European Biophysics Journal

, Volume 35, Issue 2, pp 104–124 | Cite as

Implicit solvent simulation models for biomembranes

  • Grace Brannigan
  • Lawrence C.-L. Lin
  • Frank L. H. Brown
Review

Abstract

Fully atomic simulation strategies are infeasible for the study of many processes of interest to membrane biology, biophysics and biochemistry. We review various coarse-grained simulation methodologies with special emphasis on methods and models that do not require the explicit simulation of water. Examples from our own research demonstrate that such models have potential for simulating a variety of biologically relevant phenomena at the membrane surface.

Notes

Acknowledgments

This work was supported in part by the NSF (MCB-0203221, CHE-0349196, CHE-0321368) and the donors of the American Chemical Society Petroleum Research Fund (PRF 42447-G7). F. B. is an Alfred P. Sloan Research Fellow. F. B. thanks the NSF for travel funds to participate in the “Biophysical Chemistry Meets Molecular Medicine” workshop.

References

  1. Allen MP (1993) Simulations using hard particles. Philos Trans Phys Sci Eng 344:323–337ADSGoogle Scholar
  2. Aoki K, Yonezawa F (1992) Constant-pressure molecular-dynamics simulations of the crystal-smectic transition in systems of soft parallel spherocylinders. Phys Rev A 46:6541–6549ADSGoogle Scholar
  3. Aranda-Espinoza H, Berman A, Dan N, Pincus P, Safran SA (1996) Interaction between inclusions embedded in membranes. Biophys J 71:648–656Google Scholar
  4. Ayton G, Voth GA (2002) Bridging microscopic and mesoscopic simulations of lipid bilayers. Biophys J 83:3357–3370Google Scholar
  5. Ayton G, Bardenhagen SG, McMurty P, Sulsky D, Voth GA (2001) Interfacing continuum and molecular dynamics: an application to lipid bilayers. J Chem Phys 114:6913–6924ADSGoogle Scholar
  6. Bar-Ziv R, Menes R, Moses E, Safran SA (1995) Local unbinding of pinched membranes. Phys Rev Lett 75:3356–3359ADSGoogle Scholar
  7. Ben-Shaul A (1995) Molecular theory of chain packing. In: Lipowsky R, Sackmann E (eds) Structure and dynamics of membranes, vol 1. Elsevier, AmsterdamGoogle Scholar
  8. Bloom M, Evans E, Mouritsen OG (1991) Physical-properties of the fluid lipid-bilayer component of cell membranes—a perspective. Q Rev Biophys 24:293–397Google Scholar
  9. Boyd BJ, Drummond CJ, Krodkiewska I, Grieser F (2000) How chain length, headgroup polymerization, and anomeric configuration govern the thermotropic and lyotropic liquid crystalline phase behavior and the air–water interfacial adsorption of glucose-based surfactants. Langmuir 16:7359–7367Google Scholar
  10. Brannigan G, Brown FLH (2004) Solvent-free simulations of fluid membrane bilayers. J Chem Phys 120:1059ADSGoogle Scholar
  11. Brannigan G, Brown FL (2005) Composition dependence of bilayer elasticity. J Chem Phys 122:074905ADSGoogle Scholar
  12. Brannigan G, Tamboli AC, Brown FLH (2004) The role of molecular shape in bilayer phase behavior and elasticity. J Chem Phys 121:3259–3271ADSGoogle Scholar
  13. Brannigan G, Philips PF, Brown FL (2005) Flexible lipid bilayers in implicit solvent. Phys Rev E 72:011915ADSGoogle Scholar
  14. Brochard F, Lennon JF (1975) Frequency spectrum of the flicker phenomenon in erythrocytes. J Phys (Paris) 36:1035–1047CrossRefGoogle Scholar
  15. Brown FLH (2003) Regulation of protein mobility via thermal membrane undulations. Biophys J 84:842–853Google Scholar
  16. Brown FLH, Leitner DM, McCammon JA, Wilson KR (2000) Lateral diffusion of membrane proteins in the presence of static and dynamic corrals: suggestions for appropriate observables. Biophys J 78:2257–2269CrossRefGoogle Scholar
  17. Byers TJ, Branton D (1985) Visualization of the protein associations in the erythrocyte membrane skeleton. Proc Natl Acad Sci USA 82:6153–6157ADSGoogle Scholar
  18. Canham PB (1970) The minimum energy of bending as a possible explanation of the biconcave shape of the red blood cell. J Theor Biol 26:61–81Google Scholar
  19. Chao C-Y, Chou C-F, Ho JT, Hui S, Jin A, Huang CC (1996) Nature of layer-by-layer freezing in free-standing 4o.8 films. Phys Rev Lett 77:2750–2753ADSGoogle Scholar
