Mesoscale computational studies of membrane bilayer remodeling by curvature-inducing proteins

Physics Reports

Volumn 543, Issue 1, 2014, Pages 1-60

  Ramakrishnan, N ^a,b   Sunil Kumar, P B ^c   Radhakrishnan, Ravi ^a,b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

^c INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

Author keywords

Cell membrane; Continuum models; Free energy; Helfrich Hamiltonian; Hydrophilicity; Hydrophobicity; Lipid bilayer; Molecular dynamics; Monte Carlo; Self assembly; Triangulated surfaces

Indexed keywords

EID: 84908160916     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physrep.2014.05.001     Document Type: Review

References (332)

1. Mouritsen O.G. Life-as a matter of fat: the emerging science of lipidomics. The Frontiers Collection 2005, Springer, Germany.
2. Guidotti G. Membrane proteins. Ann. Rev. Biochem. 1972, 41:731-752.
3. Voeltz G.K., Prinz W.A. Sheets, ribbons and tubules-how organelles get their shape. Nat. Rev. Mol. Cell Biol. 2007, 8:258-264.
4. Joyce J.A., Pollard J.W. Microenvironmental regulation of metastasis. Nat. Rev. Cancer 2008, 9:239-252.
5. Escribá P.V., González-Ros J.M., Goñi F.M., Kinnunen P.K.J., Vigh L., Sánchez-Magraner L., Fernández A.M., Busquets X., Horváth I., Barceló-Coblijn G. Membranes: a meeting point for lipids, proteins and therapies. J. Cell. Mol. Med. 2008, 12:829-875.
6. Cavey M., Rauzi M., Lenne P.-F., Lecuit T. A two-tiered mechanism for stabilization and immobilization of e-cadherin. Nature 2008, 453:751-756.
7. Jefferson J.J., Leung C.L., Liem R.K.H. Plakins: Goliaths that link cell junctions and the cytoskeleton. Nature 2004, 5:542-553.
8. Dannhauser P.N., Ungewickell E.J. Reconstitution of clathrin-coated bud and vesicle formation with minimal components. Nat. Cell Biol. 2012, 14:634-639.
9. Wendland B. Epsins: adaptors in endocytosis?. Nat. Rev. Mol. Cell Biol. 2002, 3:971-977.
10. Ford M.G.J., Mills I.G., Peter B.J., Vallis Y., Praefcke G.J.K., Evans P.R., McMahon H.T. Curvature of clathrin-coated pits driven by epsin. Nature 2002, 419:361-366.
11. Lai C.-L., Jao C.C., Lyman E., Gallop J.L., Peter B.J., McMahon H.T., Langen R., Voth G.A. Membrane binding and self-association of the epsin n-terminal homology domain. J. Mol. Biol. 2012, 423:800-817.
12. Angst B.D., Marcozzi C., Magee A.I. The cadherin superfamily: diversity in form and function. J. Cell Sci. 2001, 114:629-641.
13. Causeret M., Taulet N., Comunale F., Favard C., Gauthier-Rouvière C. N-cadherin association with lipid rafts regulates its dynamic assembly at cell-cell junctions in c2c12 myoblasts. Mol. Biol. Cell 2005, 16:2168-2180.
14. Márquez M.G., Favale N.O., Nieto F.L., Pescio L.G., Sterin-Speziale N. Changes in membrane lipid composition cause alterations in epithelial cell-cell adhesion structures in renal papillary collecting duct cells. Biochim. Biophys. Acta (BBA) - Biomembr. 2012, 1818:491-501.
15. Alberts B., Johnson A., Lewis J., Raff M., Roberts K., Walter P. Molecular Biology of the Cell 1994, Garland Publishing, Singapore. third ed.
16. van Meer G., Voelker D.R., Feigenson G.W. Membrane lipids: where they are and how they behave. Nat. Rev. Mol. Cell Biol. 2008, 9:112-124.
17. Farese R.V., Walther T.C. Lipid droplets finally get a little r-e-s-p-e-c-t. Cell 2009, 139:855-860.
18. Israelachvili J.N., Mitchell D.J., Ninham B.W. Theory of self-assembly of lipid bilayers and vesicles. Biochim. Biophy. Acta (BBA) - Biomembr. 1977, 470:185-201.
19. Koynova R., Caffrey M. An index of lipid phase diagrams. Chem. Phys. Lipids 2002, 115:107-219.
20. Singer S.J., Nicolson G.L. The fluid mosaic model of the structure of cell membranes. Science 1972, 175:720-731.
21. Spector A.A., Yorek M.A. Membrane lipid-composition and cellular function. J. Lipid Res. 1985, 26:1015-1035.
22. Paula S., Volkov A.G., Van Hoek A.N., Haines T.H., Deamer D.W. Permeation of protons, potassium ions, and small polar molecules through phospholipid bilayers as a function of membrane thickness. Biophys. J. 1996, 70:339-348.
23. Finkelstein A. Water and nonelectrolyte permeability of lipid bilayer membranes. J. Gen. Physiol. 1976, 68:127.
24. Honerkamp-Smith A.R., Veatch S.L., Keller S.L. An introduction to critical points for biophysicists; observations of compositional heterogeneity in lipid membranes. Biochim. Biophys. Acta (BBA) - Biomembr. 2009, 1788:53-63.
25. Semrau S., Schmidt T. Membrane heterogeneity-from lipid domains to curvature effects. Soft Matter 2009, 5:3174.
26. Munro S. Lipid rafts: elusive or illusive?. Cell 2003, 115:377-388.
27. Edidin M. Lipids on the frontier: a century of cell-membrane bilayers. Nat. Rev. Mol. Cell Biol. 2003, 4:414-418.
28. Kaiser H.-J., Lingwood D., Levental I., Sampaio J.L., Kalvodova L., Rajendran L., Simons K. Order of lipid phases in model and plasma membranes. Proc. Natl. Acad. Sci. USA 2009, 106:16645-16650.
29. Veatch S.L., Keller S.L. Organization in lipid membranes containing cholesterol. Phys. Rev. Lett. 2002, 89:268101.
30. Bagatolli L., Sunil Kumar P.B. Phase behavior of multicomponent membranes: experimental and computational techniques. Soft Matter 2009, 5:3234.
31. Veatch S.L., Keller S.L. Separation of liquid phases in giant vesicles of ternary mixtures of phospholipids and cholesterol. Biophys. J. 2003, 85:3074-3083.
32. Goñi F.M., Alonso A., Bagatolli L.A., Brown R.E., Marsh D., Prieto M., Thewalt J.L. Phase diagrams of lipid mixtures relevant to the study of membrane rafts. Biochim. Biophys. Acta (BBA) - Mol. Cell Biol. Lipids 2008, 1781:665-684.
33. Hamada T., Kishimoto Y., Nagasaki T., Takagi M. Lateral phase separation in tense membranes. Soft Matter 2011, 7:9061.
34. Ursell T.S., Klug W.S., Phillips R. Morphology and interaction between lipid domains. Proc. Natl. Acad. Sci. USA 2009, 106:13301-13306.
35. Simons K., Toomre D. Lipid rafts and signal transduction. Nat. Rev. Mol. Cell Biol. 2000, 1:31-39.
36. Simons K., Sampaio J.L. Membrane organization and lipid rafts. Cold Spring Harb. Perspect. Biol. 2011.
37. Simons K., Vaz W.L.C. Model systems, lipid rafts, and cell membranes. Ann. Rev. Biophys. Biomol. Struct. 2004, 33:269-295.
