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Semiconductor theory of ion transport in thin lipid membranes: II. Surface recombination

  • B. Y. Woo
  • Ling Y. Wei
Article

Abstract

Following the theory of surface recombination in semiconductors, we have derived an expression for the rate of ion recombination at the membrane surface. The surface recombination rate is used in the boundary conditions of current flows at the interfaces. Expressions for the ion fluxes are then derived as functions of environmental variables and membrane parameters. Our analysis strongly suggests that the ion flow through a thin lipid membrane consists of two major components: the surface barrier jumping current and the surface recombination current that are controlled decisively by surface barrier height, surface trap density and surface recombination rates. These general formulations are useful not only for the calculation but also for the understanding of ion transport in thin lipid membranes under a variety of experimental conditions. The implications of this theory to biological membranes and its possible extensions are discussed.

Keywords

Lipid Membrane Biological Membrane Electron Tunneling Surface Recombination Surface Barrier 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Literature

  1. Bangham, A. D., M. M. Standish and J. C. Walkins. 1965. “Diffusion of Univalent Ions Across the Lamella of Swollen Phospho-Lipids.”J. Molec. Biol.,13, 238–252.CrossRefGoogle Scholar
  2. Bardeen, J. and S. R. Morrison. 1954. “Surface Barriers and Surface Conductance.”Physica,20, 873.CrossRefGoogle Scholar
  3. Brattain, W. H. and J. Bardeen. 1953. “Surface Properties of Germanium.”Bell. Sys. Tech. J.,32, 1–41.Google Scholar
  4. Cohen, E. J. and J. T. Edsall. 1943.Proteins, Amino Acids and Peptides. New York: Reinhold.Google Scholar
  5. Cole, K. S. 1968.Membranes, Ions and Impulses. Berkeley: University of California Press.Google Scholar
  6. Coster, H. G. L. 1965. “A Quantitative Analysis of the Voltage-Current Relationships of Fixed Charge Membranes and the Associated Property of Punch-Through.”Biophys. J.,5, 669–686.Google Scholar
  7. Crane, F. L. and J. D. Hall, 1969. “Binary Membranes: A Re-interpretation of Membrane and Myelin Structure.”Biochem. Biophys. Res. Commun.,36, 174–178.CrossRefGoogle Scholar
  8. Davis, E. A. and N. F. Mott. 1970. “Conduction in Non-crystalline Systems—V”.Phil. Mag.,22, 903–922.Google Scholar
  9. — and R. F. Shaw. 1970. “Characteristic, Phenomena in Amorphous Semiconductors”.J. Non-Cryst. Solids,2, 406–431.CrossRefGoogle Scholar
  10. Derksen, H. E. 1965. “Axon Membrane Voltage Fluctuations.”Acta Physiol. Pharcol. Neer.,13, 373–466.Google Scholar
  11. Duke, C. B., 1969.Tunneling of Solids. New York: Academic Press.Google Scholar
  12. Flinn, I., G. Bew and F. Berz. 1967. “Low-frequency Noise in MOS Field Effect Transistors.”Solid-state Electronics,10, 833.CrossRefGoogle Scholar
  13. Fortes, P. A. G., J. Yguerabide and J. F. Hoffman. 1972. “Nanosecond Fluorescence Spectroscopy of 1-Anilino-8-Naphthalene Sulfonate (ANS) in Red Cell Ghosts.”Biophys. Soc. Abst.,12, 225a.Google Scholar
  14. Fu, H. S. and C. T. Sah. 1972. “Theory and Experiment of Surface 1/f Noise.”IEEE Trans.,ED-19, 273–284.Google Scholar
  15. Gerischer, H., 1961. “Semiconductor Electrode Reactions.” InAdvances in Electrochemistry and Electrochemical Engineering, Delahay, P., ed., New York: Interscience, Vol. I, pp. 139–232.Google Scholar
  16. Glasstone, S., K. J. Laidler and H. Eyring. 1941.The Theory of Rate Processes. New York: McGraw-Hill.Google Scholar
