Guven J (2005) Interface-mediated interactions between particles: a geometrical approach. Phys Rev E 72:061407Google Scholar
  160. 160.
    Müller 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 Google Scholar
  161. 161.
    Deserno M, Müller MM, Guven J (2007) Contact lines for fluid surface adhesion. Phys Rev E 76:011605. doi: 10.1103/PhysRevE.76.011605 Google Scholar
  162. 162.
    Schmid F (2011) Are stress-free membranes really “tensionless”? Europhys Lett 95:28008Google Scholar
  163. 163.
    Deuling H, Helfrich W (1976) The curvature elasticity of fluid membranes: a catalogue of vesicle shapes. J Phys (France) 37:1335–1345Google Scholar
  164. 164.
    David F, Leibler S (1991) Vanishing tension of fluctuating membranes. J Phys II (France) 1:959–976Google Scholar
  165. 165.
    Cai W, Lubensky TC, Nelson P, Powers T (1994) Measure factors, tension, and correlations of fluid membranes. J Phys II (France) 4:931–949Google Scholar
  166. 166.
    Jähnig F (1996) What is the surface tension of a lipid bilayer membrane? Biophys J 71:1348–1349Google Scholar
  167. 167.
    Marsh D (1997) Renormalization of the tension and area expansion modulus in fluid membranes. Biophys J 73:865–869Google Scholar
  168. 168.
    Farago O, Pincus P (2003) The effect of thermal fluctuations on Schulman area elasticity. Eur Phys J E 11:399–408Google Scholar
  169. 169.
    Imparato A (2006) Surface tension in bilayer membranes with fixed projected area. J Chem Phys 124:154714Google Scholar
  170. 170.
    Stecki J (2008) Balance of forces in simulated bilayers. J Phys Chem B 112(14):4246–4252Google Scholar
  171. 171.
    Fournier JB, Barbetta C (2008) Direct calculation from the stress tensor of the lateral surface tension of fluctuating fluid membranes. Phys Rev Lett 100:078103Google Scholar
  172. 172.
    Fournier JB (2012) Comment on “are stress-free membranes really ‘tensionless’?” by Schmid F. Europhys Lett 97:18001Google Scholar
  173. 173.
    Schmid F (2012) Reply to Comment on “are stress-free membranes really ‘tensionless’?”. Europhys Lett 97:18002Google Scholar
  174. 174.
    Farago O (2011) Mechanical surface tension governs membrane thermal fluctuations. Phys Rev E 84:051944Google Scholar
  175. 175.
    Marrink SJ, Mark AE (2001) Effect of undulations on surface tension in simulated bilayers. J Phys Chem B 105:6122–6127Google Scholar
  176. 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):138–13148Google Scholar
  177. 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):10944–10953Google Scholar
  178. 178.
    Simons K, Ikonen E (1997) Functional rafts in cell membranes. Nature 387:569–572Google Scholar
  179. 179.
    Brown DA, London E (1998) Structure and origin of ordered lipid domains in biological membranes. J Membr Biol 164(2):103–114Google Scholar
  180. 180.
    Brown DA, London E (1998) Functions of lipid rafts in biological membranes. Ann Rev Cell Develop Biol 14:111–136Google Scholar
  181. 181.
    Brown DA, London E (2000) Structure and function of sphingolipid- and cholesterol-rich membrane rafts. J Biol Chem 275(23):17221–17224Google Scholar
  182. 182.
    Singer SJ, Nicolson GK (1972) Fluid mosaic model of structure of cell-membranes. Science 175(4023):720–731Google Scholar
  183. 183.
    Munro S (2003) Lipid rafts: elusive or illusive? Cell 115(4):377–388Google Scholar
  184. 184.
    Hancock JF (2006) Lipid rafts: contentious only from simplistic standpoints. Nat Rev Mol Cell Biol 7:456–462Google Scholar
  185. 185.
    Leslie M (2011) Do lipid rafts exist? Science 334:1046–1047Google Scholar
  186. 186.
