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. 1990 May;57(5):1075–1084. doi: 10.1016/S0006-3495(90)82625-4

Calculation of deformation energies and conformations in lipid membranes containing gramicidin channels.

P Helfrich 1, E Jakobsson 1
PMCID: PMC1280812  PMID: 1692748

Abstract

In this paper we calculate surface conformation and deformation free energy associated with the incorporation of gramicidin channels into phospholipid bilayer membranes. Two types of membranes are considered. One is a relatively thin solvent-free membrane. The other is a thicker solvent-containing membrane. We follow the approach used for the thin membrane case by Huang (1986) in that we use smectic liquid crystal theory to evaluate the free energy associated with distorting the membrane to other than a flat configuration. Our approach is different from Huang, however, in two ways. One is that we include a term for surface tension, which Huang did not. The second is that one of our four boundary conditions for solving the fourth-order differential equation describing the free energy of the surface is different from Huang's. The details of the difference are described in the text. Our results confirm that for thin membranes Huang's neglect of surface tension is appropriate. However, the precise geometrical form that we calculate for the surface of the thin membrane in the region of the gramicidin channel is somewhat different from his. For thicker membranes that have to deform to a greater extent to accommodate the channel, we find that the contribution of surface tension to the total energy in the deformed surface is significant. Computed results for the shape of the deformed surface, the total energy in the deformed surface, and the contributions of different components to the total energy, are presented for the two types of membranes considered. These results may be significant for understanding the mechanisms of dimer formation and breakup, and the access resistance for ions entering gramicidin channels.

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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. Andersen O. S. Ion movement through gramicidin A channels. Interfacial polarization effects on single-channel current measurements. Biophys J. 1983 Feb;41(2):135–146. doi: 10.1016/S0006-3495(83)84415-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Andersen O. S. Ion movement through gramicidin A channels. Single-channel measurements at very high potentials. Biophys J. 1983 Feb;41(2):119–133. doi: 10.1016/S0006-3495(83)84414-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Andersen O. S. Ion movement through gramicidin A channels. Studies on the diffusion-controlled association step. Biophys J. 1983 Feb;41(2):147–165. doi: 10.1016/S0006-3495(83)84416-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Apell H. J., Bamberg E., Alpes H., Läuger P. Formation of ion channels by a negatively charged analog of gramicidin A. J Membr Biol. 1977 Feb 24;31(1-2):171–188. doi: 10.1007/BF01869403. [DOI] [PubMed] [Google Scholar]
  6. Bamberg E., Benz R. Voltage-induced thickness changes of lipid bilayer membranes and the effect of an electrin field on gramicidin A channel formation. Biochim Biophys Acta. 1976 Mar 19;426(3):570–580. doi: 10.1016/0005-2736(76)90400-4. [DOI] [PubMed] [Google Scholar]
  7. Bamberg E., Läuger P. Channel formation kinetics of gramicidin A in lipid bilayer membranes. J Membr Biol. 1973;11(2):177–194. doi: 10.1007/BF01869820. [DOI] [PubMed] [Google Scholar]
  8. Cherry R. J., Chapman D. Optical properties of black lecithin films. J Mol Biol. 1969 Feb 28;40(1):19–32. doi: 10.1016/0022-2836(69)90293-9. [DOI] [PubMed] [Google Scholar]
  9. Chiu S. W., Jakobsson E. Stochastic theory of singly occupied ion channels. II. Effects of access resistance and potential gradients extending into the bath. Biophys J. 1989 Jan;55(1):147–157. doi: 10.1016/S0006-3495(89)82786-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Dani J. A. Ion-channel entrances influence permeation. Net charge, size, shape, and binding considerations. Biophys J. 1986 Mar;49(3):607–618. doi: 10.1016/S0006-3495(86)83688-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Decker E. R., Levitt D. G. Use of weak acids to determine the bulk diffusion limitation of H+ ion conductance through the gramicidin channel. Biophys J. 1988 Jan;53(1):25–32. doi: 10.1016/S0006-3495(88)83062-5. [DOI] [PMC free article] [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. Hainsworth A. H., Hladky S. B. Gramicidin-mediated currents at very low permeant ion concentrations. Biophys J. 1987 Jul;52(1):109–113. doi: 10.1016/S0006-3495(87)83194-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Hauser H., Pascher I., Pearson R. H., Sundell S. Preferred conformation and molecular packing of phosphatidylethanolamine and phosphatidylcholine. Biochim Biophys Acta. 1981 Jun 16;650(1):21–51. doi: 10.1016/0304-4157(81)90007-1. [DOI] [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. 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]
  17. 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]
  18. 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]
  19. Jordan P. C. How pore mouth charge distributions alter the permeability of transmembrane ionic channels. Biophys J. 1987 Feb;51(2):297–311. doi: 10.1016/S0006-3495(87)83336-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. 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]
  21. Levitt D. G., Decker E. R. Electrostatic radius of the gramicidin channel determined from voltage dependence of H+ ion conductance. Biophys J. 1988 Jan;53(1):33–38. doi: 10.1016/S0006-3495(88)83063-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Levitt D. G. Strong electrolyte continuum theory solution for equilibrium profiles, diffusion limitation, and conductance in charged ion channels. Biophys J. 1985 Jul;48(1):19–31. doi: 10.1016/S0006-3495(85)83757-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Läuger P. Diffusion-limited ion flow through pores. Biochim Biophys Acta. 1976 Dec 2;455(2):493–509. doi: 10.1016/0005-2736(76)90320-5. [DOI] [PubMed] [Google Scholar]
  24. 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]
  26. Peliti L, Leibler S. Effects of thermal fluctuations on systems with small surface tension. Phys Rev Lett. 1985 Apr 15;54(15):1690–1693. doi: 10.1103/PhysRevLett.54.1690. [DOI] [PubMed] [Google Scholar]
  27. Rudnev V. S., Ermishkin L. N., Fonina L. A., Rovin YuG The dependence of the conductance and lifetime of gramicidin channels on the thickness and tension of lipid bilayers. Biochim Biophys Acta. 1981 Mar 20;642(1):196–202. doi: 10.1016/0005-2736(81)90149-8. [DOI] [PubMed] [Google Scholar]
  28. Veatch W. R., Mathies R., Eisenberg M., Stryer L. Simultaneous fluorescence and conductance studies of planar bilayer membranes containing a highly active and fluorescent analog of gramicidin A. J Mol Biol. 1975 Nov 25;99(1):75–92. doi: 10.1016/s0022-2836(75)80160-4. [DOI] [PubMed] [Google Scholar]
  29. Wallace B. A. Structure of gramicidin A. Biophys J. 1986 Jan;49(1):295–306. doi: 10.1016/S0006-3495(86)83642-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. 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]
  31. Zingsheim H. P., Neher E. The equivalence of fluctuation analysis and chemical relaxation measurements: a kinetic study of ion pore formation in thin lipid membranes. Biophys Chem. 1974 Oct;2(3):197–207. doi: 10.1016/0301-4622(74)80045-1. [DOI] [PubMed] [Google Scholar]

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