38. Simons K., Ikonen E. Functional rafts in cell membranes. Nature 1997, 387:569-572.
39. Käs J., Sackmann E. Shape transitions and shape stability of giant phospholipid vesicles in pure water induced by area-to-volume changes. Biophys. J. 1991, 60:825-844.
40. Hotani H. Transformation pathways of liposomes. J. Mol. Biol. 1984, 178:113-120.
41. Lipowsky R. The conformation of membranes. Nature 1991, 349:475.
42. Seifert U. Configurations of fluid membranes and vesicles. Adv. Phys. 1997, 46:13.
43. Devaux P.F. Static and dynamic lipid asymmetry in cell membranes. Biochemistry 1991, 30:1163-1173.
44. Slochower D.R., Wang Y.-H., Tourdot R.W., Radhakrishnan R., Janmey P.A. Counterion-mediated pattern formation in membranes containing anionic lipids. Adv. Colloid Interface Sci. 2014, 208:177-188.
45. Canham P.B. The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. J. Theoret. Biol. 1970, 26:61-81.
46. Helfrich W. Elastic properties of lipid bilayers: theory and possible experiments. Z. Naturforsch. C 1973, 28:1-12.
47. Landau L.D., Lifshitz E.M. Theory of Elasticity 1970, Pergamon Press, Oxford.
48. Woodka A.C., Butler P.D., Porcar L., Farago B., Nagao M. Lipid bilayers and membrane dynamics: insight into thickness fluctuations. Phys. Rev. Lett. 2012, 109:058102.
49. Jähnig F. What is the surface tension of a lipid bilayer membrane?. Biophys. J. 1996, 71:1348-1349.
50. do Carmo M.P. Differential Geometry of Curves and Surfaces 1976, Prentice Hall, Engelwood Cliffs, New Jersey.
51. Helfrich W. Effect of thermal undulations on the rigidity of fluid membranes and interfaces. J. Phys. France 1985, 46:1263-1268.
52. Peliti L., Leibler S. Effects of thermal fluctuations on systems with small surface tension. Phys. Rev. Lett. 1985, 54:1690-1693.
53. Föster D. On the scale dependence, due to thermal fluctuations, of the elastic properties of membranes. Phys. Lett. A 1986, 114:115-120.
54. Kleinert H. Thermal softening of curvature elasticity in membranes. Phys. Lett. 1986, 114A:263-268.
55. De Gennes P.G., Taupin C. Microemulsions and the flexibility of oil/water interfaces. J. Phys. Chem. 1982, 86:2294-2304.
56. Helfrich W. Size distributions of vesicles: the role of the effective rigidity of membranes. J. Phys. France 1986, 47:321-329.
57. Helfrich W. Measures of integration in calculating the effective rigidity of fluid surfaces. J. Phys. France 1987, 48:285-289.
58. Helfrich W. Stiffening of fluid membranes and entropy loss of membrane closure: Two effects of thermal undulations. Eur. Phys. J. B 1998, 1:481.
59. Pinnow H.A., Helfrich W. Effect of thermal undulations on the bending elasticity and spontaneous curvature of fluid membranes. Eur. Phys. J. E 2000, 3:149-157.
60. Marsh D. Renormalization of the tension and area expansion modulus in fluid membranes. Biophys. J. 1997, 73:865-869.
61. Marsh D. Elastic curvature constants of lipid monolayers and bilayers. Chem. Phys. Lipids 2006, 144:146-159.
62. Cai W., Lubensky T. Covariant hydrodynamics of fluid membranes. Phys. Rev. Lett. 1994, 73:1186-1189.
63. Cai W., Lubensky T. Hydrodynamics and dynamic fluctuations of fluid membranes. Phys. Rev. E 1995, 52:4251-4266.
64. Dill K.A., Bromberg S. Molecular Driving Forces 2003, Garland Science, New York.
65. David F., Leibler S. Vanishing tension of fluctuating membranes. J. Phys. II France 1991, 1:959-976.
66. Statistical Mechanics of Membranes and Surfaces 2003, World Scientific, Singapore. second ed. D. Nelson, T. Piran, S. Weinberg (Eds.).
67. Miao L., Seifert U., Wortis M., Döbereiner H.-G. Budding transitions of fluid-bilayer vesicles-the effect of area-difference elasticity. Phys. Rev. E 1994, 49:5389-5407.
68. Chaikin P.M., Lubensky T.C. Principles of Condensed Matter Physics 1995, Cambridge University Press, Cambridge, New York.
69. Reister-Gottfried E., Leitenberger S., Seifert U. Hybrid simulations of lateral diffusion in fluctuating membranes. Phys. Rev. E 2007, 75:011908.
70. Lin L.C.-L., Brown F.L. Brownian dynamics in fourier space: membrane simulations over long length and time scales. Phys. Rev. Lett. 2004, 93:256001.
71. Brown F.L.H. Elastic modeling of biomembranes and lipid bilayers. Annu. Rev. Phys. Chem. 2008, 59:685-712.
72. Evans E., Rawicz W. Entropy-driven tension and bending elasticity in condensed-fluid membranes. Phys. Rev. Lett. 1990, 64:2094-2097.
73. Evans E., Bowman H., Leung A., Needham D., Tirrell D. Biomembrane templates for nanoscale conduits and networks. Science 1996, 273:933-935.
74. Derényi I., Jülicher F., Prost J. Formation and interaction of membrane tubes. Phys. Rev. Lett. 2002, 88:238101.
75. Powers T., Huber G., Goldstein R. Fluid-membrane tethers: minimal surfaces and elastic boundary layers. Phys. Rev. E 2002, 65:041901.
76. Allain J.M., Storm C., Roux A., Amar M., Joanny J.F. Fission of a multiphase membrane tube. Phys. Rev. Lett. 2004, 93:158104.
77. Zhong-can O., Helfrich W. Bending energy of vesicle membranes: general expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders. Phys. Rev. A 1989, 39:5280-5288.
78. Jülicher F., Seifert U. Shape equations for axisymmetric vesicles: a clarification. Phys. Rev. E 1994, 49:4728-4731.
79. Jülicher F., Lipowsky R. Shape transformations of vesicles with intramembrane domains. Phys. Rev. E 1996, 53:2670-2683.
80. Seifert U., Berndl K., Lipowsky R. Shape transformations of vesicles: phase diagram for spontaneous- curvature and bilayer-coupling models. Phys. Rev. A 1991, 44:1182.
81. Gao H., Shi W., Freund L.B. Mechanics of receptor-mediated endocytosis. Proc. Natl. Acad. Sci. USA 2005, 102:9469-9474.
82. Liu Z.-L., Yao K.-L., Jing X.-B., Li X.-A., Sun X.-Z. Endocytic vesicle scission by lipid phase boundary forces. Proc. Natl. Acad. Sci. USA 2006, 103:10277-10282.
83. Liu J., Kaksonen M., Drubin D.G., Oster G. Endocytic vesicle scission by lipid phase boundary forces. Proc. Natl. Acad. Sci. USA 2006, 103:10277-10282.
84. Agrawal N.J., Nukpezah J., Radhakrishnan R. Minimal mesoscale model for protein-mediated vesiculation in clathrin-dependent endocytosis. PLoS Comput. Biol. 2010, 6:e1000926.