    Vereb G, Szöllosi J, Matko J, Nagy P, Farkas T, Vigh L, Matyus L, Waldmann TA, Damjanovich S (2003) Dynamic, yet structured: the cell membranes three decades after the Singer-Nicolson model. Proc Natl Acad Sci USA 100:8053–8058Google Scholar
  187. 187.
    Veatch SL, Keller SL (2003) Separation of liquid phases in giant vesicles of ternary mixtures of phospholipids and cholesterol. Biophys J 85(5):3074–3083Google Scholar
  188. 188.
    Veatch SL, Keller SL (2005) Seeing spots: complex phase behavior in simple membranes. Biochim Biophys Acta 1746:172–185Google Scholar
  189. 189.
    Pralle A, Keller P, Florin EL, Simons K, Hörber JKH (2000) Sphingolipid-cholesterol rafts diffuse as small entities in the plasma membrane of mammalian cells. J Cell Biol 148:997–1007Google Scholar
  190. 190.
    Turner MS, Sens P, Socci ND (2005) Nonequilibrium raft-like membrane domains under continuous recycling. Phys Rev Lett 95:168301Google Scholar
  191. 191.
    Yethiraj A, Weisshaar JC (2007) Why are lipid rafts not observed in vivo? Biophys J 93:3113–3119Google Scholar
  192. 192.
    Simons K, Vaz WLC (2004) Model systems, lipid rafts, and cell membranes. Annu Rev Biophys Biomol Struct 33:269–295Google Scholar
  193. 193.
    Brewster R, Pincus PA, Safran SA (2009) Hybrid lipids as a biological surface-active component. Biophys J 97:1087–1094Google Scholar
  194. 194.
    Yamamoto T, Brewster R, Safran SA (2010) Chain ordering of hybrid lipids can stabilize domains in saturated/hybrid/cholesterol lipid membranes. Europhys Lett 91:28002Google Scholar
  195. 195.
    Veatch SL, Soubias O, Keller SL, Gawrisch K (2007) Critical fluctuations in domain-forming lipid mixtures. Proc Natl Acad Sci USA 104(17):650–655Google Scholar
  196. 196.
    Honerkamp-Smith AR, Veatch SL, Keller SL (2009) An introduction to critical points for biophysicists: observations of compositional heterogeneity in lipid membranes. Biochim Biophys Acta 1788:53–63Google Scholar
  197. 197.
    Ipsen JH, Karlström G, Mouritsen OB, Wennerström H, Zuckermann MJ (1987) Phase equilibria in the phosphatidylcholine-cholesterol system. Biochim Biophys Acta 905:162–172Google Scholar
  198. 198.
    Sankaram MB, Thompson TE (1991) Cholesterol-induced fluid-phase immiscibility in membranes. Proc Natl Acad Sci USA 88:8686–8690Google Scholar
  199. 199.
    Katsaras J, Tristram-Nagle S, Liu Y, Headrick RL, Fontes E, Mason PC, Nagle JF (2000) Clarification of the ripple phase of lecithin bilayers using fully hydrated, aligned samples. Phys Rev E 61:5668Google Scholar
  200. 200.
    Sengupta K, Raghunathan VA, Katsaras J (2003) Structure of the ripple phase of phospholipid multibilayers. Phys Rev E 68(3):031710Google Scholar
  201. 201.
    Koynova R, Caffrey M (1994) Phases and phase transitions of the hydrated phosphatidylethanolamines. Chem Phys Lipids 69:1–34Google Scholar
  202. 202.
    Koynova R, Caffrey M (1998) Phases and phase transitions of the phosphatidylcholines. Biochimica Biophysica Acta Rev Biomembr 1376:91–145Google Scholar
  203. 203.
    Kranenburg M, Smit B (2005) Phase behavior of model lipid bilayers. J Phys Chem B 109:6553–6563Google Scholar
  204. 204.
    de Vries AH, Yefimov S, Mark AE, Marrink SJ (2005) Molecular structure of the lecithin ripple phase. Proc Natl Acad Sci USA 102:5392–5396Google Scholar
  205. 205.
