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. 1998 Apr;74(4):1966–1983. doi: 10.1016/S0006-3495(98)77904-4

Energetics of inclusion-induced bilayer deformations.

C Nielsen 1, M Goulian 1, O S Andersen 1
PMCID: PMC1299538  PMID: 9545056

Abstract

The material properties of lipid bilayers can affect membrane protein function whenever conformational changes in the membrane-spanning proteins perturb the structure of the surrounding bilayer. This coupling between the protein and the bilayer arises from hydrophobic interactions between the protein and the bilayer. We analyze the free energy cost associated with a hydrophobic mismatch, i.e., a difference between the length of the protein's hydrophobic exterior surface and the average thickness of the bilayer's hydrophobic core, using a (liquid-crystal) elastic model of bilayer deformations. The free energy of the deformation is described as the sum of three contributions: compression-expansion, splay-distortion, and surface tension. When evaluating the interdependence among the energy components, one modulus renormalizes the other: e.g., a change in the compression-expansion modulus affects not only the compression-expansion energy but also the splay-distortion energy. The surface tension contribution always is negligible in thin solvent-free bilayers. When evaluating the energy per unit distance (away from the inclusion), the splay-distortion component dominates close to the bilayer/inclusion boundary, whereas the compression-expansion component is more prominent further away from the boundary. Despite this complexity, the bilayer deformation energy in many cases can be described by a linear spring formalism. The results show that, for a protein embedded in a membrane with an initial hydrophobic mismatch of only 1 A, an increase in hydrophobic mismatch to 1.3 A can increase the Boltzmann factor (the equilibrium distribution for protein conformation) 10-fold due to the elastic properties of the bilayer.