85. Brakke K.A. The surface evolver. Exp. Math. 1992, 1:141-165.
86. Dasgupta S., Auth T., Gompper G. Wrapping of ellipsoidal nano-particles by fluid membranes. Soft Matter 2013, 9:5473.
87. Dasgupta S., Auth T., Gompper G. Shape and orientation matter for the cellular uptake of nonspherical particles. Nano Lett. 2014, 14:687-693.
88. Lin L.C.-L., Brown F. Brownian dynamics in fourier space: membrane simulations over long length and time scales. Phys. Rev. Lett. 2004, 93:256001.
89. Lin L.C.-L., Brown F. Dynamic simulations of membranes with cytoskeletal interactions. Phys. Rev. E 2005, 72:011910.
90. Lin L.C.-L., Brown F.L.H. Simulating membrane dynamics in nonhomogeneous hydrodynamic environments. J. Chem. Theory Comput. 2006, 2:472-483.
91. Brown F.L.H. Simple models for biomembrane structure and dynamics. Comput. Phys. Comm. 2007, 177:172-175.
92. Sigurdsson J.K., Brown F.L.H., Atzberger P.J. Hybrid continuum-particle method for fluctuating lipid bilayer membranes with diffusing protein inclusions. J. Comput. Phys. 2013, 252:65-85.
93. Polyakov A.M. Quantum geometry of fermionic strings. Phys. Lett. B 1981, 103:207-210.
94. David F. Randomly triangulated surfaces in-2 dimensions. Phys. Lett. B 1985, 159:303-306.
95. Kazakov V.A., Kostov I.K., Migdahl A.A. Critical properties of randomly triangulated planar random surfaces. Phys. Lett. B 1985, 157:295-300.
96. Maritan A., Stella A.L. Some exact results from self-avoiding random surfaces. Nuclear Phys. B 1987, 280:561-575.
97. Kantor Y., Kardar M., Nelson D.R. Statistical mechanics of tethered surfaces. Phys. Rev. Lett. 1986, 57:791.
98. Kantor Y., Nelson D.R. Phase transitions in flexible polymeric surfaces. Phys. Rev. A 1987, 36:4020.
99. Ho J.-S., Baumgärtner A. Simulations of fluid self-avoiding membranes. Europhys. Lett. 1990, 12:295.
100. Ho J.-S., Baumgärtner A. Crumpling of fluid vesicles. Phys. Rev. A 1990, 41:5747-5750.
101. Ramakrishnan N., Sunil Kumar P.B., Ipsen J.H. Monte Carlo simulations of fluid vesicles with in-plane orientational ordering. Phys. Rev. E 2010, 81:041922.
102. Frenkel D., Smit B. Understanding Molecular Simulation: From Algorithms to Applications 2001, Academic Press. second ed.
103. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., Teller E. Equation of state calculations by fast computing machines. J. Chem. Phys. 1953, 21:1087-1092.
104. Kroll D., Gompper G. Scaling behavior of randomly triangulated self-avoiding surfaces. Phys. Rev. A 1992, 46:3119-3122.
105. Gompper G., Kroll D. Phase diagram and scaling behavior of fluid vesicles. Phys. Rev. E 1995, 51:514-525.
106. Paulose J., Vliegenthart G.A., Gompper G., Nelson D.R. Fluctuating shells under pressure. Proc. Natl. Acad. Sci. USA 2012, 109:19551-19556.
107. Drouffe J.M., Maggs A.C., Leibler S. Computer simulations of self-assembled membranes. Science 1991, 254:1353-1356.
108. Ayton G., Voth G. Bridging microscopic and mesoscopic simulations of lipid bilayers. Biophys. J. 2002, 83:3357-3370.
109. Noguchi H., Takasu M. Self-assembly of amphiphiles into vesicles: a Brownian dynamics simulation. Phys. Rev. E 2001, 64:041913.
110. Noguchi H., Takasu M. Adhesion of nanoparticles to vesicles: a Brownian dynamics simulation. Biophys. J. 2002, 83:299-308.
111. Farago O. "Water-free" computer model for fluid bilayer membranes. J. Chem. Phys. 2003, 119:596.
112. Cooke I.R., Deserno M. Solvent-free model for self-assembling fluid bilayer membranes: stabilization of the fluid phase based on broad attractive tail potentials. J. Chem. Phys. 2005, 123:4710.
113. Brannigan G., Brown F.L.H. Solvent-free simulations of fluid membrane bilayers. J. Chem. Phys. 2004, 120:1059.
114. Ayton G.S., McWhirter J.L., Voth G.A. A second generation mesoscopic lipid bilayer model: connections to field-theory descriptions of membranes and nonlocal hydrodynamics. J. Chem. Phys. 2006, 124:064906.
115. Noguchi H., Gompper G. Meshless membrane model based on the moving least-squares method. Phys. Rev. E 2006, 73:21903.
116. Kohyama T. Simulations of flexible membranes using a coarse-grained particle-based model with spontaneous curvature variables. Physica A 2009, 388:3334-3344.
117. Yuan H., Huang C., Li J., Lykotrafitis G., Zhang S. One-particle-thick, solvent-free, coarse-grained model for biological and biomimetic fluid membranes. Phys. Rev. E 2010, 82:011905.
118. Ayton G.S., Blood P.D., Voth G.A. Membrane remodeling from n-bar domain interactions: insights from multi-scale simulation. Biophys. J. 2007, 92:3595-3602.
119. Ayton G.S., Lyman E., Krishna V., Swenson R.D., Mim C., Unger V.M., Voth G.A. New insights into bar domain-induced membrane remodeling. Biophys. J. 2009, 97:1616-1625.
120. Cui H., Ayton G.S., Voth G.A. Membrane binding by the endophilin n-bar domain. Biophys. J. 2009, 97:2746-2753.
121. Cui H., Lyman E., Voth G.A. Mechanism of membrane curvature sensing by amphipathic helix containing proteins. Biophys. J. 2011, 100:1271-1279.
122. Lyman E., Cui H., Voth G.A. Reconstructing protein remodeled membranes in molecular detail from mesoscopic models. Phys. Chem. Chem. Phys. 2011, 13:10430-10436.
123. Ayton G.S., Tepper H.L., Mirijanian D.T., Voth G.A. A new perspective on the coarse-grained dynamics of fluids. J. Chem. Phys. 2004, 120:4074.
124. Tobias D.J., Tu K., Klein M.L. Atomic-scale molecular dynamics simulations of lipid membranes. Curr. Opin. Colloid Interface Sci. 1997, 2:15-26.
125. Tieleman D.P., Marrink S.-J., Berendsen H.J. A computer perspective of membranes: molecular dynamics studies of lipid bilayer systems. Biochim. Biophys. Acta (BBA) - Rev. Biomembr. 1997, 1331:235-270.
126. Feller S.E. Molecular dynamics simulations of lipid bilayers. Curr. Opin. Colloid Interface 2000, 5:217-223.
127. Marrink S.-J., de Vries A.H., Tieleman D.P. Lipids on the move: simulations of membrane pores, domains, stalks and curves. Biochim. Biophys. Acta (BBA) - Biomembr. 2009, 1788:149-168.
128. van der Ploeg P. Molecular dynamics simulation of a bilayer membrane. J. Chem. Phys. 1982, 76:3271-3276.
