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. 1999 Feb;76(2):889–895. doi: 10.1016/S0006-3495(99)77252-8

Spring constants for channel-induced lipid bilayer deformations. Estimates using gramicidin channels.

J A Lundbaek 1, O S Andersen 1
PMCID: PMC1300090  PMID: 9929490

Abstract

Hydrophobic interactions between a bilayer and its embedded membrane proteins couple protein conformational changes to changes in the packing of the surrounding lipids. The energetic cost of a protein conformational change therefore includes a contribution from the associated bilayer deformation energy (DeltaGdef0), which provides a mechanism for how membrane protein function depends on the bilayer material properties. Theoretical studies based on an elastic liquid-crystal model of the bilayer deformation show that DeltaGdef0 should be quantifiable by a phenomenological linear spring model, in which the bilayer mechanical characteristics are lumped into a single spring constant. The spring constant scales with the protein radius, meaning that one can use suitable reporter proteins for in situ measurements of the spring constant and thereby evaluate quantitatively the DeltaGdef0 associated with protein conformational changes. Gramicidin channels can be used as such reporter proteins because the channels form by the transmembrane assembly of two nonconducting monomers. The monomerleft arrow over right arrow dimer reaction thus constitutes a well characterized conformational transition, and it should be possible to determine the phenomenological spring constant describing the channel-induced bilayer deformation by examining how DeltaGdef0 varies as a function of a mismatch between the hydrophobic channel length and the unperturbed bilayer thickness. We show this is possible by analyzing experimental studies on the relation between bilayer thickness and gramicidin channel duration. The spring constant in nominally hydrocarbon-free bilayers agrees well with estimates based on a continuum analysis of inclusion-induced bilayer deformations using independently measured material constants.