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Selected References

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  1. Alvarez O., Latorre R. Voltage-dependent capacitance in lipid bilayers made from monolayers. Biophys J. 1978 Jan;21(1):1–17. doi: 10.1016/S0006-3495(78)85505-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Baldwin P. A., Hubbell W. L. Effects of lipid environment on the light-induced conformational changes of rhodopsin. 2. Roles of lipid chain length, unsaturation, and phase state. Biochemistry. 1985 May 21;24(11):2633–2639. doi: 10.1021/bi00332a007. [DOI] [PubMed] [Google Scholar]
  3. Bloom M., Evans E., Mouritsen O. G. Physical properties of the fluid lipid-bilayer component of cell membranes: a perspective. Q Rev Biophys. 1991 Aug;24(3):293–397. doi: 10.1017/s0033583500003735. [DOI] [PubMed] [Google Scholar]
  4. Brown M. F. Modulation of rhodopsin function by properties of the membrane bilayer. Chem Phys Lipids. 1994 Sep 6;73(1-2):159–180. doi: 10.1016/0009-3084(94)90180-5. [DOI] [PubMed] [Google Scholar]
  5. Caffrey M., Feigenson G. W. Fluorescence quenching in model membranes. 3. Relationship between calcium adenosinetriphosphatase enzyme activity and the affinity of the protein for phosphatidylcholines with different acyl chain characteristics. Biochemistry. 1981 Mar 31;20(7):1949–1961. doi: 10.1021/bi00510a034. [DOI] [PubMed] [Google Scholar]
  6. Canham P. B. The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. J Theor Biol. 1970 Jan;26(1):61–81. doi: 10.1016/s0022-5193(70)80032-7. [DOI] [PubMed] [Google Scholar]
  7. Criado M., Eibl H., Barrantes F. J. Functional properties of the acetylcholine receptor incorporated in model lipid membranes. Differential effects of chain length and head group of phospholipids on receptor affinity states and receptor-mediated ion translocation. J Biol Chem. 1984 Jul 25;259(14):9188–9198. [PubMed] [Google Scholar]
  8. Devaux P. F., Seigneuret M. Specificity of lipid-protein interactions as determined by spectroscopic techniques. Biochim Biophys Acta. 1985 Jun 12;822(1):63–125. doi: 10.1016/0304-4157(85)90004-8. [DOI] [PubMed] [Google Scholar]
  9. Durkin J. T., Providence L. L., Koeppe R. E., 2nd, Andersen O. S. Energetics of heterodimer formation among gramicidin analogues with an NH2-terminal addition or deletion. Consequences of missing a residue at the join in the channel. J Mol Biol. 1993 Jun 20;231(4):1102–1121. doi: 10.1006/jmbi.1993.1355. [DOI] [PubMed] [Google Scholar]
  10. Elliott J. R., Haydon D. A. The interaction of n-octanol with black lipid bilayer membranes. Biochim Biophys Acta. 1979 Oct 19;557(1):259–263. doi: 10.1016/0005-2736(79)90108-1. [DOI] [PubMed] [Google Scholar]
  11. Elliott J. R., Needham D., Dilger J. P., Brandt O., Haydon D. A. A quantitative explanation of the effects of some alcohols on gramicidin single-channel lifetime. Biochim Biophys Acta. 1985 Apr 11;814(2):401–404. doi: 10.1016/0005-2736(85)90462-6. [DOI] [PubMed] [Google Scholar]
  12. Elliott J. R., Needham D., Dilger J. P., Haydon D. A. The effects of bilayer thickness and tension on gramicidin single-channel lifetime. Biochim Biophys Acta. 1983 Oct 26;735(1):95–103. doi: 10.1016/0005-2736(83)90264-x. [DOI] [PubMed] [Google Scholar]
  13. Evans E, Rawicz W. Entropy-driven tension and bending elasticity in condensed-fluid membranes. Phys Rev Lett. 1990 Apr 23;64(17):2094–2097. doi: 10.1103/PhysRevLett.64.2094. [DOI] [PubMed] [Google Scholar]
  14. Gruner S. M., Parsegian V. A., Rand R. P. Directly measured deformation energy of phospholipid HII hexagonal phases. Faraday Discuss Chem Soc. 1986;(81):29–37. doi: 10.1039/dc9868100029. [DOI] [PubMed] [Google Scholar]
  15. Helfrich P., Jakobsson E. Calculation of deformation energies and conformations in lipid membranes containing gramicidin channels. Biophys J. 1990 May;57(5):1075–1084. doi: 10.1016/S0006-3495(90)82625-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Helfrich W. Elastic properties of lipid bilayers: theory and possible experiments. Z Naturforsch C. 1973 Nov-Dec;28(11):693–703. doi: 10.1515/znc-1973-11-1209. [DOI] [PubMed] [Google Scholar]
  17. Hendry B. M., Urban B. W., Haydon D. A. The blockage of the electrical conductance in a pore-containing membrane by the n-alkanes. Biochim Biophys Acta. 1978 Oct 19;513(1):106–116. doi: 10.1016/0005-2736(78)90116-5. [DOI] [PubMed] [Google Scholar]
  18. Hladky S. B., Gruen D. W. Thickness fluctuations in black lipid membranes. Biophys J. 1982 Jun;38(3):251–258. doi: 10.1016/S0006-3495(82)84556-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Huang H. W. Deformation free energy of bilayer membrane and its effect on gramicidin channel lifetime. Biophys J. 1986 Dec;50(6):1061–1070. doi: 10.1016/S0006-3495(86)83550-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Johannsson A., Smith G. A., Metcalfe J. C. The effect of bilayer thickness on the activity of (Na+ + K+)-ATPase. Biochim Biophys Acta. 1981 Mar 6;641(2):416–421. doi: 10.1016/0005-2736(81)90498-3. [DOI] [PubMed] [Google Scholar]