129. Heller H., Schaefer M., Schulten K. Molecular dynamics simulation of a bilayer of 200 lipids in the gel and in the liquid crystal phase. J. Phys. Chem. 1993, 97:8343-8360.
130. Tu K., Tobias D.J., Blasie J.K., Klein M.L. Molecular dynamics investigation of the structure of a fully hydrated gel-phase dipalmitoylphosphatidylcholine bilayer. Biophys. J. 1996.
131. Tieleman D.P., Berendsen H.J.C. Molecular dynamics simulations of a fully hydrated dipalmitoylphosphatidylcholine bilayer with different macroscopic boundary conditions and parameters. J. Chem. Phys. 1996, 105:4871.
132. Berger O., Edholm O., Jähnig F. Molecular dynamics simulations of a fluid bilayer of dipalmitoylphosphatidylcholine at full hydration, constant pressure, and constant temperature. Biophys. J. 1997.
133. Marrink S.-J., Berger O., Tieleman P., Jähnig F. Adhesion forces of lipids in a phospholipid membrane studied by molecular dynamics simulations. Biophys. J. 1998, 74:931-943.
134. Pasenkiewicz-Gierula M., Róg T., Kitamura K., Kusumi A. Cholesterol effects on the phosphatidylcholine bilayer polar region: a molecular simulation study. Biophys. J. 2000, 78:1376-1389.
135. Mashl R.J., Scott H.L., Subramaniam S., Jakobsson E. Molecular simulation of dioleoylphosphatidylcholine lipid bilayers at differing levels of hydration. Biophys. J. 2001, 81:3005-3015.
136. Murzyn K., Rog T., Jezierski G., Takaoka Y., Pasenkiewicz-Gierula M. Effects of phospholipid unsaturation on the membrane/water interface: a molecular simulation study. Biophys. J. 2001, 81:170.
137. Marrink S.-J., Mark A.E. Molecular dynamics simulation of the formation, structure, and dynamics of small phospholipid vesicles. J. Amer. Chem. Soc. 2003, 125:15233-15242.
138. Hofsäß C., Lindahl E., Edholm O. Molecular dynamics simulations of phospholipid bilayers with cholesterol. Biophys. J. 2003, 84:2192.
139. de Vries A.H., Mark A.E., Marrink S.-J. Molecular dynamics simulation of the spontaneous formation of a small dppc vesicle in water in atomistic detail. J. Amer. Chem. Soc. 2004.
140. Leontiadou H., Mark A.E., Marrink S.-J. Molecular dynamics simulations of hydrophilic pores in lipid bilayers. Biophys. J. 2004, 86:2156-2164.
141. Marrink S.-J., Mark A.E. The mechanism of vesicle fusion as revealed by molecular dynamics simulations. J. Amer. Chem. Soc. 2003.
142. Sum A.K., Faller R., de Pablo J.J. Molecular simulation study of phospholipid bilayers and insights of the interactions with disaccharides. Biophys. J. 2003, 85:2830-2844.
143. Edholm O., Berger O., Jähnig F. Structure and fluctuations of bacteriorhodopsin in the purple membrane: a molecular dynamics study. J. Mol. Biol. 1995.
144. Pitman M.C., Grossfield A., Suits F., Feller S.E. Role of cholesterol and polyunsaturated chains in lipidprotein interactions: molecular dynamics simulation of rhodopsin in a realistic membrane environment. J. Amer. Chem. Soc. 2005, 127:4576-4577.
145. Sansom M.S.P., Bond P.J., Deol S.S., Grottesi A., Haider S., Sands Z.A. Molecular simulations and lipid-protein interactions: potassium channels and other membrane proteins. Biochem. Soc. Trans. 2005, 33:916.
146. Lindahl E., Sansom M. Membrane proteins: molecular dynamics simulations. Curr. Opin. Struct. Biol. 2008, 18:425-431.
147. de Meyer F.J.-M., Venturoli M., Smit B. Molecular simulations of lipid-mediated protein-protein interactions. Biophys. J. 2008, 95:1851-1865.
148. Lagüe P., Roux B., Pastor R.W. Molecular dynamics simulations of the influenza hemagglutinin fusion peptide in micelles and bilayers: conformational analysis of peptide and lipids. J. Mol. Biol. 2005.
149. Doi M., Edwards S.F. The Theory of Polymer Dynamics 1988, Oxford University Press, Oxford, UK.
150. Goetz R., Lipowsky R. Computer simulations of bilayer membranes: self-assembly and interfacial tension. J. Chem. Phys. 1998, 108:7397-7409.
151. Stevens M.J. Coarse-grained simulations of lipid bilayers. J. Chem. Phys. 2004, 121:11942-11948.
152. Lyubartsev A.P. Multiscale modeling of lipids and lipid bilayers. Eur. Biophys. J. 2005, 35:53-61.
153. Praprotnik M., Delle Site L., Kremer K. Multiscale simulation of soft matter: from scale bridging to adaptive resolution. Annu. Rev. Phys. Chem. 2008, 59:545-571.
154. Peter C., Kremer K. Multiscale simulation of soft matter systems-from the atomistic to the coarse-grained level and back. Soft Matter 2009.
155. Peter C., Kremer K. Multiscale simulation of soft matter systems. Faraday Discuss. 2009, 144:9-24.
156. Murtola T., Falck E., Patra M., Karttunen M., Vattulainen I. Coarse-grained model for phospholipid/cholesterol bilayer. J. Chem. Phys. 2004, 121:9156.
157. Murtola T., Falck E., Karttunen M., Vattulainen I. Coarse-grained model for phospholipid/cholesterol bilayer employing inverse Monte Carlo with thermodynamic constraints. J. Chem. Phys. 2007, 126:075101.
158. Shih A.Y., Arkhipov A., Freddolino P.L., Schulten K. Coarse grained proteinlipid model with application to lipoprotein particles. J. Phys. Chem. B 2006, 110:3674-3684.
159. Arkhipov A., Yin Y., Schulten K. Four-scale description of membrane sculpting by bar domains. Biophys. J. 2008, 95:2806-2821.
160. Yin Y., Arkhipov A., Schulten K. Simulations of membrane tubulation by lattices of amphiphysin n-bar domains. Structure 2009, 17:882-892.
161. Izvekov S., Voth G.A. Multiscale coarse graining of liquid-state systems. J. Chem. Phys. 2005, 123:134105.
162. Noid W.G., Chu J.-W., Ayton G.S., Krishna V., Izvekov S., Voth G.A., Das A., Andersen H.C. The multiscale coarse-graining method. i. A rigorous bridge between atomistic and coarse-grained models. J. Chem. Phys. 2008, 128:244114.
163. Marrink S.-J., de Vries A.H., Mark A.E. Coarse grained model for semiquantitative lipid simulations. J. Phys. Chem. B 2004, 108:750-760.
164. Marrink S.-J., Risselada H.J., Yefimov S., Tieleman D.P., de Vries A.H. The martini force field: Coarse grained model for biomolecular simulations. J. Phys. Chem. B 2007, 111:7812-7824.
165. Monticelli L., Kandasamy S.K., Periole X., Larson R.G., Tieleman D.P., Marrink S.-J. The martini coarse-grained force field: extension to proteins. J. Chem. Theory Comput. 2008, 4:819-834.
166. Reynwar B.J., Illya G., Harmandaris V.A., Muller M.M., Kremer K., Deserno M. Aggregation and vesiculation of membrane proteins by curvature-mediated interactions. Nature 2007, 447:461-464.
