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Spontaneous and Intrinsic Curvature of Lipid Membranes: Back to the Origins

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Physics of Biological Membranes

Abstract

We review the background behind the notions of spontaneous and intrinsic curvatures of lipid membranes with a goal to make clear a fundamental physical difference between them. We recall the underlying mechanical and thermodynamic models for intrinsically curved lipid monolayers, whose geometry is described by the intrinsic curvature, and for flat monolayers whose elastic stresses are captured by the spontaneous curvature. We describe the existing ideas concerning the spontaneous and intrinsic curvatures of mixed lipid membranes. We mention the conditions upon which the values of the spontaneous and intrinsic curvatures are expected to be similar and the specific systems for which each of the notions is relevant.

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References

  1. Tanford C (1973) The hydrophobic effect: formation of micelles and biological membranes. Wiley, New York

    Google Scholar 

  2. McConnell HM, Kornberg RD (1971) Inside-outside transitions of phospholipids in vesicle membranes. Biochemistry 10:1111–1120

    Article  CAS  Google Scholar 

  3. Canham PB (1970) The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. J Theor Biol 26:61–81

    Article  CAS  Google Scholar 

  4. Helfrich W (1973) Elastic properties of lipid bilayers: theory and possible experiments. Z Naturforsch 28c:693–703

    Article  Google Scholar 

  5. Luzzati V (1968) X-ray diffraction studies of lipid-water systems. In: Chapman D (ed) Biological membranes. Academic, New York, pp 71–123

    Google Scholar 

  6. McMahon HT, Boucrot E (2015) Membrane curvature at a glance. J Cell Sci 128:1065–1070

    Article  CAS  Google Scholar 

  7. Alberts B, Bray D, Lewis J, Raff M, Roberts K, Watson JD (2002) Molecualr biology of the cell. Garland, New York

    Google Scholar 

  8. Shibata Y, Hu J, Kozlov MM, Rapoport TA (2009) Mechanisms shaping the membranes of cellular organelles. Annu Rev Cell Dev Biol 25:329–354

    Article  CAS  Google Scholar 

  9. Gruner SM (1985) Intrinsic curvature hypothesis for biomembrane lipid composition: a role for nonbilayer lipids. Proc Natl Acad Sci USA 82:3665–3669

    Article  CAS  Google Scholar 

  10. Seddon J, Templer R (1993) Cubic phases of self-assembled amphiphilic aggregates. Philos Trans R Soc Lond A 344:377–401

    Article  CAS  Google Scholar 

  11. Seddon JM (1990) Structure of the inverted hexagonal (HII) phase, and non-lamellar phase transitions of lipids. Biochim Biophys Acta 1031:1–69

    Article  CAS  Google Scholar 

  12. Seddon JM, Templer RH (1995) Polymorphism of lipid-water systems. In: Lipowsky R, Sackmann E (eds) Structure and dynamics of membranes. Elsevier, Amsterdam, pp 97–160

    Google Scholar 

  13. Rand RP, Fuller NL (1994) Structural dimensions and their changes in a reentrant hexagonal-lamellar transition of phospholipids. Biophys J 66:2127–2138

    Article  CAS  Google Scholar 

  14. Gruner SM, Parsegian VA, Rand RP (1986) Directly measured deformation energy of phospholipid HII hexagonal phases. Faraday Discuss Chem Soc:29–37

    Article  CAS  Google Scholar 

  15. Gruner SM (1989) Stability of lyotropic phases with curved interfases. J Phys Chem 93:7562–7570

    Article  CAS  Google Scholar 

  16. Rand RP, Fuller NL, Gruner SM, Parsegian VA (1990) Membrane curvature, lipid segregation, and structural transitions for phospholipids under dual-solvent stress. Biochemistry 29:76–87

    Article  CAS  Google Scholar 

  17. Kozlov MM, Leikin SL, Markin VS (1989) Elastic properties of interfaces. Elasticity moduli and spontaneous geometrical characteristics. J Chem Soc Faraday Trans 2(85):277–292

    Article  Google Scholar 

  18. Kozlov MM, Winterhalter M (1991) Elastic moduli for strongly curved monolayers. Position of the neutral surface. J Phys II France 1:1077–1084

    Article  CAS  Google Scholar 

  19. Kozlov MM, Winterhalter M (1991) Elastic moduli and neutral surface for strongly curved monolayers. Analysis of experimental results. J Phys II France 1:1085–1100

    Article  CAS  Google Scholar 

  20. Leikin S, Kozlov MM, Fuller NL, Rand RP (1996) Measured effects of diacylglycerol on structural and elastic properties of phospholipid membranes. Biophys J 71:2623–2632

