Skip to main content
Log in

A physical model of nerve axon—I. Ionic distribution, potential profile, and resting potential

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

A theory which is based on a set of assumptions different from those of the sodium theory is developed. Here the mobile ions are considered to be distributed at Donnan equilibrium and the axoplasm is regarded as an analog of a cation-exchanger. Following the spirit of the Debye-Hückel theory, some important features of the ionic distribution and electrical potential of the nerve fiber have been calculated. The results appear to be in better agreement with the experimental observations than the Goldman-Hodgkin-Katz equation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature

  • Baker, P. F., A. L. Hodgkin and H. Meves. 1964. “The Effect of Diluting the Internal Solution on the Electrical Properties of a Perfused Giant Axon.”J. Physiol.,170, 541–560.

    Google Scholar 

  • Bartlett, J. H. and R. A. Kromhout. 1952. “The Donnan Equilibrium.”Bull. Math. Biophys.,14, 385–391.

    Google Scholar 

  • Caldwell, P. C. 1957. “The Sensitivity to pH of the Inhibitory Effects of Dinitrophenol on Squid Giant Axons.”Biochem. J.,67, 1p-2p.

    Google Scholar 

  • Chang, D. C. 1975. Unpublished data.

  • Curtis, H. J. and K. S. Cole. 1940. “Membrane Resting and Action Potentials from the Squid Giant Axon.”J. Cell. Comp. Physiol.,19, 135–144.

    Article  Google Scholar 

  • Damadian, R. 1971. “Biological Ion Exchange Resins—I. Quantitative Electrostatic Correspondence of Fixed Charge and Mobile Counter-Ion.”Biophys. J.,11, 739–760.

    Google Scholar 

  • — 1973. “Biological Ion Exchanger Resins.”Ann. N.Y. Acad. Sci.,204, 211–244.

    Google Scholar 

  • Davson, H. 1970.A Textbook of General Physiology. Baltimore: Williams and Wilkins.

    Google Scholar 

  • Dean, R. B. 1941. “Theories of Electrolyte Equilibrium in Muscle.”Biol. Symp.,3, 331–348.

    Google Scholar 

  • Diamond, J. M. and E. M. Wright. 1969. “Biological Membrane: The Physical Basis of Ion and Non-electrolyte Selectivity.”A. Rev. Physiol.,31, 581–645.

    Article  Google Scholar 

  • Eisenman, G. 1968. “Ion Permeation of Cell Membranes and its Models.”Fed. Proc.,27, 1249–1251.

    Google Scholar 

  • Freeman, J. C. 1973. “Do Red Cells Ghosts Pump Sodium or Potassium?”Ann. N.Y. Sci.,204, 609–615.

    Google Scholar 

  • Goldman, D. E. 1943. “Potential, Impedance, and Rectification in Membranes.”J. Gen. Physiol.,27, 37–60.

    Article  Google Scholar 

  • Grundfest, H., C. Y. Kao and M. Altamirano. 1954. “Bioelectric Effects of Ions Micro-injected into the Giant Axon of Loligo.”J. Gen. Physiol.,38, 245–282.

    Article  Google Scholar 

  • Gunn, R., P. F. Curran and C. Patlak. 1968. “Experimental and Theoretical Evaluation of Total Potential at Zero Current as Given by the Constant Field Equation (D. Goldman) for a Cation Exchange Membrane in NaCl Solution.”Biophys. J.,8(A), 173.

    Google Scholar 

  • Hodgkin, A. L. 1958. “Ionic Movement and Electrical Activity in Giant Nerve Fibres.”Proc. R. Soc.,148B, 1–37.

    Google Scholar 

  • — and A. F. Huxley. 1952. “Current Carried by Sodium and Potassium Ions Through the Membrane of the Giant Axon of Loligo.”J. Physiol.,116, 449–472.

    Google Scholar 

  • — and —. 1952. “The Components of Membrane Conductance in the Giant Axon of Loligo.” —Ibid.,,116, 473–496.

    Google Scholar 

  • — and —. 1952. “The Dual Effect of Membrane Potential on Sodium Conductance in the Giant Axon of Loligo.” —Ibid.,,116, 497–506.

    Google Scholar 

  • — and —. 1952. “A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve.” —Ibid.,,117, 500–544.

    Google Scholar 

  • — and B. Katz. 1949. “The Effect of Sodium Ions on the Electrical Activity of the Giant Axon of the Squid.” —Ibid.,,108, 37–77.

    Google Scholar 

  • — and R. D. Keynes. 1955. “Active Transport of Cations in Giant Axons from Sepia and Loligo.” —Ibid.,,128, 28–60.

    Google Scholar 

  • Hurlbut, W. P. 1970. “Ion Movements in Nerve.” InMembranes and Ion Transport, Bittar, E. E., ed., Vol. 2, pp. 95–144. London: Wiley-Interscience.

    Google Scholar 

  • Karreman, G. 1964. “Adsorption of Ions at Charged Sites and Phase Boundary Potentials.”Bull. Math. Biophys.,26, 275–290.

    MATH  Google Scholar 

  • —. 1973. “Toward a Physical Understanding of Physiological Excitation as a Cooperative Specific Adsorption Phenomenon.” —Ibid.,,35, 149–171.

    Article  Google Scholar 

  • Katz, B. 1966.Nerve, Muscles and Synapse. New York: McGraw-Hill.

