Abstract
The driven system of conducting channels in a nerve membrane is investigated. A current flow generates a coupling between the channels: the current through a channel is influenced by the presence of other conducting channels via the deformation of the equipotential surfaces within the media adjacent to the membrane. We derive an integral equation for the membrane voltageV(s) (s in the membrane plane) and solve it for different membrane conductance distributionsγ(s) including models for stochastic distributions of conducting channels.V(s) is a nonlinear functional ofγ(s). The system of coupled channels is compared with an Ising model. The system exhibits a multi-channel interaction which can be characterized by two different rangesd int andD 1. For a mean channel distanced 0≫d int interaction effects are negligible, and ford 0≪D 1 all channel-voltages are equal and thus represent a “mean-field” for the channels. Increasing conductivity of the medium decreasesd int and increasesD 1. With experimental data on sodium channels in nerve membranes we find:d int≈d 0, i.e. a 50% decrease of the channel-voltages by the interaction, andD 1≈103⋯104 d 0, which indicates mean-field behaviour of the channels. In a subsequent paper we shall treat the statistics of channels which open and close stochastically under the influence of the local membrane voltage.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cole, K.S.: Membranes, Ions and Impulses. Berkeley-Los Angeles-London: University of California Press 1968
Scott, A.C.: Rev. Mod. Phys.47, 487 (1975)
Ehrenstein, G.: Physics Today29, No. 10, 33 (1976)
Ulbricht, W.: Biophys. Struct. Mechanism1, 1 (1974) and Ann. Rev. Biophys. Bioeng.6, 7 (1977)
Hodgkin, A.L., Huxley, A.F.: J. Physiol. (Lond.)116, 449, 473 and 497 (1952); ibid.117, 500 (1952)
Changeux, J.P., Thiéry, N., Tung, I., Kittel, C.: Proc. Nat. Acad. Sci. (U.S.A.)57, 335 (1967)
Adam, G.: Z. Naturforsch.236, 181 (1968)
Blumenthal, R., Changeux, J.P., Lefever, R.: J. Membr. Biol.2, 351 (1970)
Hamel, B.B., Zimmerman, I.: Biophys. J.10, 1029 (1970)
Bass, L., Moore, W.J.: J. Membr. Biol.12, 361 (1973)
Starzak, M.E.: J. Theor. Biol.39, 487 (1973)
Bretag, A.H., Davis, B.R., Kerr, D.I.B.: J. Membr. Biol.16, 363 (1974)
Aizawa, Y., Kobatake, Y.: Progr. Theor. Phys.52, 1094 (1974); J. Stat. Phys.15, 129 (1976)
Gotoh, H.: J. Theor. Biol.53, 309 (1975)
Gosh, P.K., Sengupta, D.: J. Theor. Biol.73, 609 (1978)
Binstock, L., Adelman Jr., W.J., Senft, J.P., Lecar, H.: J. Membr. Biol.21, 25 (1975)
Keynes, R.D., Rojas, E.: J. Physiol. (Lond.)255, 157 (1976)
Takashima, S., Yantorno, R., Novack, R.: Biochim. Biophys. Acta469, 74 (1977)
von der Heydt, I., von der Heydt, N., Obermair, G.: Lecture notes in Physics84, 343, Berlin-Heidelberg-New York: Springer 1978
Jackson, J.D.: Classical Electrodynamics. New York-London-Sydney: Wiley 1965
Durand, E.: Electrostatique, Vol. III+I. Paris: Masson et Cie. 1966
Abramowitz, M., Stegun, I.A. (ed.): Handbook of Mathematical Functions, New York: Dover Publications 1965
Gradshteyn, I.S., Ryzhik, I.M.: Tables of Integrals, Series and Products, 4th ed. New York-San Francisco-London: Academic Press 1965
Läuger, P.: Biochim. Biophys. Acta455, 493 (1976)
Ewald, P.P.: Ann. Physik 464, 253 (1921)
Tosi, M.P.: Solid State Physics16, 1 (1964)
Fisher, M.E.: J. Phys. Soc. Japán (Suppl.)26, 87 (1969)
Becker, F., Hahn, H.: Phys. Lett. A42, 9 (1972)
Decker, I., Hahn, H.: Physica83A, 143 (1976); ibid.89A, 37 (1977)
Kittel, C.: Introduction to Solid State Physics, 5th ed., New York-London-Sydney-Toronto: Wiley 1976
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
von der Heydt, N., von der Heydt, I. Current-induced coupling between conductance channels in membranes. Z Physik B 37, 249–264 (1980). https://doi.org/10.1007/BF01323039
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01323039