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  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. Benz R., Fröhlich O., Läuger P., Montal M. Electrical capacity of black lipid films and of lipid bilayers made from monolayers. Biochim Biophys Acta. 1975 Jul 3;394(3):323–334. doi: 10.1016/0005-2736(75)90287-4. [DOI] [PubMed] [Google Scholar]
  3. 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]
  4. 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]
  5. Chang H. M., Reitstetter R., Gruener R. Lipid-ion channel interactions: increasing phospholipid headgroup size but not ordering acyl chains alters reconstituted channel behavior. J Membr Biol. 1995 May;145(1):13–19. doi: 10.1007/BF00233303. [DOI] [PubMed] [Google Scholar]
  6. Chang H. M., Reitstetter R., Mason R. P., Gruener R. Attenuation of channel kinetics and conductance by cholesterol: an interpretation using structural stress as a unifying concept. J Membr Biol. 1995 Jan;143(1):51–63. doi: 10.1007/BF00232523. [DOI] [PubMed] [Google Scholar]
  7. Chung H., Caffrey M. The curvature elastic-energy function of the lipid-water cubic mesophase. Nature. 1994 Mar 17;368(6468):224–226. doi: 10.1038/368224a0. [DOI] [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., 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]
  11. Girshman J., Greathouse D. V., Koeppe R. E., 2nd, Andersen O. S. Gramicidin channels in phospholipid bilayers with unsaturated acyl chains. Biophys J. 1997 Sep;73(3):1310–1319. doi: 10.1016/S0006-3495(97)78164-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Gruner S. M. Intrinsic curvature hypothesis for biomembrane lipid composition: a role for nonbilayer lipids. Proc Natl Acad Sci U S A. 1985 Jun;82(11):3665–3669. doi: 10.1073/pnas.82.11.3665. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. He K., Ludtke S. J., Wu Y., Huang H. W., Andersen O. S., Greathouse D., Koeppe R. E., 2nd Closed state of gramicidin channel detected by X-ray in-plane scattering. Biophys Chem. 1994 Feb;49(1):83–89. doi: 10.1016/0301-4622(93)e0085-j. [DOI] [PubMed] [Google Scholar]
  14. 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]
  15. 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]
  16. 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]
  17. 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]
  18. Israelachvili J. N. Refinement of the fluid-mosaic model of membrane structure. Biochim Biophys Acta. 1977 Sep 5;469(2):221–225. doi: 10.1016/0005-2736(77)90185-7. [DOI] [PubMed] [Google Scholar]
  19. 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]
  20. Katsaras J., Prosser R. S., Stinson R. H., Davis J. H. Constant helical pitch of the gramicidin channel in phospholipid bilayers. Biophys J. 1992 Mar;61(3):827–830. doi: 10.1016/S0006-3495(92)81888-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Keller S. L., Bezrukov S. M., Gruner S. M., Tate M. W., Vodyanoy I., Parsegian V. A. Probability of alamethicin conductance states varies with nonlamellar tendency of bilayer phospholipids. Biophys J. 1993 Jul;65(1):23–27. doi: 10.1016/S0006-3495(93)81040-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Kolb H. A., Bamberg E. Influence of membrane thickness and ion concentration on the properties of the gramicidin a channel. Autocorrelation, spectral power density, relaxation and single-channel studies. Biochim Biophys Acta. 1977 Jan 4;464(1):127–141. doi: 10.1016/0005-2736(77)90376-5. [DOI] [PubMed] [Google Scholar]
  23. 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]
  24. 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]
  25. 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]
  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. McIntosh T. J., Simon S. A., MacDonald R. C. The organization of n-alkanes in lipid bilayers. Biochim Biophys Acta. 1980 Apr 24;597(3):445–463. doi: 10.1016/0005-2736(80)90219-9. [DOI] [PubMed] [Google Scholar]
  28. Mobashery N., Nielsen C., Andersen O. S. The conformational preference of gramicidin channels is a function of lipid bilayer thickness. FEBS Lett. 1997 Jul 21;412(1):15–20. doi: 10.1016/s0014-5793(97)00709-6. [DOI] [PubMed] [Google Scholar]
  29. 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]
  30. 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]
  31. Nielsen C., Goulian M., Andersen O. S. Energetics of inclusion-induced bilayer deformations. Biophys J. 1998 Apr;74(4):1966–1983. doi: 10.1016/S0006-3495(98)77904-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  32. O'Connell A. M., Koeppe R. E., 2nd, Andersen O. S. Kinetics of gramicidin channel formation in lipid bilayers: transmembrane monomer association. Science. 1990 Nov 30;250(4985):1256–1259. doi: 10.1126/science.1700867. [DOI] [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]
  34. Providence L. L., Andersen O. S., Greathouse D. V., Koeppe R. E., 2nd, Bittman R. Gramicidin channel function does not depend on phospholipid chirality. Biochemistry. 1995 Dec 19;34(50):16404–16411. doi: 10.1021/bi00050a022. [DOI] [PubMed] [Google Scholar]
  35. SARGES R., WITKOP B. GRAMICIDIN A. V. THE STRUCTURE OF VALINE- AND ISOLEUCINE-GRAMICIDIN A. J Am Chem Soc. 1965 May 5;87:2011–2020. doi: 10.1021/ja01087a027. [DOI] [PubMed] [Google Scholar]
  36. Sharp K. A., Nicholls A., Fine R. F., Honig B. Reconciling the magnitude of the microscopic and macroscopic hydrophobic effects. Science. 1991 Apr 5;252(5002):106–109. doi: 10.1126/science.2011744. [DOI] [PubMed] [Google Scholar]
  37. Simon S. A., Lis L. J., MacDonald R. C., Kauffman J. W. The noneffect of a large linear hydrocarbon, squalene, on the phosphatidylcholine packing structure. Biophys J. 1977 Jul;19(1):83–90. doi: 10.1016/S0006-3495(77)85570-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  38. Starling A. P., East J. M., Lee A. G. Evidence that the effects of phospholipids on the activity of the Ca(2+)-ATPase do not involve aggregation. Biochem J. 1995 May 15;308(Pt 1):343–346. doi: 10.1042/bj3080343. [DOI] [PMC free article] [PubMed] [Google Scholar]
  39. Unwin N., Toyoshima C., Kubalek E. Arrangement of the acetylcholine receptor subunits in the resting and desensitized states, determined by cryoelectron microscopy of crystallized Torpedo postsynaptic membranes. J Cell Biol. 1988 Sep;107(3):1123–1138. doi: 10.1083/jcb.107.3.1123. [DOI] [PMC free article] [PubMed] [Google Scholar]
  40. 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]
  41. 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]
  42. Woolf T. B., Roux B. Structure, energetics, and dynamics of lipid-protein interactions: A molecular dynamics study of the gramicidin A channel in a DMPC bilayer. Proteins. 1996 Jan;24(1):92–114. doi: 10.1002/(SICI)1097-0134(199601)24:1<92::AID-PROT7>3.0.CO;2-Q. [DOI] [PubMed] [Google Scholar]

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