    Google Scholar 

  • Keynes, R. D. and G. W. Maisel. 1954. “The Energy Requirement for Sodium Extrusion from a Frog Muscle.”Proc. R. Soc., Series B,142, 383–392.

    Article  Google Scholar 

  • Koketsu, K. and Y. Kimura. 1960. “The Resting Potential and Intracellular Potassium of Skeletal Muscle in Frogs.”J. Cell. Comp. Physiol.,55, 239–244.

    Article  Google Scholar 

  • Levi, H. and H. H. Ussing. 1949. “Exchange of Sodium and Chloride in Frog Muscle.”Acta Physiol. Scand.,16, 232–249.

    Google Scholar 

  • Ling, G. N. 1952. “The Role of Phosphate in the Maintenance of the Resting Potential and Selective Ionic Accumulation in Frog Muscle Cells.”Phosphorous Metabolism, McElroy, W. D. and Glass, B., eds., Vol. 2, pp. 748–795. Baltimore: Johns Hopkins Press.

    Google Scholar 

  • —. 1960. “The Interpretation of Selective Ionic Permeability and Cellular Potentials in Terms of the Fixed Charge-Induction Hypothesis.”J. Gen. Physiol. Suppl.,43, 149–174.

    Article  Google Scholar 

  • —. 1962.Physical Theory of the Living State. Philadelphia: Balisdell.

    Google Scholar 

  • —. 1965a. “Physiology and Anatomy of the Cell Membrane: The Physical State of Water in the Living Cell.”Fed. Proc.,24(2), 103–112.

    Google Scholar 

  • —. 1965b. “The Membrane Theory and Other Views for Solute Permeability, Distribution, and Transport in Living Cells.”Perspect. Biol. Med.,9, 87–105.

    Google Scholar 

  • —, C. Miller and M. M. Ochsenfeld. 1973. “The Physical State of Solutes and Water in Living Cells according to the Association-Induction Hypothesis.”Ann. New York Acad. Sci.,283, 6–47.

    Google Scholar 

  • Landahl, H. D. 1953. “Note on the Donnan Equilibrium.”Bull. Math. Biophys.,15, 153–159.

    Google Scholar 

  • Maizels, M. 1951. “Factors in the Active Transport of Cations.”J. Physiol.,112, 59–83.

    Google Scholar 

  • Minkoff, L. and R. Damadian. 1973a. “Caloric Catastrophy.”Biophys. J.,13, 167–178.

    Google Scholar 

  • — and —. 1973b. “Energy Requirements of Bacterial Ion Exchange.”Ann, New York Acad. Sci.,204, 249–260.

    Google Scholar 

  • Proverbio, F., M. Condrescu-Guidi and G. Whittenbury. 1975. “Ouabain-Insensitive Na+ Stimulation of an Mg2+-Dependent ATPase in Kidney Tissue.”Biochim. Biophys. Acta,293, 281–292.

    Google Scholar 

  • Reichenberg, D. 1969. “Ion-Exchange Selectivity.”Ion-Exchange,1, 227–275.

    Google Scholar 

  • Romualdez, A. G. and R. I. Sha'afi. 1975. “Effect of ATP on Sodium and Potassium Transport in Dog Erythrocytes.”Fed. Proc.,34(3), 237.

    Google Scholar 

  • Singer, I. and I. Tasaki. 1968. “Nerve Excitability and Membrane Macromolecules.” InBiological Membranes: Physical Facts and Function, Chapman, D., ed., pp. 347–410. New York: Academic Press.

    Google Scholar 

  • Tasaki, I. 1968.Nerve Excitation: A Macromolecular Approach. Springfield, Illinois: Charles C. Thomas.

    Google Scholar 

  • —, I. Singer and T. Takenaka. 1965. “Effect of Internal and External Ionic Environment on Excitability of Squid Giant Axon.”J. Gen. Physiol.,48, 1095–1123.

    Article  Google Scholar 

  • — and T. Takenaka. 1964. “Ion Fluxes and Excitability in Squid Giant Axon.” InThe Cellular Function of Membrane Transport. Hoffman, J. F., ed., pp. 95–111. Englewood Cliffs: Prentice-Hall.

    Google Scholar 

  • Troshin, A. S. 1966.Problem of Cell Permeability. Oxford: Pergamon Press.

    Google Scholar 

  • Wei, L. Y. 1969. “Molecular Mechanisms of Nerve Excitation and Conduction.”Bull. Math. Biophys.,31, 39–58.

    Google Scholar 

  • Wiggins, P. M. 1973. “Ionic Partition between Surface and Bulk Water in Silica Gel.”Biophys. J.,13, 385–398.

    Google Scholar 

  • Yeh, H., F. J. Brinley and E. D. Becker. 1973. “Nuclear Magnetic Resonance Studies on Intracellular Sodium in Human Erythrocytes and Frog Muscle.”Biophys. J.,13, 56–71.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

A summary of this work has been reported in the 1974 March meeting of the American Physical Society and the 1976 annual meeting of the Biophysical Society.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chang, D.C. A physical model of nerve axon—I. Ionic distribution, potential profile, and resting potential. Bltn Mathcal Biology 39, 1–22 (1977). https://doi.org/10.1007/BF02460678

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02460678

Keywords

Navigation