  20. Cheng M, Ho JT, Hui SW, Pindak R (1988) Observation of two-dimensional hexatic behavior in free-standing liquid crystal films. Phys Rev Lett 61:550–553ADSGoogle Scholar
  21. Cherry RJ (1979) Rotational and lateral diffusion of membrane proteins. Biochim Biophys Acta 559:289–327Google Scholar
  22. Chiu SW, Jakobsson E, Mashl RJ, Scott HL (2002) Cholesterol-induced modifications in lipid bilayers: a simulation study. Biophys J 83:1842–1853Google Scholar
  23. Chiu S, Vasudevan S, Jakobsson E, Mashl RJ, Scott HL (2003) Structure of sphingomyelin bilayers: a simulation study. Biophys J 85:3624–3635Google Scholar
  24. Chou C-F, Jin AJ, Hui S, Huang CC, Ho JT (1998) Multiple-step melting in two-dimensional hexatic liquid-crystal films. Science 280:1424–1426ADSGoogle Scholar
  25. Cooke IR, Kremer K, Deserno M (2005) Tunable generic model for fluid bilayer membranes. Phys Rev E 72:011506Google Scholar
  26. Corbett JD, Agre P, Palek J, Golan DE (1994) Differential control of band 3 lateral and rotational mobility in intact red cells. J Clin Invest 94:683–688CrossRefGoogle Scholar
  27. Dan N, Pincus P, Safran SA (1993) Membrane-induced interactions between inclusions. Langmuir 9:2768–2771Google Scholar
  28. Dan N, Berman A, Pincus P, Safran SA (1994) Membrane-induced interactions between inclusions. J Phys II France 4:1713–1725Google Scholar
  29. Deuling HJ, Helfrich W (1976) The curvature elasticity of fluid membranes: a catalogue of vesicle shapes. J Phys (Paris) 37:1335–1345Google Scholar
  30. Dill KA, Bromberg S, Yue K, Fiebig KM, Yee DP, Thomas PD, Chan HS (1995) Principles of protein folding—a perspective from simple exact models. Protein Sci 4:561–602Google Scholar
  31. Doi M, Edwards SF (1986) The theory of polymer dynamics. Clarendon Press, OxfordGoogle Scholar
  32. Drouffe J-M, Maggs AC, Leibler S (1991) Computer simulations of self-assembled membranes. Science 254:1353–1356ADSGoogle Scholar
  33. Edidin M, Kuo SC, Sheetz MP (1991) Lateral movements of membrane glycoproteins restricted by dynamic cytoplasmic barriers. Science 254:1379–1382ADSGoogle Scholar
  34. Edwards L, Peng Y, Reggia JA (1998) Computational models for the formation of protocell structures. Artif Life 4:61–77Google Scholar
  35. Ermak DL, McCammon JA (1978) Brownian dynamics with hydrodynamic interactions. J Chem Phys 69:1352–1360ADSGoogle Scholar
  36. Evans E (1974) Bending resistance and chemically induced moments in membrane bilayers. Biophys J 14:923–931CrossRefGoogle Scholar
  37. Evans E, Skalak R (1980) Mechanisms and thermodyanmics of biomembranes. CRC Press, Boca RatonGoogle Scholar
  38. Farago O (2003) “Water-free” computer model for fluid bilayer membranes. J Chem Phys 119:596–605ADSGoogle Scholar
  39. Farago O (2004) Statistical mechanics of bilayer membrane with a fixed projected area. J Chem Phys 120:2934–2950ADSGoogle Scholar
  40. Fattal D, Ben-Shaul A (1993) A molecular model for lipid–protein interaction in membranes: the role of hydrophobic mismatch. Biophys J 65:1795–1809Google Scholar
  41. Feig M, Brooks CL III (2004) Recent advances in the development and application of implicit solvent models in biomolecule simulations. Curr Opin Struct Biol 14:217–224Google Scholar
  42. Feller SE (2000) Molecular dynamics simulations of lipid bilayers. Curr Opin Colloid Interface 5:217–223Google Scholar
  43. Geer R, Stoebe T, Huang CC, Pindak R, Goodby J, Cheng M, Ho JT, Hui SW (1992) Liquid–hexatic phase transitions in single molecular layers of liquid-crystal films. Nature 355:152–154ADSGoogle Scholar
  44. deGennes P, Prost J (1993) The physics of liquid crystals, 2nd edn. Clarendon Press, OxfordGoogle Scholar
  45. Gennis RB (1989) Biomembranes: molecular structure and function. Springer, Berlin Heidelberg New YorkGoogle Scholar
  46. Goetz R, Lipowsky R (1998) Computer simulations of bilayer membranes: self assembly and interfacial tension. J Chem Phys 108:7397–7409ADSGoogle Scholar
  47. Goetz R, Gompper G, Lipowsky R (1999) Mobility and elasticity of self-assembled membranes. Phys Rev Lett 82:221–224ADSGoogle Scholar