  17. Goldman, D. E. 1943. “Potential, Impedance and Rectification in Membranes.”J. gen. Physiol. 27, 37–60.CrossRefGoogle Scholar
  18. Hopfer, U., A. L. Lehninger and J. L. Lennarz. 1970. “The Effect of Polar Moiety of Lipids on the Ion Permeability of Bilayer Membranes.”J. Memb. Biology,2, 41–58.CrossRefGoogle Scholar
  19. Hung, C. S. and J. R. Gleissman. 1950. “The Resistivity and Hall Effect of Germanium at Low Temperatures.”Phys. Rev.,79, 726–727.CrossRefGoogle Scholar
  20. Kalkware, D. R., D. L. Frasco and W. H. Brattain. 1970. “Current Rectification and Action Potentials Across Thin Lipid Membranes.” InPhysical Principles of Biological Membranes, Snell, F., J. Wolken, G. Iverson and J. Lam, eds. New York: Gordon and Breach, pp. 165–174.Google Scholar
  21. Kaufman, J. W. and C. H. Mead. 1970. “Electrical Characteristics of Sphingomyelin Bilayer Membranes.”Biophys. J.,10, 1087–1089.Google Scholar
  22. Kavanau, J. S. 1965.Structure and Function in Biological Membranes. New York: Holden-Day, Vol. I.Google Scholar
  23. Kemeny, G. and B. Rosenberg. 1970. “Theory of Pre-exponential Factor, in Organic Semiconductors”.J. Chem. Phys.,52, 4151–4153.CrossRefGoogle Scholar
  24. Kingston, R. 1956. “Review of Germanium Surface Phenomena.”J. Appl. Phys.,27, 101.CrossRefGoogle Scholar
  25. Kishimoto, U. and W. J. Adelman, Jr. 1964. “Effect of Detergent on Electrical Properties of Squid Axon Membrane.”J. gen. Physiol.,47, 975–986.CrossRefGoogle Scholar
  26. Klinger, M. S. and E. Blakher. 1969. “On a Special Mechanism of Electromagnetic Waves by Impurity Polarons.”Phys. Status Solidi,31, 515–530.Google Scholar
  27. Levich, V. G. 1966. “Present State of the Theory of Oxidation-Reduction in Solution (Bulk and Electrode Reaction)” InAdvances in Electrochemistry and Electrochemical Engineering, Delahay, P., ed. New York: Interscience, Vol. 4, pp. 249–372.Google Scholar
  28. McLaugrhlin, S. G. A., G. Szabo, G. Eisenman and S. M. Ciani. 1970. “Surface Charge and the conductance of Phospholipid Membranes.”Proc. Nat. Acad. Sci.,67, 1268–1275.CrossRefGoogle Scholar
  29. McWhorter, A. L. 1957. “l/f Noise and Germanium Surface Properties.” InSemiconductor Surface Physics, Kingston, R. H., ed. Philadelphia: University of Pennsylvania Press, pp. 207–228.Google Scholar
  30. Many, A., E. Harnik and Y. Margoninski. 1957. “Surface Recombination Processes in Germanium and their Investigation by Means of Transverse Electric Fields.”Ibid.,, pp. 85–107.Google Scholar
  31. Mauzerall, D. and A. Finkelstein 1969. “Light Induced Changes in the Conductivity of Thin Lipid Membranes.”Nature,224, 690–692.CrossRefGoogle Scholar
  32. Miller, A. and E. Abrahams. 1960. “Impurity Conduction at Low Concentrations.”Phys. Rev.,120, 745–755.MATHCrossRefGoogle Scholar
  33. Moll, J. L. 1964.Physics, of Semiconductors. New York: McGraw-Hill, p. 150.MATHGoogle Scholar
  34. Mott, N. F. 1967. “Electrons in Disordered Structures.”Adv. Phys.,16, 50–144.CrossRefGoogle Scholar
  35. — 1969. “Conduction in Non-crystalline Materials—III.”Phil. Mag.,19, 835–852.Google Scholar
  36. — and R. W. Gurney. 1964.Electronic Processes in Ionic Crystals. New York: Dover Publications, p. 43.Google Scholar
  37. — and W. D. Twose. 1961. “The Theory of Impurity Conduction”.Adv. Phys.,10, 107–163.CrossRefGoogle Scholar
  38. Offner, F. F. 1971. “I/f Fluctuation in Membrane Potential as Related to Membrane Theory.”Biophys. J.,11, 123–124.CrossRefGoogle Scholar
  39. Ohki, S., 1968. “Dielectric Constant and Refractive Index of Lipid, Bilayers.”J. Theor. Biology,19, 97–115.CrossRefGoogle Scholar
  40. Onsager, L. 1934. “Deviations from Ohm’s Law in Weak Electrolytes.”J. Chem. Phys.,2, 599–615.CrossRefGoogle Scholar
