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1/f noise in membranes

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Abstract

The present situation of 1/f noise in the passage of ions across membranes is examined. A survey of biological and synthetic membranes is given at which a l/f frequency dependence has been observed in the spectrum of voltage or current fluctuations. Empirical relations and theories of 1/f noise in membranes are critically discussed.

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References

  • Bean, C. P., Golibersuch, D. C.: Voltage fluctuations across current carrying membranes. In: Electrical phenomena at the biological membrane level (ed. E. Roux), pp. 311–324. Amsterdam: Elsevier 1977

    Google Scholar 

  • Bell, D. A.: Electrical noise. London: van Nostrand 1960

    MATH  Google Scholar 

  • Bezanilla, F., Armstrong, C. M.: Negative conductance caused by entry of sodium and cesium ions into the potassium channels of squid axons. J. gen. Physiol.60, 588–608 (1972)

    Article  Google Scholar 

  • Bird, J. F.: Neuronal 1/f noise and membrane models. Biophys. J.14, 563–565 (1974a)

    Google Scholar 

  • Bird, J. F.: Noise spectrum analysis of a Markov process vs. random walk computer solutions simulating 1/f noise spectra. J. appl. Phys.45, 499–500 (1974b)

    Article  ADS  Google Scholar 

  • Caloyannides, M. A.: Microcycle spectral estimates of 1/f noise in semiconductors. J. appl. Phys.45, 307–316 (1974)

    Article  ADS  Google Scholar 

  • Ciani, S., Gambale, F., Gliozzi, A., Rolandi, R.: Effects of unstirred layers on the steady-state zero-current conductance of bilayer membranes mediated by neutral carriers of ions. J. Membrane Biol.24, 1–34 (1975)

    Article  Google Scholar 

  • Clapham, D. E., DeFelice, L. J.: The theoretical small signal impedance of the frog node, Rana pipiens. Pflügers Arch.366, 273–276 (1976)

    Article  Google Scholar 

  • Clay, J. R., Shlesinger, M. F.: Theoretical model of the ionic mechanism of 1/f noise in nerve membrane. Biophys. J.16, 121–136 (1976)

    Google Scholar 

  • Clay, J. R., Shlesinger, M. F.: Unified theory of 1/f and conductance noise in nerve membrane. J. theor. Biol.66, 763–773 (1977)

    Article  Google Scholar 

  • Cole, K. S.: Membranes, ions and impulses. Berkeley: University of California Press 1968

    Google Scholar 

  • Conti, F., Wanke, E.: Channel noise in membranes and lipid bilayers. Quart. Rev. Biophys.8, 451–506 (1975)

    Article  Google Scholar 

  • Conti, F., DeFelice, L. J., Wanke, E.: K+ and Na+ current noise in the membrane of the squid giant axon. J. Physiol. (Lond.)248, 45–82 (1975)

    Google Scholar 

  • Conti, F., Hille, B., Neumcke, B., Nonner, W., Stämpfli, R.: Measurement of the conductance of the sodium channel from current fluctuations at the node of Ranvier. J. Physiol. (Lond.)262, 699–727 (1976a)

    Google Scholar 

  • Conti, F., Hille, B., Neumcke, B., Nonner, W., Stämpfli, R.: Conductance of the sodium channel in myelinated nerve fibres with modified sodium inactivation. J. Physiol. (Lond.)262, 729–742 (1976b)

    Google Scholar 

  • DeFelice, L. J.: 1/f resistor noise. J. appl. Phys.47, 350–352 (1976)

    Article  ADS  Google Scholar 

  • DeFelice, L. J., Michalides, J. P.: Electrical noise from synthetic membranes. J. Membrane Biol.9, 261–290 (1972a)

    Article  Google Scholar 

  • DeFelice, L. J., Michalides, J. P.: Electrical noise from synthetic membranes. In: Biomembranes, vol. 3 (ed. F. Kreuzer, J. F. G. Siegers), pp. 293–298. New York: Plenum Press 1972b

    Google Scholar 

  • DeFelice, L. J., Sokol, B. A.: Correlation analysis of membrane noise. J. Membrane Biol.26, 405–406 (1976a)