  21. Jähnig F. What is the surface tension of a lipid bilayer membrane? Biophys J. 1996 Sep;71(3):1348–1349. doi: 10.1016/S0006-3495(96)79336-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Lundbaek J. A., Andersen O. S. Lysophospholipids modulate channel function by altering the mechanical properties of lipid bilayers. J Gen Physiol. 1994 Oct;104(4):645–673. doi: 10.1085/jgp.104.4.645. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Lundbaek J. A., Birn P., Girshman J., Hansen A. J., Andersen O. S. Membrane stiffness and channel function. Biochemistry. 1996 Mar 26;35(12):3825–3830. doi: 10.1021/bi952250b. [DOI] [PubMed] [Google Scholar]
  24. Lundbaek J. A., Maer A. M., Andersen O. S. Lipid bilayer electrostatic energy, curvature stress, and assembly of gramicidin channels. Biochemistry. 1997 May 13;36(19):5695–5701. doi: 10.1021/bi9619841. [DOI] [PubMed] [Google Scholar]
  25. Marcelja S. Lipid-mediated protein interaction in membranes. Biochim Biophys Acta. 1976 Nov 11;455(1):1–7. doi: 10.1016/0005-2736(76)90149-8. [DOI] [PubMed] [Google Scholar]
  26. McCallum C. D., Epand R. M. Insulin receptor autophosphorylation and signaling is altered by modulation of membrane physical properties. Biochemistry. 1995 Feb 14;34(6):1815–1824. doi: 10.1021/bi00006a001. [DOI] [PubMed] [Google Scholar]
  27. Miao L, Seifert U, Wortis M, Döbereiner HG. Budding transitions of fluid-bilayer vesicles: The effect of area-difference elasticity. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1994 Jun;49(6):5389–5407. doi: 10.1103/physreve.49.5389. [DOI] [PubMed] [Google Scholar]
  28. Mouritsen O. G., Bloom M. Mattress model of lipid-protein interactions in membranes. Biophys J. 1984 Aug;46(2):141–153. doi: 10.1016/S0006-3495(84)84007-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Navarro J., Toivio-Kinnucan M., Racker E. Effect of lipid composition on the calcium/adenosine 5'-triphosphate coupling ratio of the Ca2+-ATPase of sarcoplasmic reticulum. Biochemistry. 1984 Jan 3;23(1):130–135. doi: 10.1021/bi00296a021. [DOI] [PubMed] [Google Scholar]
  30. Needham D., Nunn R. S. Elastic deformation and failure of lipid bilayer membranes containing cholesterol. Biophys J. 1990 Oct;58(4):997–1009. doi: 10.1016/S0006-3495(90)82444-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Neher E., Eibl H. The influence of phospholipid polar groups on gramicidin channels. Biochim Biophys Acta. 1977 Jan 4;464(1):37–44. doi: 10.1016/0005-2736(77)90368-6. [DOI] [PubMed] [Google Scholar]
  32. Owicki J. C., McConnell H. M. Theory of protein-lipid and protein-protein interactions in bilayer membranes. Proc Natl Acad Sci U S A. 1979 Oct;76(10):4750–4754. doi: 10.1073/pnas.76.10.4750. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Owicki J. C., Springgate M. W., McConnell H. M. Theoretical study of protein--lipid interactions in bilayer membranes. Proc Natl Acad Sci U S A. 1978 Apr;75(4):1616–1619. doi: 10.1073/pnas.75.4.1616. [DOI] [PMC free article] [PubMed] [Google Scholar]
  35. Ring A. Gramicidin channel-induced lipid membrane deformation energy: influence of chain length and boundary conditions. Biochim Biophys Acta. 1996 Jan 31;1278(2):147–159. doi: 10.1016/0005-2736(95)00220-0. [DOI] [PubMed] [Google Scholar]
  36. Seddon J. M. Structure of the inverted hexagonal (HII) phase, and non-lamellar phase transitions of lipids. Biochim Biophys Acta. 1990 Feb 28;1031(1):1–69. doi: 10.1016/0304-4157(90)90002-t. [DOI] [PubMed] [Google Scholar]
  37. Servuss R. M., Harbich W., Helfrich W. Measurement of the curvature-elastic modulus of egg lecithin bilayers. Biochim Biophys Acta. 1976 Jul 15;436(4):900–903. doi: 10.1016/0005-2736(76)90422-3. [DOI] [PubMed] [Google Scholar]
  38. Singer S. J., Nicolson G. L. The fluid mosaic model of the structure of cell membranes. Science. 1972 Feb 18;175(4023):720–731. doi: 10.1126/science.175.4023.720. [DOI] [PubMed] [Google Scholar]
  39. Song J., Waugh R. E. Bending rigidity of SOPC membranes containing cholesterol. Biophys J. 1993 Jun;64(6):1967–1970. doi: 10.1016/S0006-3495(93)81566-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  40. Unwin N. The structure of ion channels in membranes of excitable cells. Neuron. 1989 Dec;3(6):665–676. doi: 10.1016/0896-6273(89)90235-3. [DOI] [PubMed] [Google Scholar]
  41. Unwin P. N., Ennis P. D. Two configurations of a channel-forming membrane protein. Nature. 1984 Feb 16;307(5952):609–613. doi: 10.1038/307609a0. [DOI] [PubMed] [Google Scholar]
  42. White S. H. Formation of "solvent-free" black lipid bilayer membranes from glyceryl monooleate dispersed in squalene. Biophys J. 1978 Sep;23(3):337–347. doi: 10.1016/S0006-3495(78)85453-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  43. Wiener M. C., White S. H. Structure of a fluid dioleoylphosphatidylcholine bilayer determined by joint refinement of x-ray and neutron diffraction data. III. Complete structure. Biophys J. 1992 Feb;61(2):434–447. doi: 10.1016/S0006-3495(92)81849-0. [DOI] [PMC free article] [PubMed] [Google Scholar]

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