  48. Gompper G, Kroll DM (1997) Network models of fluid, hexatic and polymerized membranes. J Phys Condens Matter 9:8795–8834ADSGoogle Scholar
  49. Gouliaev N, Nagle JF (1998a) Simulations of a single membrane between two walls using a Monte Carlo method. Phys Rev E 58:881–888ADSGoogle Scholar
  50. Gouliaev N, Nagle JF (1998b) Simulations of interacting membranes in the soft confinement regime. Phys Rev Lett 81:2610–2613ADSGoogle Scholar
  51. Gov N (2004) Membrane undulations driven by force fluctuations of active proteins. Phys Rev Lett 93:268104ADSGoogle Scholar
  52. Gov N, Safran SA (2004) Pinning of fluid membranes by periodic harmonic potentials. Phys Rev E 69:011101ADSMathSciNetGoogle Scholar
  53. Gov N, Zilman AG, Safran S (2003) Cytoskeleton confinement and tension of red blood cells. Phys Rev Lett 90:228101ADSGoogle Scholar
  54. Gov N, Zilman AG, Safran SA (2004) Hydrodynamics of confined membranes. Phys Rev E 70:011104ADSMathSciNetGoogle Scholar
  55. Gove PB (ed) (1970) Webster’s seventh new collegiate dictionary. G. & C. Merriam, SpringfieldGoogle Scholar
  56. Grakoui A, Bromley SK, Sumen C, Davis MM, Shaw AS, Allen PM, Dustin ML (1999) The immunological synapse: a molecular machine controlling t cell activation. Science 285:221–227Google Scholar
  57. Granek R (1997) From semi-flexible polymers to membranes: anomalous diffusion and reptation. J Phys II (Paris) 7:1761–1788Google Scholar
  58. Granek R, Klafter J (2001) Anomalous motion of membranes under a localized external potential. Europhys Lett 56:15–21ADSGoogle Scholar
  59. Groot RD, Rabone KL (2001) Mesoscopic simulation of cell membrane damage, morphology change and rupture by nonionic surfactants. Biophys J 81:725Google Scholar
  60. Gruhn T, Lipowsky R (2005) Temperature dependence of vesicle adhesion. Phys Rev E 71:011903ADSGoogle Scholar
  61. Harries D, Ben-Shaul A (1997) Conformational chain statistics in a model lipid bilayer: comparison between mean field and Monte Carlo calculations. J Chem Phys 106:1609–1619ADSGoogle Scholar
  62. Harroun TA, Heller WT, Weiss T, 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
  63. Helfrich W (1973) Elastic properties of lipid bilayers: theory and possible experiments. Z Naturforsch 28c:693–703Google Scholar
  64. Helfrich W (1978) Steric interaction of fluid membranes in multilayer systems. Z Naturforsch 33a:305–315ADSGoogle Scholar
  65. Helfrich P, Jakobsson E (1990) Calculation of deformation energies and conformations in lipid membranes containing gramicidin channels. Biophys J 57:1075–1084CrossRefGoogle Scholar
  66. Holzöhner R, Schoen M (1999) Attractive forces between anisotropic inclusions in the membrane of a vesicle. Eur Phys J B 12:413–419ADSGoogle Scholar
  67. Huang H (1986) Deformation free energy of bilayer membrane and its effects on gramicidin channel lifetime. Biophys J 50:1061–1070Google Scholar
  68. Illya G, Lipowsky R, Shillcock JC (2005) Effect of chain length and asymmetry on material properties of bilayer membranes. J Chem Phys 122:244901ADSGoogle Scholar
  69. Im W, Feig M, Brooks CL III (2003) An implicit membrane generalized born theory for the study of structure, stability and interactions of membrane proteins. Biophys J 85:2900–2918Google Scholar
  70. Imparato A, Shillcock J, Lipowsky R (2005) Shape fluctuations and elastic properties of two-component bilayer membranes. Europhys Lett 69:650–656ADSGoogle Scholar
  71. Izvekov S, Voth GA (2005) A multi-scale coarse-graining method for biomolecular systems. J Phys Chem B 109:2469Google Scholar
  72. Jamney P (1995) Cell membranes and the cytoskeleton. In: Structure and dynamics of membranes: part A. From cells to vesicles. Elsevier, Amsterdam, pp 805–849Google Scholar
  73. Jensen MO, Mouritsen OG (2004) Lipids do influence protein function—the hydrophobic matching hypothesis revisited. Biochim Biophys Acta 1666:205–226Google Scholar
  74. Kaizuka Y, Groves JT (2004) Structure and dynamics of supported intermembrane junctions. Biophys J 86:905–912CrossRefGoogle Scholar
