Analysis of Membrane Properties Using Extrinsic Noise

  • Richard T. Mathias


Biological membranes have been studied using a wide variety of techniques. One of the newest and most exciting of these techniques is to observe the random component of membrane current which occurs in response to the opening and closing of intrinsic membrane channels. A closely related approach is to drive the channels with an extrinsic signal of random time course and observe the correlation between fluctuations in membrane current and fluctuations in the input voltage. These approaches are related in the sense that each requires frequency domain analysis and each uses the same model of channel gating to interpret the data. They differ in that each experiment emphasizes a different aspect of the model for gating; but in situations where both techniques can be applied, this difference makes them complementary.


Membrane Property Membrane Voltage Volterra Series Volterra Kernel Current Voltage Relationship 
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  1. Abramowitz, M. and Stegun, I. A., 1972, “Handbook of Mathematical Functions,” Dover, N.Y.Google Scholar
  2. Adrian, R. H. and Freygang, W. H., 1962, The potassium and chloride conductance of frog muscle membrane, J. Physiol., 163:61.PubMedGoogle Scholar
  3. Aimers, W., Fink, R. and Palade, P.T., 1981, Calcium depletion in frog muscle tubules: the decline of calcium current under maintained depolarization, J. Physiol., 312:177.Google Scholar
  4. Andersen, O. S., 1978, Permeability properties of unmodified lipid bilayer membranes, in: “Membrane Transport in Biology, Vol. I, “D. C. Tosteson, ed., Springer-Verlag, Berlin.Google Scholar
  5. Armstrong, C. M. and Bezanilla, F., 1973, Currents related to movement of the gating particles of the sodium channels, Nature, 242:459.PubMedCrossRefGoogle Scholar
  6. Armstrong, C. M. and Bezanilla, F., 1977, Inactivation of the sodium channel. II. Gating current experiments. J. Gen.Physiol., 70:567.Google Scholar
  7. Armstrong, C. M. and Gilly, W. F., 1979, Fast and slow steps in the activation of sodium channels, J. Gen. Physiol., 74:691.Google Scholar
  8. Attwell, D., Eisner, D. and Cohen, I., 1979, Voltage clamp and tracer flux data: effects of a restricted extra-cellular space, Quart. Rev. Biophys., 12:213.Google Scholar
  9. Barry, P. H. and Adrian, R. H., 1973, Slow conductance changes due to potassium depletion in the transverse tubules of frog muscle fibers during hyperpolarizing pulses, J. Membrane Biol., 14:243.CrossRefGoogle Scholar
  10. Bendat, J. S. and Piersol, A. G., 1971, “Random Data : Analysis and Measurement Procedures,” Wiley, N.Y.Google Scholar
  11. Bezanilla, F. and Armstrong, C. M., 1975, Kinetic properties of the gating currents of sodium channels in squid axon, Phil. Trans. R. soc. Lond. B., 270:449.CrossRefGoogle Scholar
  12. Carrier, G. F., Krook, M. and Pearson, C. E., 1966, “Functions of a Complex Variable,” McGraw-Hill, N.Y.Google Scholar
  13. Clausen, C. and Fernandez, J. M., 1981, A low-cost method for rapid transfer function measurements with direct application to biological impedance analysis, Pflugers Arch., 390:290.PubMedCrossRefGoogle Scholar
  14. Cole, K. S., 1972, “Membranes Ions and Impulses,” University of California Press, Berkeley.Google Scholar
  15. DeFelice, L. J., Adelman, Jr., W. J., Clapbam, D. E. and Mauro, A., 1981, Second-order admittance in squid axon, in: “The Biophysical Approach to Excitable Systems,” W. J. Adelman, Jr., ed., Plenum, N.Y.Google Scholar
  16. Desoer, C. A. and Kuh, E. S., 1969, “Basic Circuit Theory,” McGraw-Hill, N.Y.Google Scholar
  17. Eisenberg, R. S. and Mathias, R. T., 1980, Structural analysis of electrical properties of cells and tissues, in: “Critical Reviews in Bioengineering,” J. R. Bourne, ed., CRC Press, Boca Raton, FL.Google Scholar