167. Shillcock J.C. Insight or illusion? Seeing inside the cell with mesoscopic simulations. HFSP J. 2008, 2:1-6.
168. Shillcock J.C. Vesicles and vesicle fusion: coarse-grained simulations. Methods Mol. Biol. 2013, 924:659-697.
169. Vácha R., Martinez-Veracoechea F.J., Frenkel D. Intracellular release of endocytosed nanoparticles upon a change of ligand-receptor interaction. ACS Nano 2012, 6:10598-10605.
170. Klein M., Shinoda W. Large-scale molecular dynamics simulations of self-assembling systems. Science 2008, 321:798-800.
171. Henderson D. Fundamentals of Inhomogeneous Fluids 1992, CRC Press.
172. Schofield P., Henderson J.R. Statistical mechanics of inhomogeneous fluids. Proc. R. Soc. Lond. Ser. A 1982, 379:231.
173. Walton J., Gubbins K.E. The pressure tensor in an inhomogeneous fluid of non-spherical molecules. Mol. Phys. 1985.
174. Rossi G., Testa M. The stress tensor in thermodynamics and statistical mechanics. J. Chem. Phys. 2009.
175. Irving J., Kirkwood J. The statistical mechanical theory of transport processes. The equations of hydrodynamics. J. Chem. Phys. 1950, 18:817.
176. Varnik F., Baschnagel J., Binder K. Molecular dynamics results on the pressure tensor of polymer films. J. Chem. Phys. 2000, 113:4444.
177. Venturoli M., MaddalenaSperotto M., Kranenburg M., Smit B. Mesoscopic models of biological membranes. Phys. Rep. 2006, 437:1-54.
178. Ollila O.H.S., Risselada H.J., Louhivuori M., Lindahl E., Vattulainen I., Marrink S.-J. 3d pressure field in lipid membranes and membrane-protein complexes. Phys. Rev. Lett. 2009, 102:078101.
179. Jakobsen A.F., Mouritsen O.G., Besold G. Artifacts in dynamical simulations of coarse-grained model lipid bilayers. J. Chem. Phys. 2005, 122:204901.
180. Venturoli M., Sperotto M.M., Kranenburg M. Mesoscopic models of biological membranes. Phys. Rep. 2006.
181. Grafmuller A., Shillcock J., Lipowsky R. Pathway of membrane fusion with two tension dependent energy barriers. Phys. Rev. Lett. 2007, 98:218107.
182. Safran S.A. Curvature elasticity of thin films. Adv. Phys. 1999, 48:395-448.
183. Szleifer I., Kramer D., Benshaul A., Gelbart W.M., Safran S.A. Molecular theory of curvature elasticity in surfactant films. J. Chem. Phys. 1990, 92:6800-6817.
184. Goetz R., Lipowsky R. Computer simulations of bilayer membranes: self-assembly and interfacial tension. J. Chem. Phys. 1998, 108:7397.
185. Farago O., Pincus P. Statistical mechanics of bilayer membrane with a fixed projected area. J. Chem. Phys. 2004, 120:2934-2950.
186. Hu M., de Jong D.H., Marrink S.-J., Deserno M. Gaussian curvature elasticity determined from global shape transformations and local stress distributions: a comparative study using the martini model. Faraday Discuss. 2012, 161:365-382.
187. Hu M., Briguglio J.J., Deserno M. Determining the Gaussian curvature modulus of lipid membranes in simulations. Biophys. J. 2012, 102:1403-1410.
188. Hu M., Diggins P., Deserno M. Determining the bending modulus of a lipid membrane by simulating buckling. J. Chem. Phys. 2013, 138:214110.
189. Shibata Y., Hu J., Kozlov M.M., Rapoport T.A. Mechanisms shaping the membranes of cellular organelles. Ann. Rev. Cell Dev. Biol. 2009, 25:329-354.
190. Kozlov M.M. Biophysics: joint effort bends membrane. Nature 2010, 463:439-440.
191. Zimmerberg J., Kozlov M.M. How proteins produce cellular membrane curvature. Nat. Rev. Mol. Cell Biol. 2006, 7:9-19.
192. Wiggins P., Phillips R. Analytic models for mechanotransduction: gating a mechanosensitive channel. Proc. Natl. Acad. Sci. USA 2004, 101:4071-4076.
193. Aimon S., Callan-Jones A., Berthaud A., Pinot M., Toombes G.E.S., Bassereau P. Membrane shape modulates transmembrane protein distribution. Dev. Cell 2014, 28:212-218.
194. Praefcke G.J.K., McMahon H.T. The dynamin superfamily: universal membrane tubulation and fission molecules?. Nat. Rev. Mol. Cell Biol. 2004, 5:133-147.
195. Shibata Y., Voss C., Rist J.M., Hu J., Rapoport T.A., Prinz W.A., Voeltz G.K. The reticulon and Dp1/Yop1p proteins form immobile oligomers in the tubular endoplasmic reticulum. J. Biol. Chem. 2008, 283:18892-18904.
196. Hu J., Shibata Y., Voss C., Shemesh T., Li Z., Coughlin M., Kozlov M.M., Rapoport T.A., Prinz W.A. Membrane proteins of the endoplasmic reticulum induce high-curvature tubules. Science 2008, 319:1247-1250.
197. Campelo F., McMahon H., Kozlov M. The hydrophobic insertion mechanism of membrane curvature generation by proteins. Biophys. J. 2008, 95:2325.
198. Dawson J.C., Legg J.A., Machesky L.M. Bar domain proteins: a role in tubulation, scission and actin assembly in clathrin-mediated endocytosis. Trends Cell Biol. 2006, 16:493-498.
199. Farsad K., Ringstad N., Takei K., Floyd S.R., Rose K., Camilli P.D. Generation of high curvature membranes mediated by direct endophilin bilayer interactions. J. Cell Biol. 2001, 155:193-200.
200. Peter B.J., Kent H.M., Mills I.G., Vallis Y., Butler P.J.G., Evans P.R., McMahon H.T. Bar domains as sensors of membrane curvature: the amphiphysin bar structure. Science 2004, 303:495-499.
201. Habermann B. The bar-domain family of proteins: a case of bending and binding?. EMBO Rep. 2004, 5:250-255.
202. Frost A., Unger V.M., de Camilli P. The bar domain superfamily: membrane-molding macromolecules. Cell 2009, 137:191-196.
203. Gallop J.L., Jao C.C., Kent H.M., Butler P.J.G., Evans P.R., Langen R., McMahon H.T. Mechanism of endophilin n-bar domain-mediated membrane curvature. EMBO J. 2006, 25:2898-2910.
204. Henne W.M., Kent H.M., Ford M.G.J., Hegde B.G., Daumke O., Butler P.J.G., Mittal R., Langen R., Evans P.R., McMahon H.T. Structure and analysis of fcho2 f-bar domain: a dimerizing and membrane recruitment module that effects membrane curvature. Structure 2007, 15:839-852.
205. Frost A., de Camilli P., Unger V.M. F-bar proteins join the bar family fold. Structure 2007, 15:751-753.
206. Frost A., Perera R., Roux A., Spasov K., Destaing O., Egelman E.H., de Camilli P., Unger V.M. Structural basis of membrane invagination by f-bar domains. Cell 2008, 132:807-817.