    Sun X, Gezelter JD (2008) Dipolar ordering in the ripple phases of molecular-scale models of lipid membranes. J Phys Chem B 112:1968–1975Google Scholar
  206. 206.
    Jamroz D, Kepczynski M, Nowakowska M (2010) Molecular structure of the dioctadecyldimethylammonium bromide (DODAB) bilayer. Langmuir 26(15):076–15079Google Scholar
  207. 207.
    Chen R, Poger D, Mark AE (2011) Effect of high pressure on fully hydrated DPPC and POPC bilayers. J Phys Chem B 115:1038–1044Google Scholar
  208. 208.
    Dolezel S (2010) Computer simulation of lipid bilayers. Diploma thesis, University of MainzGoogle Scholar
  209. 209.
    Brazovskii SA (1975) Phase transitions of an isotropic system to a nonuniform state. Soviet Phys JETP 41:85–89Google Scholar
  210. 210.
    Marsh D (2008) Protein modulation of lipids, and vice-versa, in membranes. Biochim Biophys Acta 1778:1545–1575Google Scholar
  211. 211.
    Benjamini A, Smit B (2012) Robust driving forces for transmembrane helix packing. Biophys J 103:1227–1235Google Scholar
  212. 212.
    Cantor RS (1997) Lateral pressures in cell membranes: a mechanism for modulation of protein function. J Phys Chem B 101:1723–1725Google Scholar
  213. 213.
    Elliott J, Needham D, Dilger J, Haydon D (1983) The effects of bilayer thickness and tension on gramicidin single-channel lifetimes. Biochim Biophys Acta 735:95–103Google Scholar
  214. 214.
    Botelho AV, Huber T, Sakmar TP, Brown MF (2006) Curvature and hydrophobic forces drive oligomerization and modulate activity of rhodopsin in membranes. Biophys J 91:4464–4477Google Scholar
  215. 215.
    Antonny B (2006) Membrane deformation by protein coats. Curr Opin Cell Biol 18(4):386–394Google Scholar
  216. 216.
    Lee AG (2005) How lipids and proteins interact in a membrane: a molecular approach. Mol Biosyst 3:203–212Google Scholar
  217. 217.
    Gil T, Sabra MC, Ipsen JH, Mouritsen OG (1997) Wetting and capillary condensation as means of protein organization in membranes. Biophys J 73(4):1728–1741Google Scholar
  218. 218.
    Gil T, Ipsen JH, Mouritsen OG, Sabra MC, Sperotto MM, Zuckermann MJ (1998) Theoretical analysis of protein organization in lipid membranes. Biochim Biophys Acta 1376(3):245–266Google Scholar
  219. 219.
    Reynwar BJ, Deserno M (2008) Membrane composition-mediated protein–protein interactions. Biointerphases 3:FA117–FA125Google Scholar
  220. 220.
    Machta BB, Veatch SL, Sethna JP (2012) Critical Casimir forces in cellular membranes. Phys Rev Lett 109:138101Google Scholar
  221. 221.
    May S, Ben-Shaul A (1999) Molecular theory of lipid-protein interaction and the Lalpha-HII transition. Biophys J 76(2):751–767Google Scholar
  222. 222.
    May S (2000) Protein-induced bilayer deformations: the lipid tilt degree of freedom. Eur Biophys J 29(1):17–28Google Scholar
  223. 223.
    Kozlovsky Y, Zimmerberg J, Kozlov MM (2004) Orientation and interaction of oblique cylindrical inclusions embedded in a lipid monolayer: a theoretical model for viral fusion peptides. Biophys J 87(2):999–1012Google Scholar
  224. 224.
    Deserno M (2009) Membrane elasticity and mediated interactions in continuum theory: a differential geometric approach. In: Faller R, Jue T, Longo ML, Risbud SH (eds) Biomembrane frontiers: nanostructures, models, and the design of life, vol 2. Springer, New York, pp 41–74Google Scholar
  225. 225.