  75. van Kampen NG (1992) Stochastic processes in physics and chemistry. North-Holland, Amsterdam, pp 63, 83, 220-221Google Scholar
  76. Kohyama T, Kroll D, Gompper G (2003) Budding of crystalline domains in fluid membranes. Phys Rev E 68:061905ADSGoogle Scholar
  77. Kolinski A, Skolnick J (2004) Reduced models of proteins and their applications. Polymer 45:511–524Google Scholar
  78. Koppel DE, Sheetz MP, Schindler M (1981) Matrix control of protein diffusion in biological membranes. Proc Natl Acad Sci USA 78:3576–3580ADSGoogle Scholar
  79. Kralchevsky P, Paunov V, Dekov ND, Nagayama K (1991) Stresses in lipid membranes and interactions between inclusions. J Chem Soc Faraday Trans 91:3415–3432Google Scholar
  80. Kumar PS, Rao M (1998) Shape instabilities in the dynamics of a two-component fluid membrane. Phys Rev Lett 80:2489–2492ADSGoogle Scholar
  81. Kumar PS, Gompper G, Lipowsky R (2001) Budding dynamics of multicomponent membranes. Phys Rev Lett 86:3911–3914ADSGoogle Scholar
  82. Kusumi A, Sako Y (1996) Cell surface organization by the membrane skeleton. Curr Opin Cell Biol 8:566–574Google Scholar
  83. Kusumi A, Sako Y, Yamamoto M (1993) Confined lateral diffusion of membrane receptors as studied by single particle tracking. Effects of calcium-induced differentiation in cultured epithelial cells. Biophys J 65:2021–2040Google Scholar
  84. Lambacher A, Fromhertz P (1996) Fluorescence interference-contrast microscopy on oxidized silicon using a monomolecular dye layer. Appl Phys A 63:207–216ADSGoogle Scholar
  85. Laradji M (1999) Polymer adsorption on fluctuating surfaces. Europhys Lett 47:694–700ADSGoogle Scholar
  86. Laradji M (2002) Elasticity of polymer-anchored membranes. Europhys Lett 60:594–600ADSGoogle Scholar
  87. Laradji M (2004) A Monte Carlo study of fluctuating polymer-grafted membranes. J Chem Phys 121:1591–1600ADSGoogle Scholar
  88. Laradji M, Kumar PS (2004) Dynamics of domain growth in self-assembled fluid vesicles. Phys Rev Lett 93:198105ADSGoogle Scholar
  89. Leitner DM, Brown FLH, Wilson KR (2000) Regulation of protein mobility in cell membranes: a dynamic corral model. Biophys J 78:125–135Google Scholar
  90. Lim HWG, Wortis M, Mukhopadhyay R (2002) Stomatocyte–discocyte–echinocyte sequence of the human red blood cell: evidence for the bilayer-couple hypothesis from membrane mechanics. Proc Natl Acad Sci 99:16766–16769ADSGoogle Scholar
  91. Lin LC-L, Brown FLH (2004a) Brownian dynamics in fourier space: membrane simulations over long length and time scales. Phys Rev Lett 93:256001ADSGoogle Scholar
  92. Lin LC-L, Brown FLH (2004b) Dynamics of pinned membranes with application to protein diffusion on the surface of red blood cells. Biophys J 86:764–780Google Scholar
  93. Lin LC-L, Brown FLH (2005) Dynamic simulations of membranes with cytoskeletal interactions. Phys Rev E 72:011910ADSGoogle Scholar
  94. Lindahl E, Edholm O (2000a) Mesoscopic undulations and thickness fluctuations in lipid bilayers from molecular dynamics simulations. Biophys J 79:426–633Google Scholar
  95. Lindahl E, Edholm O (2000b) Spatial and energetic-entropic decomposition of surface tension in lipid bilayers from molecular dynamics simulations. J Chem Phys 113:3882–3893ADSGoogle Scholar
  96. Lipowsky R (1991) The conformation of membranes. Nature 349:475–481ADSGoogle Scholar
  97. Lipowsky R, Grotehans S (1994) Renormalization of hydration forces by collective protrusion modes. Biophys Chem 49:27–37Google Scholar
  98. Lipowsky R, Sackmann E (1995) Structure and dynamics of membranes. Elsevier, AmsterdamMATHGoogle Scholar
  99. Lipowsky R, Zielenska B (1989) Binding and unbinding of lipid membranes: a Monte Carlo study. Phys Rev Lett 62:1572–1575ADSGoogle Scholar
  100. Liu S, Derick L, Palek J (1987) Visualization of the hexagonal lattice in the erythrocyte membrane skeleton. J Cell Biol 104:527–536Google Scholar
  101. Lodish H, Baltimore D, Berk A, Zipursky SL, Matsudaira P, Darnell J (1995) Molecular cell biology, 3rd edn. Scientific American Books, New YorkGoogle Scholar