207. Ahmed S., Goh W.I., Bu W. I-bar domains, irsp53 and filopodium formation. Semin. Cell Dev. Biol. 2010, 21:350-356.
208. Weissenhorn W. Crystal structure of the endophilin-a1 bar domain. J. Mol. Biol. 2005, 351:653-661.
209. Huttner W., Schmidt A. Membrane curvature: a case of endofeelin'. Trends Cell Biol. 2002, 12:155-158.
210. Masuda M., Takeda S., Sone M., Ohki T., Mori H., Kamioka Y., Mochizuki N. Endophilin bar domain drives membrane curvature by two newly identified structure-based mechanisms. EMBO J. 2006, 25:2889-2897.
211. Zimmerberg J., McLaughlin S. Membrane curvature: how bar domains bend bilayers. Curr. Biol. 2004, 14:R250-R252.
212. Blood P.D., Voth G.A. Direct observation of bin/amphiphysin/rvs (bar) domain-induced membrane curvature by means of molecular dynamics simulations. Proc. Natl. Acad. Sci. USA 2006, 103:15068-15072.
213. Arkhipov A., Yin Y., Schulten K. Four-scale description of membrane sculpting by bar domains. Biophys. J. 2008, 95:2806-2821.
214. Arkhipov A., Yin Y., Schulten K. Membrane-bending mechanism of amphiphysin n-bar domains. Biophys. J. 2009, 97:2727-2735.
215. Collins R.N. How the er stays in shape. Cell 2006, 124:464-466.
216. McMahon H.T., Gallop J.L. Membrane curvature and mechanisms of dynamic cell membrane remodelling. Nature 2005, 438:590-596.
217. Shibata Y., Voeltz G.K., Rapoport T.A. Rough sheets and smooth tubules. Cell 2006, 126:435-439.
218. Shibata Y., Shemesh T., Prinz W.A., Kozlov M.M., Rapoport T.A. Mechanisms determining the morphology of the peripheral er. Cell 2010, 143:774-788.
219. Graham T.R., Kozlov M.M. Interplay of proteins and lipids in generating membrane curvature. Curr. Opin. Cell Biol. 2010, 22:430-436.
220. Bahrami A.H., Lipowsky R., Weikl T.R. Tubulation and aggregation of spherical nanoparticles adsorbed on vesicles. Phys. Rev. Lett. 2012, 109:188102.
221. Šarić A., Cacciuto A. Mechanism of membrane tube formation induced by adhesive nanocomponents. Phys. Rev. Lett. 2012, 109:188101.
222. Zhang S., Nelson A., Beales P.A. Freezing or wrapping: the role of particle size in the mechanism of nanoparticle-biomembrane interaction. Langmuir 2012, 28:12831-12837.
223. Zhang P., Hinshaw J.E. Three-dimensional reconstruction of dynamin in the constricted state. Nat. Cell Biol. 2001, 3:922-926.
224. Roux A., Koster G., Lenz M., Sorre B., Manneville J.-B., Nassoy P., Bassereau P. Membrane curvature controls dynamin polymerization. Proc. Natl. Acad. Sci. USA 2010, 107:4141-4146.
225. Morlot S., Lenz M., Prost J., Joanny J.-F., Roux A. Deformation of dynamin helices damped by membrane friction. Biophys. J. 2010, 99:3580-3588.
226. Blood P., Swenson R., Voth G. Factors influencing local membrane curvature induction by n-bar domains as revealed by molecular dynamics simulations. Biophys. J. 2008, 95:1866-1876.
227. Kranenburg M., Smit B. Phase behavior of model lipid bilayers. J. Phys. Chem. B 2005, 109:6553-6563.
228. Smith G.S., Sirota E.B., Safinya C.R., Clark N.A. Structure of the lβ phases in a hydrated phosphatidylcholine multimembrane. Phys. Rev. Lett. 1988, 60:813.
229. Smith G.S., Sirota E.B., Safinya C.R., Plano R.J., Clark N.A. X-ray structural studies of freely suspended ordered hydrated DMPC multimembrane films. J. Chem. Phys. 1990, 92:4519-4529.
230. Tardieu A., Luzzati V., Reman F.C. Structure and polymorphism of the hydrocarbon chains of lipids: a study of lecithin-water phases. J. Mol. Biol. 1973, 75:711-718.
231. Selinger J., Spector M., Schnur J. Theory of self-assembled tubules and helical ribbons. J. Phys. Chem. B 2001, 105:7157-7169.
232. Sarasij R., Mayor S., Rao M. Chirality-induced budding: a raft-mediated mechanism for endocytosis and morphology of caveolae?. Biophys. J. 2007, 92:3140.
233. Harris A.B., Kamien R.D., Lubensky T.C. Molecular chirality and chiral parameters. Rev. Modern Phys. 1999, 71:1745.
234. Helfrich W., Prost J. Intrinsic bending force in anisotropic membranes made of chiral molecules. Phys. Rev. A 1988, 38:3065.
235. Nelson P., Powers T. Rigid chiral membranes. Phys. Rev. Lett. 1992, 69:3409-3412.
236. Selinger J.V., Schnur J.M. Theory of chiral lipid tubules. Phys. Rev. Lett. 1993, 71:4091.
237. Schnur J.M. Lipid tubules: a paradigm for molecularly engineered structures. Science 1993, 262:1669-1676.
238. Kralj-Iglic V., Iglic A., Gomiscek G., Sevsek F., Arrigler V., Hägerstrand H. Microtubes and nanotubes of a phospholipid bilayer membrane. J. Phys. A 2002, 35:1533-1549.
239. Oda R., Huc I., Candau S. Gemini surfactants, the effect of hydrophobic chain length and dissymmetry. Chem. Commun. 1997, 2105-2106.
240. Groves J.T. Bending mechanics and molecular organization in biological membranes. Annu. Rev. Phys. Chem. 2007, 58:697-717.
241. Neto J.C., Agero U., Gazzinelli R.T., Mesquita O.N. Measuring optical and mechanical properties of a living cell with defocusing microscopy. Biophys. J. 2006, 91:1108-1115.
242. Marguet D., Lenne P.F., Rigneault H., He H.T. Dynamics in the plasma membrane: how to combine fluidity and order. Embo J. 2006, 25:3446-3457.
243. Sorre B., Callan-Jones A., Manneville J.-B., Nassoy P., Joanny J.-F., Prost J., Goud B., Bassereau P. Curvature-driven lipid sorting needs proximity to a demixing point and is aided by proteins. Proc. Natl. Acad. Sci. USA 2009, 106:5622-5626.
244. Sorre B., Callan-Jones A., Manzi J., Goud B., Prost J., Bassereau P., Roux A. Nature of curvature coupling of amphiphysin with membranes depends on its bound density. Proc. Natl. Acad. Sci. USA 2012, 109:173-178.
245. Tian A., Baumgart T. Sorting of lipids and proteins in membrane curvature gradients. Biophys. J. 2009, 96:2676-2688.
246. Tian A., Capraro B.R., Esposito C., Baumgart T. Bending stiffness depends on curvature of ternary lipid mixture tubular membranes. Biophys. J. 2009, 97:1636-1646.
247. Heinrich M., Tian A., Esposito C., Baumgart T. Dynamic sorting of lipids and proteins in membrane tubes with a moving phase boundary. Proc. Natl. Acad. Sci. USA 2010, 107:7208-7213.