    Article  Google Scholar 

  • DeFelice, L. J., Sokol, B. A.: A new analysis for membrane noise. The integral spectrum. Biophys. J.16, 827–838 (1976b)

    Google Scholar 

  • DeFelice, L. J., Wanke, E., Conti, F.: Potassium and sodium current noise from squid axon membranes. Fed. Proc.34, 1338–1342 (1975)

    Google Scholar 

  • de Goede, J., Verveen, A. A.: Electrical membrane noise: Its origin and interpretation. In: Electrical phenomena at the biological membrane level (ed. E. Roux), pp. 337–348. Amsterdam: Elsevier 1977

    Google Scholar 

  • Derksen, H. E.: Axon membrane voltage fluctuations. Acta physiol. pharmacol. neerl.13, 373–466 (1965)

    Google Scholar 

  • Derksen, H. E., Verveen, A. A.: Fluctuations of resting neural membrane potential. Science151, 1388–1389 (1966)

    ADS  Google Scholar 

  • Dorset, D. L., Fishman, H. M.: Excess electrical noise during current flow through porous membranes separating ionic solutions. J. Membrane Biol.21, 291–309 (1975)

    Article  Google Scholar 

  • Fishman, H. M.: Relaxation spectra of potassium channel noise from squid axon membranes. Proc. nat. Acad. Sci. (Wash.)70, 876–879 (1973)

    Article  ADS  Google Scholar 

  • Fishman, H. M.: Noise measurements in axon membranes. Fed. Proc.34, 1330–1337 (1975)

    Google Scholar 

  • Fishman, H. M., Moore, L. E., Poussart, D. J. M.: Potassium-ion conduction noise in squid axon membrane. J. Membrane Biol.24, 305–328 (1975)

    Article  Google Scholar 

  • Fishman, H. M., Moore, L. E., Poussart, D.: Ion movements and kinetics in squid axon. II. Spontaneous electrical fluctuations. Ann. N.Y. Acad. Sci. (in press) (1977a)

  • Fishman, H. M., Poussart, D. J. M., Moore, L. E., Siebenga, E.: K+ conduction description from the low frequency impedance and admittance of squid axon. J. Membrane Biol.32, 255–290 (1977b)

    Article  Google Scholar 

  • Frankenhaeuser, B., Hodgkin, A. L.: The after-effects of impulses in the giant nerve fibres of Loligo. J. Physiol. (Lond.)131, 341–376 (1956)

    Google Scholar 

  • Frehland, E.: 1/f-noise generated by constrained diffusion through a flux-controlling boundary. Z. Naturforsch.31a, 942–948 (1976)

    ADS  Google Scholar 

  • Frehland, E.: Diffusion as a source of 1/f noise. J. Membrane Biol.32, 195–196 (1977)

    Article  Google Scholar 

  • Frehland, E., Läuger, P.: Ion transport through pores: Transient phenomena. J. theor. Biol.47, 189–207 (1974)

    Article  Google Scholar 

  • Glasstone, S., Laidler, K. J., Eyring, H.: The theory of rate processes, chapter 9. New York: McGraw-Hill 1941

    Google Scholar 

  • Green, M. E.: Noise spectra of ion transport across an anion membrane. J. physic. Chem.78, 761–762 (1974)

    Article  ADS  Google Scholar 

  • Green, M. E.: Diffusion and 1/f noise. J. Membrane Biol.28, 181–186 (1976)

    Article  Google Scholar 

  • Green, M. E.: Diffusion and 1/f noise. Part II. J. Membrane Biol.32, 197–199 (1977)

    Article  Google Scholar 

  • Green, M. E., Yafuso, M.: A study of the noise generated during ion transport across membranes. J. physic. Chem.72, 4072–4078 (1968); corrections: J. physic. Chem.73, 1626 (1969)

    Article  Google Scholar 

  • Heiden, C.: Power spectrum of stochastic pulse sequences with correlation between the pulse parameters. Phys. Rev.188, 319–326 (1969)