  102. 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 119:13138–13148ADSGoogle Scholar
  103. Luna EJ, Hitt AL (1992) Cytoskeleton–plasma membrane interactions. Science 258:955–964ADSGoogle Scholar
  104. Luzzati V (1968) X-ray diffraction studies of lipid-water systems. In: Chapman D (ed) Biological membranes, vol 1. Academic, New York, pp 71–123Google Scholar
  105. Luzzati V, Husson F (1962) Structure of liquid-crystalline phases of lipid water systems. J Cell Biol 12:207Google Scholar
  106. Manneville J-B, Bassereau P, Levy D, Prost J (1999) Activity of transmembrane proteins induces magnification of shape fluctuations of lipid membranes. Phys Rev Lett 82:4356–4359ADSGoogle Scholar
  107. Manneville J-B, Bassereau P, Ramaswamy S, Prost J (2001) Active membrane fluctuations studied by micropipet aspiration. Phys Rev E 64:021908ADSGoogle Scholar
  108. Marčelja S (1976) Lipid-mediated protein interaction in membranes. Biochim Biophys Acta 455:1–7Google Scholar
  109. Marrink SJ, Mark AE (2001) Effect of undulations on surface tension in simulated bilayers. J Phys Chem 105:6122–6127Google Scholar
  110. Marrink S-J, Berkowitz M, Berendsen HJC (1993) Molecular dynamics simulation of a membrane/water interface: the ordering of water and its relation to the hydration force. Langmuir 9:3122–3131Google Scholar
  111. Marrink S-J, Lindahl E, Edholm O, Mark AE (2001) Simulation of the spontaneous aggregation of phospholipids into bilayers. J Am Chem Soc 2001:8638–8639Google Scholar
  112. Marrink S, de Vries A, Mark AE (2004) Coarse grained model for semiquantitative lipid simulations. J Phys Chem B 108:750–760Google Scholar
  113. May S (2000) Theories on structural perturbations of lipid bilayers. Curr Opin Colloid Interface Sci 5:244–249Google Scholar
  114. McWhirter JL, Ayton G, Voth GA (2004) Coupling field theory with mesoscopic dynamical simulations of multicomponent lipid bilayers. Biophys J 87:3242–3263Google Scholar
  115. Miao L, Fourcade B, Wortis MRM, Zia RKP (1991) Equilibrium budding and vesiculation in the curvature model of fluid lipid vesicles. Phys Rev A 43:6843–6856ADSGoogle Scholar
  116. Miao L, Seifert U, Wortis M, Döbereiner H (1994) Budding transitions of fluid-bilayer vesicles: the effect of area-difference elasticity. Phys Rev E 49:5389–5407ADSGoogle Scholar
  117. Milner ST, Safran SA (1987) Dynamical fluctuations of droplet microemulsions and vesicles. Phys Rev A 36:4371–4379ADSGoogle Scholar
  118. Moore GE (1985) Cramming more components onto integrated circuits. Electronics 38:114–117Google Scholar
  119. Morikawa R, Saito Y (1994) Hard rod and frustum model of two-dimensional vesicles. J Phys II 4:145Google Scholar
  120. Mukhopadhyay R, Lim HWG, Wortis M (2002) Echinocyte shapes: bending, stretching, and shear determine spicule shape and spacing. Biophys J 82:1756–1772Google Scholar
  121. Murtola T, Falck E, Patra M, Karttunen M, Vattulainen I (2004) Coarse-grained model for phospholipid/cholesterol bilayer. J Chem Phys 121:9156–9165ADSGoogle Scholar
  122. Nagle JF, Tristram-Nagle S (2000) Structure of lipid bilayers. Biochim Biophys Acta 1469:159–195Google Scholar
  123. Netz RR (1997) Inclusions in fluctuating membranes: exact results. J Phys I France 7:833–852Google Scholar
  124. Nielsen C, Goulian M, Andersen OS (1998) Energetics of inclusion-induced bilayer deformations. Biophys J 74:1966–1983Google Scholar
  125. Nielsen SO, Ensing B, Ortiz V, Moore PB, Klein ML (2005) Lipid bilayer perturbations around a transmembrane nanotube: a coarse grain molecular dynamics study. Biophys J 88:3822–3828Google Scholar
  126. Noguchi H (2002) Fusion and toroidal formation of vesicles by mechanical forces: a brownian dynamics simulation. J Chem Phys 117:8130–8137ADSGoogle Scholar
  127. Noguchi H (2003) Polyhedral vesicles: a brownian dynamics simulation. Phys Rev E 67:041901ADSGoogle Scholar
  128. Noguchi H, Gompper G (2004) Fluid vesicles with viscous membranes in shear flow. Phys Rev Lett 93:258102ADSGoogle Scholar
  129. Noguchi H, Takasu M (2001a) Fusion pathways of vesicles: a brownian dynamics simulation. J Chem Phys 115:9547–9551ADSGoogle Scholar