248. Seifert U. Curvature-induced lateral phase segregation in two-component vesicles. Phys. Rev. Lett. 1993, 70:1335-1338.
249. Capraro B.R., Yoon Y., Cho W., Baumgart T. Curvature sensing by the epsin n-terminal homology domain measured on cylindrical lipid membrane tethers. J. Am. Chem. Soc. 2010, 132:1200-1201.
250. Mim C., Cui H., Gawronski-Salerno J.A., Frost A., Lyman E., Voth G.A., Unger V.M. Structural basis of membrane bending by the n-bar protein endophilin. Cell 2012, 149:137-145.
251. Marino M., Moon K.-H., Hinshaw J.E. The role of dynamin in membrane constriction revealed by cryo-em. Microsc. Microanal. 2005, 11.
252. Baumgart T., Capraro B.R., Zhu C., Das S.L. Thermodynamics and mechanics of membrane curvature generation and sensing by proteins and lipids. Annu. Rev. Phys. Chem. 2011, 62:483-506.
253. Jiang H., Powers T. Curvature-driven lipid sorting in a membrane tubule. Phys. Rev. Lett. 2008, 101:018103.
254. Singh P., Mahata P., Baumgart T., Das S.L. Curvature sorting of proteins on a cylindrical lipid membrane tether connected to a reservoir. Phys. Rev. E 2012, 85:051906.
255. Zhu C., Das S.L., Baumgart T. Nonlinear sorting, curvature generation, and crowding of endophilin n-bar on tubular membranes. Biophys. J. 2012, 102:1837-1845.
256. Sunil Kumar P.B., Gompper G., Lipowsky R. Modulated phases in multicomponent fluid membranes. Phys. Rev. E 1999, 60:4610-4618.
257. Sunil Kumar P.B., Gompper G., Lipowsky R. Budding dynamics of multicomponent membranes. Phys. Rev. Lett. 2001, 86:3911-3914.
258. Ramakrishnan N., Sunil Kumar P.B., Ipsen J.H. Membrane-mediated aggregation of curvature-inducing nematogens and membrane tubulation. Biophys. J. 2013, 104:1018-1028.
259. Ramakrishnan N., Ipsen J.H., Sunil Kumar P.B. Role of disclinations in determining the morphology of deformable fluid interfaces. Soft Matter 2012, 8:3058.
260. Liu J., Tourdot R., Ramanan V., Agrawal N.J., Radhakrishanan R. Mesoscale simulations of curvature-inducing protein partitioning on lipid bilayer membranes in the presence of mean curvature fields. Mol. Phys. 2012, 110:1127-1137.
261. Ramanan V., Agrawal N.J., Liu J., Engles S., Toy R., Radhakrishnan R. Systems biology and physical biology of clathrin-mediated endocytosis. Integr. Biol. 2011, 3:803.
262. Gov N. Diffusion in curved fluid membranes. Phys. Rev. E 2006, 73:041918.
263. Divet F., Danker G., Misbah C. Fluctuations and instability of a biological membrane induced by interaction with macromolecules. Phys. Rev. E 2005, 72:041901.
264. Naji A., Brown F. Diffusion on ruffled membrane surfaces. J. Chem. Phys. 2007, 126:235103-235106.
265. Reister-Gottfried E., Leitenberger S.M., Seifert U. Hybrid simulations of lateral diffusion in fluctuating membranes. Phys. Rev. E 2007, 75:11908-11911.
266. Atilgan E., Sun S.X. Shape transitions in lipid membranes and protein mediated vesicle fusion and fission. J. Chem. Phys. 2007, 126:095102.
267. Weinstein J., Radhakrishnan R. A coarse-grained methodology for simulating interfacial dynamics in complex fluids: application to protein mediated membrane processes. Mol. Phys. 2006, 104:3653-3666.
268. Agrawal N.J., Weinstein J., Radhakrishnan R. Landscape of finite-temperature equilibrium behaviour of curvature-inducing proteins on a bilayer membrane explored using a linearized elastic free energy model. Mol. Phys. 2008, 106:1913-1923.
269. Chou T., Kim K.S., Oster G. Statistical thermodynamics of membrane bending-mediated protein-protein attractions. Biophys. J. 2001, 80:1075-1087.
270. Grabe M., Neu J., Oster G., Nollert P. Protein interactions and membrane geometry. Biophys. J. 2003, 84:854-868.
271. Kim K.S., Neu J., Oster G. Curvature-mediated interactions between membrane proteins. Biophys. J. 1998, 75:2274-2291.
272. Dan N., Derman A., Pincus P., Safran S. Membrane-induced interactions between inclusions. J. Physique II 1994, 4:1713-1725.
273. Wallace E.J., Hooper N.M., Olmsted P.D. The kinetics of phase separation in asymmetric membranes. Biophys. J. 2005, 88:4072-4083.
274. Aranda-Espinoza H., Berman A., Dan N., Pincus P., Safran S. Interaction between inclusions embedded in membranes. Biophys. J. 1996, 71:648-656.
275. Berman A., Pincus P., Safran S.A. Membrane-induced interactions between inclusions. J. Physique II 1994, 4:1713-1725.
276. Dan N., Pincus P., Safran S.A. Membrane-induced interactions between inclusions. Langmuir 1993, 9:2768-2771.
277. Goulian M., Bruinsma R., Pincus P. Long-range forces in heterogeneous fluid membranes. Europhys. Lett. 2007, 22:145-150.
278. Golestanian R., Goulian M., Kardar M. Fluctuation-induced interactions between rods on a membrane. Phys. Rev. E 1996, 54:6725-6734.
279. Goulian M. Inclusions in membranes. Curr. Opin. Colloid Interface Sci. 1996, 1:358.
280. Goulian M., Libchaber A. A new technique for probing inter-membrane interactions. J. Gen. Physiol. 1996, 107:311-312.
281. Zhao Y., Liu J., Yang C., Capraro B.R., Baumgart T., Bradley R.P., Ramakrishnan N., Xu X., Radhakrishnan R., Svitkina T., Guo W. Exo70 generates membrane curvature for morphogenesis and cell migration. Dev. Cell 2013, 26:266-278.
282. Kozlov M.M. Biophysics: bending over to attract. Nature 2007, 447:387-389.
283. Agrawal N., Radhakrishnan R. Calculation of free energies in fluid membranes subject to heterogeneous curvature fields. Phys. Rev. E 2009, 80:011925.
284. Weikl T.R. Fluctuation-induced aggregation of rigid membrane inclusions. Europhys. Lett. 2001, 54:547.
285. Lee S.-J.E., Hori Y., Groves J.T., Dustin M.L., Chakraborty A.K. The synapse assembly model. Trends Immunol. 2002, 23:500-502.
286. Liu J., Agrawal N., Eckmann D., Ayyaswamy P., Radhakrishnan R. Top-down mesocale models and free energy calculations of multivalent protein-protein and protein-membrane interactions in nanocarrier adhesion and receptor trafficking. Innovations in Biomolecular Modeling and Simulations 2012, 272-287. Royal Society of Chemistry, Cambridge UK. T. Schlick (Ed.).
287. Iglic A., Babnik B., Bohinc K., Fosnaric M., Hagerstrand H., Kralj-Iglic V. On the role of anisotropy of membrane constituents in formation of a membrane neck during budding of a multicomponent membrane. J. Biomech. 2007, 40:579-585.