    May S (2000) Theories on structural perturbations of lipid bilayers. Curr Opin Colloid Interface Sci 5:244–249Google Scholar
  226. 226.
    Bloom M, Evans E, Mouritsen OG (1991) Physical properties of the fluid lipid-bilayer component of cell membranes: a perspective. Quart Rev Biophys 24(3):293–297Google Scholar
  227. 227.
    Killian JA (1998) Hydrophobic mismatch between proteins and lipids in membranes. Biochim Biophys Acta 1376:401–416Google Scholar
  228. 228.
    Dumas F, Lebrun MC, Tocanne JF (1999) Is the protein/lipid hydrophobic matching principle relevant to membrane organization and functions? FEBS Lett 458:271–277Google Scholar
  229. 229.
    Harroun TA, Heller WT, Weiss TM, Yang L, Huang HW (1999) Experimental evidence for hydrophobic matching and membrane-mediated interactions in lipid bilayers containing gramicidin. Biophys J 76:937–945Google Scholar
  230. 230.
    De Planque MRR, Killian JA (2003) Protein-lipid interactions studied with designed transmembrane peptides: role of hydrophobic matching and interfacial anchoring (review). Mol Membr Biol 20:271–284Google Scholar
  231. 231.
    Marsh D (2008) Energetics of hydrophobic matching in lipid–protein interactions. Biophys J 94:3996–4013Google Scholar
  232. 232.
    Cybulski LE, de Mendoza D (2011) Bilayer hydrophobic thickness and integral membrane protein function. Curr Protein Pept Sci 12:760–766Google Scholar
  233. 233.
    Strandberg E, Esteban-Martin S, Ulrich AS, Salgado J (2012) Hydrophobic mismatch of mobile transmembrane helices: merging theory and experiments. Biochim Biophys Acta 1818:1242–1249Google Scholar
  234. 234.
    Venturoli M, Smit B, Sperotto MM (2005) Simulation studies of protein-induced bilayer deformations, and lipid-induced protein tilting, on a mesoscopic model for lipid bilayers with embedded proteins. Biophys J 88:1778Google Scholar
  235. 235.
    Park SH, Opella SJ (2005) Tilt angle of a trans-membrane helix is determined by hydrophobic mismatch. J Mol Biol 350:310–318Google Scholar
  236. 236.
    Holt A, Killian JA (2010) Orientation and dynamics of transmembrane peptides: the power of simple models. Eur Biophys J 39:609–621Google Scholar
  237. 237.
    Strandberg E, Tremouilhac P, Wadhwani P, Ulrich AS (2009) Synergistic transmembrane insertion of the heterodimeric PGLA/magainin 2 complex studied by solid-state NMR. Biochim Biophys Acta 1788:1667–1679Google Scholar
  238. 238.
    Schmidt U, Weiss M (2010) Hydrophobic mismatch-induced clustering as a primer for protein sorting in the secretory pathway. Biophys Chem 151:34–38Google Scholar
  239. 239.
    Harzer U, Bechinger B (2000) Alignment of lysine-anchored membrane peptides under conditions of hydrophobic mismatch: A CD, 15N and 31P solid-state NMR spectroscopy investigation. Biochemistry 39(13):106–13114Google Scholar
  240. 240.
    Özdirekcan S, Rijkers DTS, Liskamp RMJ, Killian JA (2005) Influence of flanking residues on tilt and rotation angles of transmembrane peptides in lipid bilayers. a solid-state 2H NMR study. Biochemistry 44:1004–1012Google Scholar
  241. 241.
    Vostrikov VV, Grant CV, Daily AE, Opella SJ, Koeppe RE II (2008) Comparison of “polarization inversion with spin exchange at magic angle” and “geometric analysis of labeled alanines” methods for transmembrane helix alignment. J Am Chem Soc 130(12):584–12585Google Scholar
  242. 242.
    Chiang C, Shirinian L, Sukharev S (2005) Capping transmembrane helices of MscL with aromatic residues changes channel response to membrane stretch. Biochemistry 44(12):589–12597Google Scholar
  243. 243.