  130. Noguchi H, Takasu M (2001b) Self-assembly of amphiphiles into vesicles: a brownian dynamics simulation. Phys Rev E 64:041913ADSGoogle Scholar
  131. Noguchi H, Takasu M (2002a) Adhesion of nanoparticles to vesicles: a brownian dynamics simulation. Biophys J 83:299–308CrossRefGoogle Scholar
  132. Noguchi H, Takasu M (2002b) Structural changes of pulled vesicles: a brownian dynamics simulation. Phys Rev E 65:051907ADSGoogle Scholar
  133. Owicki J, McConnell HM (1979) Theory of protein–lipid and protein–protein interactions in bilayer membranes. Proc Natl Acad Sci 76:4750–4754ADSGoogle Scholar
  134. Partenskii MB, Jordan PC (2002) Membrane deformation and the elastic energy of insertion: perturbation of membrane elastic constants to due peptide insertion. J Chem Phys 117:10768–10776ADSGoogle Scholar
  135. Parthasarathy R, Groves JT (2004) Optical techniques for imaging membrane topography. Cell Biochem Biophys 41:391–414Google Scholar
  136. Pastor RW (1994) Molecular-dynamics and Monte-Carlo simulations of lipid bilayers. Curr Opin Struct Biol 4:486–492Google Scholar
  137. Petrache H, Zuckerman D, Sachs J, Killian J, Koeppe R, Woolf TB (2002) Hydrophobic matching mechanism investigated by molecular dynamics simulations. Langmuir 18:1340–1351Google Scholar
  138. Pindak R, Moncton DE, Davey SC, Goodby JW (1981) X-ray observation of a stacked hexatic liquid-crystal b phase. Phys Rev Lett 46:1135ADSGoogle Scholar
  139. Pitman MC, Grossfield A, Suits F, Feller SE (2005) Role of cholesterol and polyunsaturated chains in lipid–protein interactions: molecular dynamics simulation of rhodopsin in a realistic membrane environment. J Am Chem Soc 127:4576–4577Google Scholar
  140. de Planque M, Killian J (2003) Protein–lipid interactions studied with designed transmembrane peptides: role of hydrophobic matching and interfacial anchoring. Mol Membr Biol 20:271–284Google Scholar
  141. Planque MRD, Greathouse D, Koeppe R, Schäfer H, Marsh D, Killian JA (1998) Influence of lipid/peptide hydrophobic mismatch on the thickness of diacylphosphatidylcholine bilayers: a 2H-nmr and esr study using designed transmembrane α-helical peptides and gramicidin a. Biochemistry 37:9333–9345Google Scholar
  142. Prost J, Bruinsma R (1996) Shape fluctuations of active membranes. Europhys Lett 33:321–326ADSGoogle Scholar
  143. Prost J, Manneville J-B, Bruinsma R (1998) Fluctuation-magnification of non-equilibrium membranes near a wall. Eur Phys J B 1:465–480ADSGoogle Scholar
  144. Purcell EM (1977) Life at low reynolds number. Am J Phys 45:3–10ADSGoogle Scholar
  145. Qi SY, Groves JT, Chakraborty AK (2001) Synaptic pattern formation during cellular recognition. Proc Natl Acad Sci USA 98:6548–6553ADSGoogle Scholar
  146. Ramaswamy S, Toner J, Prost J (1999) Nonequilibrium noise and instabilities in membranes with active pumps. Pramana J Phys 53:237–242ADSGoogle Scholar
  147. Ramaswamy S, Toner J, Prost J (2000) Nonequilibrium fluctuations, traveling waves, and instabilities in active membranes. Phys Rev Lett 84:3494–3497ADSGoogle Scholar
  148. Rand RP, Parsegian VA (1989) Hydration forces between phospholipid-bilayers. Biochim Biophys Acta 988:351–376Google Scholar
  149. Rawicz W, Oldbrich 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
  150. Rekvig L, Kranenburg M, Vreede J, Hafskjold B, Smit B (2003) Investigation of surfactant efficiency using dissipative particle dynamics. Langmuir 19:4897Google Scholar
  151. Sackmann E (1995a) Biological membranes architecture and function. In: Structure and dynamics of membranes: part A. From cells to vesicles. Elsevier, Amsterdam, pp 1–62Google Scholar
  152. Sackmann E (1995b) Physical basis of self-organization and function of membranes: physics of vesicles. In: Lipowsky R, Sackmann E (eds) Structure and dynamics of membranes, vol 1. Elsevier, AmsterdamGoogle Scholar
  153. Sackmann E (1996) Supported membranes: scientific and practical applications. Science 271:43–48ADSGoogle Scholar