288. Bohinc K., Lombardo D., Kraljiglic V., Fosnaric M., May S., Pernus F., Hagerstrand H., Iglic A. Shape variation of bilayer membrane daughter vesicles induced by anisotropic membrane inclusions. Cell Mol. Biol. Lett. 2006, 11:90-101.
289. Leibler S., Andelman D. Ordered and curved meso-structures in membranes and amphiphilic films. J. Phys. France 1987, 48:2013-2018.
290. Leibler S. Curvature instability in membranes. J. Phys. France 1986, 47:507-516.
291. Lipowsky R. Budding of membranes induced by intramembrane domains. J. Physique II 1992, 2:1825-1840.
292. Jülicher F., Lipowsky R. Domain-induced budding of vesicles. Phys. Rev. Lett. 1993, 70:2964-2967.
293. Sunil Kumar P.B., Rao M. Shape instabilities in the dynamics of a two-component fluid membrane. Phys. Rev. Lett. 1998, 80:2489-2492.
294. Kohyama T., Kroll D.M., Gompper G. Budding of crystalline domains in fluid membranes. Phys. Rev. E 2003, 68:061905.
295. Hui S.W., Sen A. Effects of lipid packing on polymorphic phase behavior and membrane properties. Proc. Natl. Acad. Sci. USA 1989, 86:5825-5829.
296. Döbereiner H.-G., Selchow O., Lipowsky R. Spontaneous curvature of fluid vesicles induced by trans-bilayer sugar asymmetry. Eur. Biophys. J. 1999, 28:174-178.
297. Markowitz M., Singh A. Self-assembling properties of 1,2-diacyl-sn-glycero-3-phosphohyroxyethanol-a headgroup modified diacetylenic phospholipd. Langmuir 1991, 7:16-18.
298. Fournier J.-B. Nontopological saddle-splay and curvature instabilities from anisotropic membrane inclusions. Phys. Rev. Lett. 1996, 76:4436-4439.
299. Fournier J.-B., Galatola P. Bilayer membranes with 2d-nematic order of the surfactant polar heads. Braz. J. Phys. 1998, 28:329.
300. Hinshaw J.E. Dynamin and its role in membrane fission. Annu. Rev. Cell Dev. Biol. 2000, 16:483-519.
301. Praefcke G.J.K., McMahon H.T. The dynamin superfamily: universal membrane tubulation and fission molecules?. Nature 2004, 5:133-147.
302. Voeltz G.K., Prinz W.A., Shibata Y., Rist J.M., Rapoport T.A. A class of membrane proteins shaping the tubular endoplasmic reticulum. Cell 2006, 124:573-586.
303. Dawson J.C., Legg J.A., Machesky L.M. Bar domain proteins: a role in tubulation, scission and actin assembly in clathrin-mediated endocytosis. Trends Cell Biol. 2006, 16:493-498.
304. Lopez-Leon T., Koning V., Devaiah K.B.S., Vitelli V., Fernandez-Nieves A. Frustrated nematic order in spherical geometries. Nat. Phys. 2011, 7:391.
305. Ramakrishnan N., Sunil Kumar P.B., Ipsen J.H. Modeling anisotropic elasticity of fluid membranes. Macromol. Theory Simul. 2011, 20:446-450.
306. Lebwohl P.A., Lasher G. Nematic-liquid-crystal order-Monte-Carlo calculation. Phys. Rev. A 1972, 6:426-429.
307. Frank J.R., Kardar M. Defects in nematic membranes can buckle into pseudospheres. Phys. Rev. E 2008, 77:41705.
308. De Gennes P.G., Prost J. The Physics of Liquid Crystals, The International Series of Monographs on Physics 1993, Clarendon Press, Oxford.
309. Lubensky T., Prost J. Orientational order and vesicle shape. J. Phys. II France 1992, 2:371-382.
310. Dijkstra E.W. A note on two problems in connexion with graphs. Numer. Math. 1959, 1:269-271.
311. Bowick M., Giomi L. Two-dimensional matter: order, curvature and defects. Adv. Phys. 2009, 58:449.
312. Vitelli V., Nelson D.R. Nematic textures in spherical shells. Phys. Rev. E 2006, 74:21711.
313. Ramakrishnan N. Effect of in-plane order and activity on vesicular morphology 2012, (Ph.D. thesis), Indian Institute of Technology Madras, Chennai.
314. Sweitzer S.M., Hinshaw J.E. Dynamin undergoes a gtp-dependent conformational change causing vesiculation. Cell 1998, 93:1021-1029.
315. Hinshaw J.E. Dynamin and its role in membrane fission. Ann. Rev. Cell Dev. Biol. 2000, 16:483-519.
316. Roux A., Koster G., Lenz M., Sorre B., Manneville J.-B., Nassoy P., Bassereau P. Membrane curvature controls dynamin polymerization. Proc. Natl. Acad. Sci. USA 2010, 107:4141-4146.
317. Ayton G.S., Blood P.D., Voth G.A. Membrane remodeling from n-bar domain interactions: insights from multi-scale simulation. Biophys. J. 2007, 92:3595-3602.
318. Noguchi H., Gompper G. Fluid vesicles with viscous membranes in shear flow. Phys. Rev. Lett. 2004, 93:258102.
319. Noguchi H., Gompper G. Vesicle dynamics in shear and capillary flows. J. Phys.: Condens. Matter. 2005, 17:3439.
320. Noguchi H., Gompper G. Shape transitions of fluid vesicles and red blood cells in capillary flows. Proc. Natl. Acad. Sci. USA 2005, 102:14159-14164.
321. Lyman E., Cui H., Voth G.A. Reconstructing protein remodeled membranes in molecular detail from mesoscopic models. Phys. Chem. Chem. Phys. 2011, 13:10430.
322. Tourdot R.W., Ramakrishnan N., Radhakrishnan R. Defining the free energy landscape of curvature inducing proteins on membrane bilayers. Phys. Rev. E 2014, submitted for publication.
323. Taubin G. Estimating the tensor of curvature of a surface from a polyhedral approximation. Proc. Int. Conf. Comput. Vis. 1995.
324. Hildebrandt K., Polthier K. Anisotropic filtering of non-linear surface features. Eurographics 2004, 23:1-10.
325. Hildebrandt K., Polthier K., Wardetzky M. Smooth feature lines on surface meshes. Eurogr. Symp. Geom. Process. 2005, 1-6.
326. K. Polthier, Polyhedral Surfaces of Constant Mean Curvature (Ph.D. thesis), TU-Berlin, 2002.
327. Hameiri E., Shimsoni I. Estimating the principal curvatures and the darboux frame from real 3-d range data. IEEE Trans. Syst. Man Cybern. B 2003, 33:626-633.
328. Han Y., Shokef Y., Alsayed A.M., Yunker P., Lubensky T.C., Yodh A.G. Geometric frustration in buckled colloidal monolayers. Nature 2008, 456:898-903.
329. Shin H., Bowick M., Xing X. Topological defects in spherical nematics. Phys. Rev. Lett. 2008, 101:037802.
330. MacKintosh F., Lubensky T. Orientational order, topology, and vesicle shapes. Phys. Rev. Lett. 1991, 67:1169-1172.
331. Park J., Lubensky T.C., Mackintosh F.C. n-atic order and continuous shape changes of deformable surfaces of genus zero. Europhys. Lett. 1992, 20:279.
332. Peskin C.S. The immersed boundary method. ANU 2002, 11:479-517.