    Vostrikov VV, Koeppe RE II (2011) Response of GWALP transmembrane peptides to changes in the tryptophan anchor positions. Biochemistry 50:7522–7535Google Scholar
  244. 244.
    Neder J, Nielaba P, West B, Schmid F (2012) Interactions of membranes with coarse-grain proteins: a comparison. New J Phys 14:125017Google Scholar
  245. 245.
    Mouritsen OG, Bloom M (1984) Mattress model of lipid-protein interactions in membranes. Biophys J 36:141–153Google Scholar
  246. 246.
    Fattal DR, Ben-Shaul A (1993) A molecular model for lipid-protein interaction in membranes: the role of hydrophobic mismatch. Biophys J 65:1795–1809Google Scholar
  247. 247.
    Fattal DR, Ben-Shaul A (1995) Lipid chain packing and lipid–protein interaction in membranes. Phys A 220:192–216Google Scholar
  248. 248.
    Cordomi A, Perez JJ (2007) Molecular dynamics simulations of rhodopsin in different one-component lipid bilayers. J Phys Chem B 111:7052–7063Google Scholar
  249. 249.
    Neder J, West B, Nielaba P, Schmid F (2010) Membrane-mediated protein–protein interaction: a Monte Carlo study. Curr Nanosci 7:656–666Google Scholar
  250. 250.
    Schmidt U, Guigas G, Weiss M (2008) Cluster formation of transmembrane proteins due to hydrophobic mismatching. Phys Rev Lett 101:128104Google Scholar
  251. 251.
    de Meyer FJM, Venturoli M, Smit B (2008) Molecular simulations of lipid-mediated protein–protein interactions. Biophys J 95:1851–1865Google Scholar
  252. 252.
    Koltover I, Rädler JO, Safinya CR (1999) Membrane mediated attraction and ordered aggregation of colloidal particles bound to giant phospholipid vesicles. Phys Rev Lett 82:1991–1994Google Scholar
  253. 253.
    Goulian M, Bruinsma R, Pincus P (1993) Long-range forces in heterogeneous fluid membranes. Europhys Lett 22:145Google Scholar
  254. 254.
    Goulian M, Bruinsma R, Pincus P (1993) Long-range forces in heterogeneous fluid membranes: erratum. Europhys Lett 23:155Google Scholar
  255. 255.
    Fournier JB, Dommersnes PG (1997) Comment on “long-range forces in heterogeneous fluid membranes”. Europhys Lett 39(6):681Google Scholar
  256. 256.
    Dommersnes P, Fournier JB (1999) N-body study of anisotropic membrane inclusions: membrane mediated interactions and ordered aggregation. Eur Phys J E 12:9–12Google Scholar
  257. 257.
    Dommersnes P, Fournier J (2002) The many-body problem for anisotropic membrane inclusions and the self-assembly of “saddle” defects into an “egg carton”. Biophys J 83:2898–2905Google Scholar
  258. 258.
    Fournier JB, Dommersnes PG, Galatola P (2003) Dynamin recruitment by clathrin coats: a physical step? C R Biol 326:467–476Google Scholar
  259. 259.
    Wu SHW, McConnell HM (1975) Phase separations in phospholipid membranes. Biochemistry 14(4):847–854Google Scholar
  260. 260.
    Gebhardt C, Gruler H, Sackmann E (1977) Domain-structure and local curvature in lipid bilayers and biological membranes. Z Naturforsch C 32(7–8):581–596Google Scholar
  261. 261.
    Markin VS (1981) Lateral organization of membranes and cell shapes. Biophys J 36(1):1–19Google Scholar
  262. 262.
    Andelman D, Kawakatsu T, Kawasaki K (1992) Equilibrium shape of two-component unilamellar membranes and vesicles. Europhys Lett 19(1):57–62Google Scholar
  263. 263.
    Seifert U (1993) Curvature-induced lateral phase segregation in two-component vesicles. Phys Rev Lett 70:1335–1338Google Scholar
  264. 264.