  41. Pollack, H. and T. H. Geballe. 1961. “Low-frequency Conductivity due to Hopping Processes in Silicon.”Phys. Rev.,122, 1742–1953.CrossRefGoogle Scholar
  42. Poussart, D. J. M. 1971. “Membrane Current Noise in Lobster Axon Under Voltage Clamp.”Biophys. J.,11, 211–234.Google Scholar
  43. Rosenberg, B. and H. C. Pant 1970. “The Semiconducting Rectifier Behavior, of a Bimolecular Lipid Membrane.”Chem. Phys. Lipids,4, 203–207.CrossRefGoogle Scholar
  44. Shah, D. O. 1970. “Surface Chemistry of Lipids,” InAdvances in Lipid, Research, Paoletti, R. and D. Kvitchevsky, eds. New York: Academic Press, Vol. 8, pp. 347–431.Google Scholar
  45. Shockley, W. 1950.Electrons and Holes in Semiconductors. Princeton: Van Nostrand, p. 319.Google Scholar
  46. Sproull, R. L. 1963.Modern Physics. New York: Wiley, pp. 442–446.MATHGoogle Scholar
  47. Szabo, G. G., Eisenman and S. M. Ciani. 1970. “Ion Distribution Equilibria in Bulk Phases and the Ion Transport Properties of Bilayer Membranes Produced by Neutral Macrocyclic Antibiotics.” InPhysical Principles of Biological Membranes, Snell, F., J. Woken, G. Iverson and J. Lam, eds. New York: Gordon and Breach, pp. 79–136.Google Scholar
  48. Tien, H. T. 1968a. “Light Induced Phenomena in Black Lipid Membranes Constituted from Photosynthetic Pigments”.Nature,219, 272–274.CrossRefGoogle Scholar
  49. —, 1968b. “Photoelectric Effects in Thin and Bilayer Lipid Membranes in Aqueous Media.”J. Phys. Chem.,72, 4512–4519.CrossRefGoogle Scholar
  50. — and N. Kobamoto. 1969. “Carotenoid Bilayer Lipid Membrane Model for the Visual Receptor.”Nature,224, 1107–1108.Google Scholar
  51. Vandenheuvel, F. A. 1965. “Study of Biological Structure at the Molecular Level with Stereomodel Projections—II. The Structure of Myelin in Relation to Other Membrane Systems.”J. Amer. Oil Chem. Soc.,22, 490.Google Scholar
  52. Van der Ziel. 1950. “On the Noise Spectra of Semiconductor Noise and of Flicker Effect.”Physica,16, 359–372.CrossRefGoogle Scholar
  53. —. 1968.Solid State Physical Electronics. Englewood Cliffs: Prentice-Hall.Google Scholar
  54. Verveen, A. A. and H. E. Derksen. 1968. “Fluctuation Phenomena in Nerve Membrane.”Proc. IEEE 56, 906.CrossRefGoogle Scholar
  55. Vodyanoi, V. Y., I. Y. Vodyanoi and N. A. Fedorovich. 1971. “Mechanism of Comduction in Bimolecular Phospholipid Membranes.”Soviet Phys. Solid State,12, 2690–2692.Google Scholar
  56. Walz, D., E. Bamberg and P. Lauger. 1969. “Nonlinear Electrical Effects in Lipid Bilayer Membranes—I. Ion Injection.”Biophys. J.,9, 1150–1159.Google Scholar
  57. Webster, W. M. 1954. “On the Variation of Junction-Transistor Current Amplification Factor with Emitter Current.”Proc. IRE,42, 914–920.Google Scholar
  58. Wei, L. Y. 1966. “A New Theory of Nerve Conduction.”IEEE Spectrum,3, 123–127.CrossRefGoogle Scholar
  59. — 1967. “Possibility of Electron Tunneling Through a Nerve Membrane.”Bull. Math. Biophysics,29, 411–418.Google Scholar
  60. — 1969. “Molecular Mechanisms of Nerve Excitation and Conduction.”Ibid.,31, 39–58.Google Scholar
  61. — and B. Y. Woo 1973a. “Ion Transport Through Thin Lipid Films.”J. Biol. Phys.,1, 50–68.CrossRefGoogle Scholar
  62. — and—. 1973b. “Electronic Conduction in Thin Lipid Films with Metal Contacts”.Biophys. J.,13, 877.Google Scholar
  63. Woo, B. Y. and L. Y. Wei. 1973. “Electrical Capacitances of Thin Lipid Films.”J. Biol. Phys.,1, 36–49.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 1974

Authors and Affiliations

  • B. Y. Woo
    • 1
  • Ling Y. Wei
    • 1
  1. 1.Electrical Engineering DepartmentUniversity of WaterlooWaterlooCanada

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