    Article  CAS  Google Scholar 

  21. Hafez IM, Cullis PR (2001) Roles of lipid polymorphism in intracellular delivery. Adv Drug Deliver Rev 47:139–148

    Article  CAS  Google Scholar 

  22. Kozlov MM, Leikin S, Rand RP (1994) Bending, hydration and void energies quantitatively account for the hexagonal-lamellar-hexagonal reentrant phase transition in dioleoylphosphatidylethanolamine. Biophys J 67:1603–1611

    Article  CAS  Google Scholar 

  23. Chen Z, Rand RP (1997) The influence of cholesterol on phospholipid membrane curvature and bending elasticity. Biophys J 73:267–276

    Article  CAS  Google Scholar 

  24. Chen Z, Rand RP (1998) Comparative study of the effects of several n-alkanes on phospholipid hexagonal phases. Biophys J 74:944–952

    Article  CAS  Google Scholar 

  25. Fuller N, Benatti CR, Rand RP (2003) Curvature and bending constants for phosphatidylserine-containing membranes. Biophys J 85:1667–1674

    Article  CAS  Google Scholar 

  26. Fuller N, Rand RP (2001) The influence of lysolipids on the spontaneous curvature and bending elasticity of phospholipid membranes. Biophys J 81:243–254

    Article  CAS  Google Scholar 

  27. Zimmerberg J, Kozlov MM (2006) How proteins produce cellular membrane curvature. Nat Rev Mol Cell Biol 7:9–19

    Article  CAS  Google Scholar 

  28. Sodt AJ, Venable RM, Lyman E, Pastor RW (2016) Nonadditive compositional curvature energetics of lipid bilayers. Phys Rev Lett 117:138104

    Article  CAS  Google Scholar 

  29. Kooijman EE, Chupin V, Fuller NL, Kozlov MM, de Kruijff B, Burger KN, Rand PR (2005) Spontaneous curvature of Phosphatidic acid and Lysophosphatidic acid. Biochemistry 44:2097–2102

    Article  CAS  Google Scholar 

  30. Frank FC (1958) On the theory of liquid crystals. Discuss Faraday Soc 25:19–28

    Article  Google Scholar 

  31. Helfrich W (1990) Elasticity and thermal undulations of fluid films of amphiphiles. In: Charvolin J, Joanny J-F, Zinn-Justin J (eds) Les Houches, 1988—liquids and interfaces. North-Holland, Amsterdam, pp 212–237

    Google Scholar 

  32. Landau LD, Lifshitz EM (1970) Theory of elasticity. Pergamon Press, London

    Google Scholar 

  33. Spivak M (1970) A comprehensive introduction to differential geometry. Brandeis University, Waltham

    Google Scholar 

  34. Dimova R (2014) Recent developments in the field of bending rigidity measurements on membranes. Adv Colloid Interf Sci 208:225–234

    Article  CAS  Google Scholar 

  35. Lorenzen S, Servuss RM, Helfrich W (1986) Elastic torques about membrane edges—a study of pierced egg lecithin vesicles. Biophys J 50:565–572

    Article  CAS  Google Scholar 

  36. Templer RH, Khoo BJ, Seddon JM (1998) Gaussian curvature modulus of an amphiphilic monolayer. Langmuir 14:7427–7434

    Article  CAS  Google Scholar 

  37. Siegel DP, Kozlov MM (2004) The Gaussian curvature elastic modulus of N-monomethylated dioleoylphosphatidylethanolamine: relevance to membrane fusion and lipid phase behavior. Biophys J 87:366–374

    Article  CAS  Google Scholar 

  38. Shemesh T, Luini A, Malhotra V, Burger KN, Kozlov MM (2003) Prefission constriction of Golgi tubular carriers driven by local lipid metabolism: a theoretical model. Biophys J 85:3813–3827

    Article  CAS  Google Scholar 

  39. Mitov MD (1978) Third and fourth order curvature elasticity of lipid bilayers. Comptes Rendus de l Academie bulgare des Sciences 31:513–515

    Google Scholar 

  40. Kozlov MM, Helfrich W (1992) Effects of a cosurfactant on the stretching and bending elasticities of a surfactant monolayer. Langmuir 8:2792–2797

    Article  CAS  Google Scholar 

  41. Gibbs JW (1961) The scientific papers. Dover, New York

    Google Scholar 

  42. Murphy CL (1966) Thermodynamics of low tension and highly curved interfaces. University of Minnesota, Department of Chemical Engineering

    Google Scholar 

  43. Markin VS (1981) Lateral organization of membranes and cell shapes. Biophys J 36:1–19

    Article  CAS  Google Scholar 

  44. Kozlov MM, Markin VS (1983) Possible mechanism of membrane fusion. Biofizika 28:255–261

    CAS  Google Scholar 

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Correspondence to Michael M. Kozlov .

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Kozlov, M.M. (2018). Spontaneous and Intrinsic Curvature of Lipid Membranes: Back to the Origins. In: Bassereau, P., Sens, P. (eds) Physics of Biological Membranes. Springer, Cham. https://doi.org/10.1007/978-3-030-00630-3_12

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