    Bretscher MS (1972) Asymmetrical lipid bilayer structure for biological membranes. Nature 236(61):11–12Google Scholar
  265. 265.
    Daleke DL (2007) Phospholipid flippases. J Biol Chem 282(2):821–825Google Scholar
  266. 266.
    Deserno M (2004) Elastic deformation of a fluid membrane upon colloid binding. Phys Rev E 69:031903Google Scholar
  267. 267.
    Reynwar BJ, Deserno M (2011) Membrane-mediated interactions between circular particles in the strongly curved regime. Soft Matter 7:8567–8575Google Scholar
  268. 268.
    Weikl TR, Kozlov MM, Helfrich W (1998) Interaction of conical membrane inclusions: effect of lateral tension. Phys Rev E 57:6988–6995. doi: 10.1103/PhysRevE.57.6988 Google Scholar
  269. 269.
    Yolcu C, Deserno M (2012) Membrane-mediated interactions between rigid inclusions: an effective field theory. Phys Rev E 86:031906Google Scholar
  270. 270.
    Rothstein IZ (2003) TASI lectures on effective field theories. Available from arXiv.org, ArXiv:hep-ph/0308266Google Scholar
  271. 271.
    Goldberger WD, Rothstein IZ (2006) An effective field theory of gravity for extended objects. Phys Rev D 73:104029Google Scholar
  272. 272.
    Porto RA, Ross A, Rothstein IZ (2011) Spin induced multipole moments for the gravitational wave flux from binary inspirals to third post-newtonian order. J Cosmol Astropart Phys 3:009Google Scholar
  273. 273.
    Galley CR, Leibovich AK, Rothstein IZ (2010) Finite size corrections to the radiation reaction force in classical electrodynamics. Phys Rev Lett 105:094802Google Scholar
  274. 274.
    Yolcu C, Rothstein IZ, Deserno M (2011) Effective field theory approach to Casimir interactions on soft matter surfaces. Europhys Lett 96:20003Google Scholar
  275. 275.
    Yolcu C, Rothstein IZ, Deserno M (2012) Effective field theory approach to fluctuation-induced forces between colloids at an interface. Phys Rev E 85:011140Google Scholar
  276. 276.
    Dommersnes PG, Fournier JB (1999) Casimir and mean-field interactions between membrane inclusions subject to external torques. Europhys Lett 46:256Google Scholar
  277. 277.
    Kardar M, Golestanian R (1999) The “friction” of vacuum, and other fluctuation-induced forces. Rev Mod Phys 71:1233–1245Google Scholar
  278. 278.
    Park J-M, Lubensky TC (1996) Interactions between membrane inclusions on fluctuating membranes. J Phys I France 6(9):1217–1235Google Scholar
  279. 279.
    Helfrich W, Weikl TR (2001) Two direct methods to calculate fluctuation forces between rigid objects embedded in fluid membranes. Eur Phys J E 5:423–439Google Scholar
  280. 280.
    Gosselin HP, Morbach H, Müller MM (2012) Interface-mediated interactions: entropic forces of curved membranes. Phys Rev E 83:051921Google Scholar
  281. 281.
    Brakke KA (1992) The surface evolver. Exp Math 1:141–165Google Scholar
  282. 282.
    Reynwar BJ, Illya G, Harmandaris VA, Müller MM, Kremer K, Deserno M (2007) Aggregation and vesiculation of membrane proteins by curvature-mediated interactions. Nature 447:461–464Google Scholar
  283. 283.
    Kim KS, Neu J, Oster G (1998) Curvature-mediated interactions between membrane proteins. Biophys J 75(5):2274–2291Google Scholar
  284. 284.
    Kim KS, Neu JC, Oster GF (1999) Many-body forces between membrane inclusions: a new pattern-formation mechanism. Europhys Lett 48(1):99–105Google Scholar
  285. 285.