    Article  ADS  Google Scholar 

  • Hill, T. L., der Chen, Y.: On the theory of ion transport across the nerve membrane. IV Noise from the open-close kinetics of K+ channels. Biophys. J.12, 948–959 (1972)

    Google Scholar 

  • Hille, B.: Pharmacological modifications of the sodium channels of frog nerve. J. gen. Physiol.51, 199–219 (1968)

    Article  Google Scholar 

  • Hille, B.: Ionic selectivity, saturation, and block in sodium channels: A four barrier model. J. gen. Physiol.66, 535–560 (1975)

    Article  Google Scholar 

  • Holden, A. V.: Flicker noise and structural changes in nerve membrane. J. theor. Biol.57, 243–246 (1976)

    Google Scholar 

  • Holden, A. V., Rubio, J. E.: A model for Flicker noise in nerve membranes. Biol. Cybern.24, 227–236 (1976)

    Article  MATH  Google Scholar 

  • Hooge, F. N.: Discussion of recent experiments on 1/f noise. Physica60, 130–144 (1972)

    Article  ADS  Google Scholar 

  • Hooge, F. N.: 1/f noise. Physica83B, 14–23 (1976)

    Google Scholar 

  • Kingston, R. H., McWhorter, A. L.: Relaxation time of surface states on germanium. Phys. Rev.103, 534–540 (1956)

    Article  ADS  Google Scholar 

  • Kolb, H.-A., Läuger, P.: Electrical noise from lipid bilayer membranes in the presence of hydrophobic ions. J. Membrane Biol. (1977) in press

  • Läuger, P.: Shot noise in ion channels. Biochim. biophys. Acta (Amst.)413, 1–10 (1975)

    Google Scholar 

  • Läuger, P.: Discussion remark. In: Electrical phenomena at the biological membrane level (ed. E. Roux), p. 348. Amsterdam: Elsevier 1977

    Google Scholar 

  • Lax, M., Mengert, P.: Influence of trapping, diffusion and recombination on carrier concentration fluctuations. J. physic. Chem. Solids14, 248–267 (1960)

    Article  ADS  Google Scholar 

  • LeBlanc, O. H.: Tetraphenylborate conductance through lipid bilayer membranes. Biochim. biophys. Acta (Amst.)193, 350–360 (1969)

    Google Scholar 

  • Lundström, I., McQueen, D.: A proposed 1/f noise mechanism in nerve cell membranes. J. theor. Biol.45, 405–409 (1974)

    Article  Google Scholar 

  • Lundström, I., McQueen, D., Klason, C.: On low frequency and 1/f noise from diffusion like processes. Solid State Comm.13, 1941–1944 (1973)

    Article  ADS  Google Scholar 

  • Mauro, A., Conti, F., Dodge, F., Schor, R.: Subthreshold behaviour and phenomenological impedance of the squid giant axon. J. gen. Physiol.55, 497–523 (1970)

    Article  Google Scholar 

  • Michalides, J. P., Wallaart, R. A., DeFelice, L. J.: Electrical noise from PVC-membranes. Pflügers Arch.341, 97–104 (1973)

    Article  Google Scholar 

  • Mikulinsky, M. A., Mikulinsky-Fishman, S. N.: The theory of 1/f noise. Phys. Lett.58A, 46–48 (1976)

    ADS  Google Scholar 

  • Moolenaar, H. W.: Membrane noise in cultured cells and the protozoan Paramecium. Abstracts 5th International Biophysics Congress, P-521A, Copenhagen 1975

  • Moolenaar, W. H., de Goede, J., Verveen, A. A.: Membrane noise in Paramecium. Nature (Lond.)260, 344–346 (1976)

    Article  ADS  Google Scholar 

  • Moore, W. J.: Statistical studies of 1/f noise from carbon resistors. J. appl. Phys.45, 1896–1901 (1974)

    Article  ADS  Google Scholar 

  • Neher, E., Zingsheim, H. P.: The properties of ionic channels measured by noise analysis in thin lipid membranes. Pflügers Arch.351, 61–67 (1974)