  154. Sackmann E, Tanaka M (2000) Supported membranes on soft polymer cushions: fabrication, characterization, and applications. Trends Biotechnol 18:58–64Google Scholar
  155. Saffman PG, Delbruck M (1975) Brownian motion in biological membranes. Proc Natl Acad Sci USA 73:3111–3113ADSGoogle Scholar
  156. Safinya CR, Sirota EB, Roux D, Smith GS (1989) Universality in interacting membranes: the effect of cosurfactants on the interfacial rigidity. Phys Rev Lett 62:1134–1137ADSGoogle Scholar
  157. Safran SA (1983) Fluctuations of spherical microemulsions. J Chem Phys 78:2073–2076ADSGoogle Scholar
  158. Safran SA (1994) Statistical thermodynamics of surfaces, interfaces and membranes. Westview Press, BoulderGoogle Scholar
  159. Saxton MJ (1989) The spectrin network as a barrier to lateral diffusion in erythrocytes: a percolation analysis. Biophys J 55:21–28CrossRefGoogle Scholar
  160. Saxton MJ (1990a) The membrane skeleton of erythrocytes: a percolation model. Biophys J 57:1167–1177Google Scholar
  161. Saxton MJ (1990b) The membrane skeleton of erythrocytes: models of its effect on lateral diffusion. Int J Biochem 22:801–809Google Scholar
  162. Saxton MJ (1995) Single-particle tracking: effects of corrals. Biophys J 69:389–398ADSGoogle Scholar
  163. Schindler M, Koppel DE, Sheetz MP (1980) Modulation of protein lateral mobility by polyphosphates and polyamines. Proc Natl Acad Sci USA 77:1457–1461ADSGoogle Scholar
  164. Schneider M, Jenkins J, Webb W (1984) Thermal fluctuations of large quasi-spherical bimolecular phospholipid-vesicles. J Phys (Paris) 45:1457Google Scholar
  165. Seifert U (1994) Dynamics of a bound membrane. Phys Rev E 49:3124–3127ADSGoogle Scholar
  166. Seifert U, Lipowsky R (1995) Morphology of vesicles. In: Lipowsky R, Sackmann E (eds) Structure and dynamics of membranes, vol 1. Elsevier, AmsterdamGoogle Scholar
  167. Seifert U, Berndl K, Lipowsky R (1991) Shape transformations of vesicles: phase diagram for spontaneous-curvature and bilayer-coupling models. Phys Rev A 44:1182–1202ADSGoogle Scholar
  168. Sheetz MP (1983) Membrane skeletal dynamics: role in modulation of red blood deformability, mobility of transmembrane proteins and shape. Sem Hematol 20:175–188Google Scholar
  169. Sheetz MP, Schindler M, Koppel DE (1980) The lateral mobility of integral membrane proteins is increased in spherocytic erythrocytes. Nature 285:510–512ADSGoogle Scholar
  170. Shelley JC, Shelley MY (2000) Computer simulation of surfactant solutions. Curr Opin Colloid Interface Sci 5:101–110Google Scholar
  171. Shelley JC, Shelley MY, Reeder RC, Bandyopadhyay S, Klein ML (2001) A coarse grain model for phospholipid simulations. J Phys Chem B 105:4464–4470Google Scholar
  172. Shillcock J, Lipowsky R (2002) Equilibrium structure and lateral stress distribution of amphiphilic bilayers from dissipative particle dynamics. J Chem Phys 117:5048–5061ADSGoogle Scholar
  173. Singer SJ, Nicolson GL (1972) The fluid mosaic model of the structure of cell membranes. Science 175:720–731ADSGoogle Scholar
  174. Sintes T, Baumgärtner A (1998a) Interaction of wedge-shaped proteins in flat bilayer membranes. J Phys Chem B 1998:7050–7057Google Scholar
  175. Sintes T, Baumgärtner A (1998b) Membrane-mediated protein attraction. a Monte-Carlo study. Physica A 249:571–575Google Scholar
  176. Smit B, Hilbers P, Esselink K, Rupert L, van Os N, Schlijper AG (1991) Structure of a water oil interface in the presence of micelles—a computer simulation study. J Phys Chem 95:6361Google Scholar
  177. Smith G, Sirota E, Safinya C, Clark N (1988) Structure of the l β phases in a hydrated phosphatidylcholine multimembrane. Phys Rev Lett 60:813–816ADSGoogle Scholar
  178. Smith G, Sirota E, Safinya C, Plano R, Clark N (1990) X-ray structural studies of freely suspended ordered hydrated dmpc multimembrane films. J Chem Phys 92:4519–4529ADSGoogle Scholar
  179. Smondyrev AM, Berkowitz ML (1999) Structure of dipalmitoylphosphatidylcholine/cholesterol bilayer at low and high cholesterol concentrations: molecular dynamics simulation. Biophys J 77:2075–2089Google Scholar