    Kim KS, Chou T, Rudnick J (2008) Degenerate ground-state lattices of membrane inclusions. Phys Rev E 78:011401. doi: 10.1103/PhysRevE.78.011401 Google Scholar
  286. 286.
    Müller MM, Deserno M (2010) Cell model approach to membrane mediated protein interactions. Progr Theor Phys Suppl 184:351–363Google Scholar
  287. 287.
    Auth T, Gompper G (2009) Budding and vesiculation induced by conical membrane inclusions. Phys Rev E 80:031901. doi: 10.1103/PhysRevE.80.031901 Google Scholar
  288. 288.
    Johnson ME, Head-Gordon T, Louis AA (2007) Representability problems for coarse-grained water potentials. J Chem Phys 126(14):144509Google Scholar
  289. 289.
    Nielsen SO, Lopez CF, Srinivas G, Klein ML (2003) A coarse grain model for n-alkanes parameterized from surface tension data. J Chem Phys 119:7043–7049Google Scholar
  290. 290.
    Mognetti BM, Yelash L, Virnau P, Paul W, Binder K, Müller M, Macdowell LG (2008) Efficient prediction of thermodynamic properties of quadrupolar fluids from simulation of a coarse-grained model: the case of carbon dioxide. J Chem Phys 128:104501Google Scholar
  291. 291.
    DeVane R, Shinoda W, Moore PB, Klein ML (2009) Transferable coarse grain nonbonded interaction model for amino acids. J Chem Theory Comput 5:2115–2124Google Scholar
  292. 292.
    Tschöp W, Kremer K, Batoulis J, Burger T, Hahn O (1998) Simulation of polymer melts. I. coarse-graining procedure for polycarbonates. Acta Polym 49(2–3):61–74Google Scholar
  293. 293.
    Lyubartsev AP, Laaksonen A (1995) Calculation of effective interaction potentials from radial-distribution functions – a reverse Monte-Carlo approach. Phys Rev E 52:3730–3737Google Scholar
  294. 294.
    Reith D, Putz M, Müller-Plathe F (2003) Deriving effective mesoscale potentials from atomistic simulations. J Comp Chem 24:1624–1636Google Scholar
  295. 295.
    Peter C, Delle Site L, Kremer K (2008) Classical simulations from the atomistic to the mesoscale: coarse graining an azobenzene liquid crystal. Soft Matter 4:859–869Google Scholar
  296. 296.
    Murtola T, Karttunen M, Vattulainen I (2009) Systematic coarse graining from structure using internal states: application to phospholipid/cholesterol bilayer. J Chem Phys 131:055101Google Scholar
  297. 297.
    Lyubartsev A, Mirzoev A, Chen LJ, Laaksonen A (2010) Systematic coarse-graining of molecular models by the Newton inversion method. Faraday Discuss 144:43–56Google Scholar
  298. 298.
    Savelyev A, Papoian GA (2009) Molecular renormalization group coarse-graining of electrolyte solutions: application to aqueous NaCl and KCl. J Phys Chem B 113:7785–7793Google Scholar
  299. 299.
    Megariotis G, Vyrkou A, Leygue A, Theodorou DN (2011) Systematic coarse graining of 4-cyano-4′-pentylbiphenyl. Ind Eng Chem Res 50:546–556Google Scholar
  300. 300.
    Mukherjee B, Site LD, Kremer K, Peter C (2012) Derivation of a coarse grained model for multiscale simulation of liquid crystalline phase transitions. J Phys Chem B 116:8474–8484Google Scholar
  301. 301.
    Shell MS (2008) The relative entropy is fundamental to multiscale and inverse thermodynamic problems. J Chem Phys 129:144108Google Scholar
  302. 302.
    Silbermann JR, Klapp SHL, Schoen M, Chennamsetty N, Bock H, Gubbins KE (2006) Mesoscale modeling of complex binary fluid mixtures: towards an atomistic foundation of effective potentials. J Chem Phys 124:074105Google Scholar
  303. 303.
    Allen EC, Rutledge GC (2009) Evaluating the transferability of coarse-grained, density-dependent implicit solvent models to mixtures and chains. J Chem Phys 130:034904Google Scholar
  304. 304.