    Article  Google Scholar 

  • Neumcke, B.: Diffusion polarization at lipid bilayer membranes. Biophysik7, 95–105 (1971)

    Article  Google Scholar 

  • Neumcke, B.: 1/f membrane noise generated by diffusion processes in unstirred solution layers. Biophys. Struct. Mechanism1, 295–309 (1975)

    Article  Google Scholar 

  • Offner, F. F.: 1/f noise in semiconductors. J. appl. Phys.41, 5033–5034 (1970)

    Article  ADS  Google Scholar 

  • Offner, F. F.: 1/f fluctuation in membrane potential as related to membrane theory. Biophys. J.11, 123–124 (1971a)

    Article  Google Scholar 

  • Offner, F. F.: Quantitative measurement of 1/f noise and membrane theory. Biophys. J.11, 969–971 (1971b)

    Google Scholar 

  • Offner, F. F.: Comments on “Modified randon-walk model of 1/f noise”. J. appl. Phys.43, 1277–1278 (1972)

    Article  ADS  Google Scholar 

  • Pfeiffer, H.: Elektronisches Rauschen, Teil 1: Rauschquellen. Aachen: Mayer 1962

    Google Scholar 

  • Poussait, D. J. M.: Nerve membrane current noise: Direct measurements under voltage clamp. Proc. nat. Acad. Sci. (Wash.)64, 95–99 (1969)

    Article  ADS  Google Scholar 

  • Poussart, D. J. M.: Membrane current noise in lobster axon under voltage clamp. Biophys. J.11, 211–234 (1971)

    Google Scholar 

  • Poussart, D. J. M.: Comments on the analysis of membrane noise by the “Integral spectrum” procedure. Biophys. J.18, 134–137 (1977)

    Google Scholar 

  • Roa, R. L., Pickard, W. F.: The use of membrane electrical noise in the study of Characean electrophysiology. J. exp. Botany27, 460–472 (1976)

    Google Scholar 

  • Robinson, R. A., Stokes, R. H.: Electrolyte solutions. London: Butterworths 1955

    Google Scholar 

  • Romine, W. O., Sherette, G. R., Brown, G. B., Bradley, R. J.: Evidence that nystatine may not form channels in thin lipid membranes. Biophys. J.17, 269–274 (1977)

    Google Scholar 

  • Schick, K. L.: Power spectra of pulse sequences and implications for membrane fluctuations. Acta biotheor. (Leiden)23, 1–17 (1974)

    Article  ADS  Google Scholar 

  • Schick, K. L., Verveen, A. A.: 1/f noise with a low frequency white noise limit. Nature (Lond.)251, 599–601 (1974)

    Article  ADS  Google Scholar 

  • Schönfeld, H.: Beitrag zum 1/f-Gesetz beim Rauschen von Halbleitern. Z. Naturforsch.10a, 291–300 (1955)

    ADS  Google Scholar 

  • Schwarz, J. R., Vogel, W.: Potassium inactivation in single myelinated nerve fibres of Xenopus laevis. Pflügers Arch.330, 61–73 (1971)

    Article  Google Scholar 

  • Siebenga, E., Verveen, A. A.: The dependence of the 1/f noise intensity of the node of Ranvier on membrane potential. In: Proceedings First European Biophysics Congress, vol. V, pp. 219–223. Wien: Medizinische Akademie 1971

    Google Scholar 

  • Siebenga, E., Verveen, A. A.: Membrane noise and ion transport in the node of Ranvier. In: Biomembranes, vol. 3 (ed. F. Kreuzer, J. F. G. Siegers), pp. 473–482. New York: Plenum Press 1972

    Google Scholar 

  • Siebenga, E., de Goede, J., Verveen, A. A.: The influence of TTX, DNP and TEA on membrane Flicker noise and shot effect noise of the frog node of Ranvier. Pflügers Arch.351, 25–34 (1974)

    Article  Google Scholar 

  • Siebenga, E., Meyer, A., Verveen, A. A.: Membrane shot-noise in electrically depolarized nodes of Ranvier. Pflügers Arch.341, 87–96 (1973)