  180. Soddemann T, Dunweg B, Kremer K (2001) A generic computer model for amphiphilic systems. Eur Phys J E 6:409–419Google Scholar
  181. Stadler C, Schmid F (1999) Phase behavior of grafted chain molecules: influence of head size and chain length. J Chem Phys 110:9697ADSGoogle Scholar
  182. Steck TL (1989) Red cell shape. In: Stein W, Bronner F (eds) Cell shape: determinants, regulation and regulatory role. Academic, New York, pp 205–246Google Scholar
  183. Stevens MJ (2004) Coarse-grained simulations of lipid bilayers. J Chem Phys 121:11942ADSGoogle Scholar
  184. Tien HT, Ottova-Leitmannova A (2003) Planar lipid bilayers (BLMs) and their applications. Elsevier, AmsterdamGoogle Scholar
  185. Tobias DJ, Tu KC, Klein ML (1997) Atomic-scale molecular dynamics simulations of lipid membranes. Curr Opin Colloid Interface 2:15–26CrossRefGoogle Scholar
  186. Tomishige M, Sako Y, Kusumi A (1998) Regulation mechanism of the lateral diffusion of band 3 in erythrocyte membranes by the membrane skeleton. J Cell Biol 142:989–1000Google Scholar
  187. Tsuji A, Ohnishi S (1986) Restriction of the lateral motion of band 3 in the erythrocyte membrane by the cytoskeletal network: dependence on spectrin association state. Biochemistry 25:6133–6139Google Scholar
  188. Tsuji A, Kawasaki K, Ohnishi S, Merkle H, Kusumi A (1988) Regulation of band 3 mobilities in erythrocyte ghost membranes by protein association and cytoskeletal meshwork. Biochemistry 27:7447–7452Google Scholar
  189. 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 88:1778–1798Google Scholar
  190. Wang Z, Frenkel D (2005) Modeling flexible amphiphilic bilayers: a solvent-free off-lattice Monte Carlo study. J Chem Phys 135:234711ADSGoogle Scholar
  191. Weikl TR, Lipowsky R (2000) Local adhesion of membranes to striped surface domains. Langmuir 16:9338–9346Google Scholar
  192. Weis J, Levesque D, Zarragoicoechea G (1992) Orientational order in simple dipolar liquid-crystal models. Phys Rev Lett 69:913–916ADSGoogle Scholar
  193. Weiss TM, van der Wel PC, Killian JA, Koeppe RE, Huang HW (2003) Hydrophobic mismatch between helices and lipid bilayers. Biophys J 84:379–385CrossRefGoogle Scholar
  194. Whitehead L, Edge CM, Essex JW (2001) Molecular dynamics simulation of the hydrocarbon region of a biomembrane using a reduced representation model. J Comput Chem 22:1622–1633Google Scholar
  195. Yamamoto S, Maruyama Y, Hyodo S-A (2002) Dissipative particle dynamics study of spontaneous vesicle formation of amphiphilic molecules. J Chem Phys 116:5842–5849ADSGoogle Scholar
  196. Zangi R, Rice SA (2003) Freezing transition and correlated motion in a quasi-two-dimensional colloid suspension. Phys Rev E 68:061508ADSGoogle Scholar
  197. Zeman K, Engelhard H, Sackmann E (1990) Bending undulations and elasticity of the erythrocyte membrane: effects of cell shape and membrane organization. Eur Biophys J 18:203–219Google Scholar
  198. Zhang D, Klyatkin A, Bolin JT, Low PS (2000) Crystallographic structure and functional interpretation of the cytoplasmic domain of erythrocyte membrane band 3. Blood 96:2925–2933Google Scholar
  199. Zilker A, Engelhardt H, Sackmann E (1987) Dynamic reflection interference contrast (ric-) microscopy: a new method to study surface excitations of cells and to measure membrane bending elastic moduli. J Phys (Paris) 48:2139–2151Google Scholar
  200. Zilker A, Engelhardt H, Sackmann E (1992) Spectral analysis of erythrocyte flickering in the 0.3–4 μm−1 regime by microinterferometry combined with fast image processing. Phys Rev A 46:7998–8001ADSGoogle Scholar
  201. Zilman AG, Granek R (1996) Undulations and dynamic structure factor of membranes. Phys Rev Lett 77:4788–4791ADSGoogle Scholar

Copyright information

© EBSA 2005

Authors and Affiliations

  • Grace Brannigan
    • 1
  • Lawrence C.-L. Lin
    • 1
  • Frank L. H. Brown
    • 2
  1. 1.Department of Physics and AstronomyUniversity of CaliforniaSanta BarbaraUSA
  2. 2.Department of Chemistry and BiochemistryUniversity of CaliforniaSanta BarbaraUSA

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