    Mullinax JW, Noid WG (2009) Extended ensemble approach for deriving transferable coarse-grained potentials. J Chem Phys 131:104110Google Scholar
  305. 305.
    Villa A, Peter C, van der Vegt NFA (2010) Transferability of nonbonded interaction potentials for coarse-grained simulations: benzene in water. J Chem Theory Comput 6:2434–2444Google Scholar
  306. 306.
    Izvekov S, Chung PW, Rice BM (2010) The multiscale coarse-graining method: assessing its accuracy and introducing density dependent coarse-grain potentials. J Chem Phys 133:064109Google Scholar
  307. 307.
    Shen JW, Li C, van der Vegt NFA, Peter C (2011) Transferability of coarse grained potentials: implicit solvent models for hydrated ions. J Chem Theory Comput 7:1916–1927Google Scholar
  308. 308.
    Brini E, Marcon V, van der Vegt NFA (2011) Conditional reversible work method for molecular coarse graining applications. Phys Chem Chem Phys 13(10):468–10474Google Scholar
  309. 309.
    Liu Z, Yan H, Wang K, Kuang T, Zhang J, Gul L, An X, Chang W (2004) Crystal structure of spinach major light-harvesting complex at 2.72 Å resolution. Nature 428:287–292Google Scholar
  310. 310.
    Standfuss R, van Scheltinga ACT, Lamborghini M, Kühlbrandt W (2005) Mechanisms of photoprotection and nonphotochemical quenching in pea light-harvesting complex at 2.5 Å resolution. EMBO J 24:919–928Google Scholar
  311. 311.
    Schmid VH (2008) Light-harvesting complexes of vascular plants. Cell Mol Life Sci 65(22):3619–3639Google Scholar
  312. 312.
    Yang C, Horn R, Paulsen H (2003) The light-harvesting chlorophyll a/b complex can be reconstituted in vitro from its completely unfolded apoprotein. Biochemistry 42:4527–4533Google Scholar
  313. 313.
    Horn R, Grundmann G, Paulsen H (2007) Consecutive binding of chlorophylls a and b during the assembly in vitro of light-harvesting chlorophyll-a/b protein (LHCIIb). J Mol Biol 366:1045–1054Google Scholar
  314. 314.
    Dockter C, Volkov A, Bauer C, Polyhach Y, Joly-Lopez Z, Jeschke G, Paulsen H (2009) Refolding of the integral membrane protein light-harvesting complex II monitored by pulse EPR. Proc Natl Acad Sci USA 106(44):18485–18490Google Scholar
  315. 315.
    Horn R, Paulsen H (2004) Early steps in the assembly of light-harvesting chlorophyll a/b complex. J Biol Chem 279(43):44400–44406Google Scholar
  316. 316.
    Dockter C, Müller AH, Dietz C, Volkov A, Polyhach Y, Jeschke G, Paulsen H (2012) Rigid core and flexible terminus: structure of solubilized light-harvesting chlorophyll a/b complex (LHCII) measured by EPR. J Biol Chem 287:2915–2925. doi: 10.1074/jbc.M111.307728 Google Scholar
  317. 317.
    Garab G, Lohner K, Laggner P, Farkas T (2000) Self-regulation of the lipid content of membranes by non-bilayer lipids: a hypothesis. Trends Plant Sci 5(11):489–494Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Markus Deserno
    • 1
    Email author
  • Kurt Kremer
    • 2
  • Harald Paulsen
    • 3
  • Christine Peter
    • 4
  • Friederike Schmid
    • 5
  1. 1.Department of PhysicsCarnegie Mellon UniversityPittsburghUSA
  2. 2.Max-Planck-Institute for Polymer ResearchMainzGermany
  3. 3.Department of BiologyUniversity of MainzMainzGermany
  4. 4.Department of ChemistyUniversity of KonstanzConstanceGermany
  5. 5.Institute of PhysicsUniversity of MainzMainzGermany

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