    Article  Google Scholar 

  • Smejtek, P., Hsu, K., Perman, W. H.: Electrical conductivity in lipid bilayer membranes induced by pentachlorphenol. Biophys. J.16, 319–336 (1976)

    Google Scholar 

  • van den Berg, R. J., Beekman, R. E.: How many ions do ionic pores of the Ranvier node contain? In: 18th Dutch Federative Meeting, Abstract p. 127, 1977

  • van den Berg, R. J., de Goede, J., Verveen, A. A.: Conductance fluctuations in Ranvier nodes. Pflügers Arch.360, 17–23 (1975)

    Article  Google Scholar 

  • van den Berg, R. J., Siebenga, E., de Bruin, G.: Potassium ion noise currents and inactivation in voltage-clamped node of Ranvier. Nature (Lond.)265, 177–179 (1977)

    Article  ADS  Google Scholar 

  • van den Berg, R. J., Siebenga, E., de Goede, J., Moolenaar, W. H., Verveen, A. A.: 1/f noise in nerve membranes. In: Proceedings of the “Symposium on 1/f fluctuations”, Tokyo, July 1977, pp. 97–105.

  • van Vliet, K. M., Fassett, J. R.: Fluctuations due to electronic transitions and transport solids. In: Fluctuation phenomena in solids (ed. R. E. Burgess), pp. 267–354. New York: Academic Press 1965

    Google Scholar 

  • Verveen, A. A., DeFelice, L. J.: Membrane noise. Progr. Biophys. molec. Biol.28, 189–265 (1974)

    Article  Google Scholar 

  • Verveen, A. A., Derksen, H. E.: Fluctuations in membrane potential of axons and the problem of coding. Kybernetik2, 152–160 (1965)

    Google Scholar 

  • Verveen, A. A., Derksen, H. E.: Fluctuation phenomena in nerve membrane. Proc. IEEE56, 906–916 (1968)

    Article  Google Scholar 

  • Verveen, A. A., Derksen, H. E.: Amplitude distribution of axon membrane noise voltage. Acta physiol. pharmacol. neerl.15, 353–379 (1969)

    Google Scholar 

  • Verveen, A. A., Derksen, H. E., Schick, K. L.: Voltage fluctuations of neural membrane. Nature (Lond.)216, 588–589 (1967)

    ADS  Google Scholar 

  • Voss, R. F., Clarke, J.: 1/f noise from systems in thermal equilibrium. Phys. Rev. Lett.36, 42–45 (1976)

    Article  ADS  Google Scholar 

  • Wanke, E.: Monazomycin and nystatin channel noise. In: Abstracts 5th International Biophysics Congress, P-368. Copenhagen 1975

  • Wanke, E., DeFelice, L. J., Conti, F.: Voltage noise, current noise and impedance in space clamped squid giant axon. Pflügers Arch.347, 63–74 (1974)

    Article  Google Scholar 

  • Warncke, J.: Das Rauschen biologischer Membranen als Indikator für die am Ladungstransport beteiligte Trägerzahl. In: Jahrestagung der deutschen Gesellschaft für Biophysik, Programm S. 97, Freiburg i. Br. 1974

  • Weissman, M. B.: Models for 1/f noise in nerve membranes. Biophys. J.16, 1105–1108 (1976)

    Google Scholar 

  • Weissman, M. B.: A model for 1/f noise from singularities in the fluctuation weighting function. J. appl. Phys.48, 1705–1707 (1977)

    Article  ADS  Google Scholar 

  • Yafuso, M., Green, M. E.: Noise spectra associated with hydrochloric acid transport through some cation-exchange membranes. J. physic. Chem.75, 654–662 (1971)

    Article  Google Scholar 

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  1. I. Physiologisches Institut der Universität des Saarlandes, D-6650, Homburg/Saar, Federal Republic of Germany

    B. Neumcke

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Supported by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 38 “Membranforschung”

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Neumcke, B. 1/f noise in membranes. Biophys. Struct. Mechanism 4, 179–199 (1978). https://doi.org/10.1007/BF02426084

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