  18. Eisenberg, F. S., 1983, Chapter II. Impedance measurement of the electrical structure of skeletal muscle, in: “Handbook of General Physiology,” L. D. Peachey, ed., Williams and Wilkens, Inc., Baltimore, MD.Google Scholar
  19. Falk, G. and Fatt, P., 1964, Linear electrical properties of striated muscle fibers observed with intracellular electrodes, Proc. R. Soc. Lond. B. Biol. Sci., 160:69.PubMedCrossRefGoogle Scholar
  20. Fernandez, J. M., Bezanilla, F. and Taylor, R. E., 1982, Distribution and kinetics of membrane dielectric polarization, J. Gen. Physiol., 79:41.Google Scholar
  21. Fishman, H. M., Moore, L. E. and Poussart, P., 1981, Squid axon K conduction: admittance and noise during short- versus long-duration step clamps, in: “The Biophysical Approach to Excitable Systems,” W. J. Adelman, Jr., ed., Plenum, N.Y.Google Scholar
  22. Goldman, L. and Hahin, R., 1978, Initial conditions and the kinetics of the sodium conductance in Myxicola giant axons, J. Gen. Physiol., 72:879.Google Scholar
  23. Hodgkin, A. L. and Huxleyy A. F., 1952, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol., 117:500.PubMedGoogle Scholar
  24. Kootsey, J. M. and Johnson, E. A., 1973, Buffer amplifier with femtofarad input capacity using operational amplifiers, IEEE Tran. Biomed. Engr., 20:389.Google Scholar
  25. Levis, R., Mathias, R. T. and Eisenberg, R. S., 1983. Electrical properties of sheep Purkinje strands. Electrical and chemical potentials in the clefts. Biophys. J., 44:225.Google Scholar
  26. Marmarelis, P. Z. and Naka, K. I., 1974, Identification of multi-input biological systems, IEEE Trans. on Biomed. Engr., 21:88.Google Scholar
  27. Mathias, R. T., Rae, J. L. and Eisenberg, R. S., 1979, Electrical properties of structural components of the crystalline lens, Biophys. J., 25:181.Google Scholar
  28. Mathias, R. T., Rae, J. L. and Eisenberg, R. S., 1981, The lens as a nonuniform spherical syncytium, Biophys. J., 34:61.Google Scholar
  29. Mathias, R. T., Ebihara, L., Lieberman, M. and Johnson, E. A., 1981, Linear electrical properties of and active currents in spherical heart cell clusters, Biophys. J., 36:221.Google Scholar
  30. Palm, G. and Poggio, T., 1977a, The Volterra representation and the Wiener expansion: validity and pitfalls, SIAM J., 33:195.Google Scholar
  31. Palm, G. and Poggio, T., 1977b, Wiener-like system identification in physiology, J. Math. Biol., 4:375.Google Scholar
  32. Papoulis, A., 1965, “Probability, Random Variables, and Stochastic Processes,” McGraw-Hill, N.Y.Google Scholar
  33. Papoulis, A., 1977, “Signal Analysis,” McGraw-Hill, N.Y.Google Scholar
  34. Poussart, D. J. M. and Ganguly, U. S., 1977, Rapid measurement of system kinetics — an instrument for real-time transfer function analysis, Proc. IEEE, 65:741.CrossRefGoogle Scholar
  35. Schetzen, M., 1980, “The Volterra and Wiener Theories of Nonlinear Systems,” Wiley, N.Y.Google Scholar
  36. Sigworth, F. J. 1981, Interpreting power spectra from nonstationary membrane current fluctuations, Biophys. J., 35:289.PubMedCrossRefGoogle Scholar
  37. Smith, J. I., 1971, “Modern Operational Circuit Design,” Wiley, N.Y.Google Scholar
  38. Valdiosera, R., Clausen, C. and Fisenberg, R. S., 1974, Measurement of the impedance of frog skeletal muscle fibers, Biophys. J., 14:295.PubMedCrossRefGoogle Scholar
  39. Weiner, N., 1958, “Nonlinear Problems in Random Theory,” Wiley, N.Y.Google Scholar
  40. Zadeh, L. A., and Desoer, C. A., 1963, “Linear System Theory: The State Space Approach,” McGraw-Hill, N.Y.Google Scholar

Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • Richard T. Mathias
    • 1
  1. 1.Department of PhysiologyRush Medical CollegeChicagoUSA

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