Summary
A fundamental approach to calculate the diffusion of ions through membranes is introduced. The membran eis considered as a heterogeneous structure with molecules that can have a selective affinity for a certain class of diffusing ions. To diffuse through a membrane an ion must become associated with, or dissolved into, at least one component of that membrane. Diffusion is produced by thermal jumps from one molecular site to another. It is assumed that the electric field can change the binding properties between ions and membrane molecules. The kinetics of the conductances are calculated from the chemical kinetic theory. The calculations are compared to the squid axon data and the unknown parameters are adjusted to fit the data curves. The results are very satisfactory. The calculated activation energies correspond to the measuredQ 10 in the squid axon. The calculated and measured action potentials are quite similar.
Similar content being viewed by others
References
Blumenthal, R., Changeux, J.-P., Lefever, R. 1970. Membrane excitability and dissipative instabilities.J. Membrane Biol. 2:351.
Cole, K. S. 1949. Dynamic electrical characteristics of the squid axon membrane.Arch. Sci. Physiol. 3:253.
— 1968. Nonlinear and active membrane behaviors: Mechanisms.In: Membranes, Ions and Impulses. C. A. Tobias, editor. p. 184. University of California Press, Berkeley, Calif.
Ehrenstein, G., Gilbert, D. L. 1966. Slow changes in potassium permeability in squid giant axon.Biophys. J. 6:533.
Frenkel, J. 1946. Heat motion in liquids and their mechanical properties.In: Kinetic Theory of Liquids. Sir Fowler, N. F. Mott, and P. Kapitza, editors. p. 188. Oxford University Press, England.
Glasstone, S., Laidler, K. J., Eyring, H. 1941. The theory of absolute reaction rates.In: Theory of Rate Processes. L. P. Hammett, editor. p. 148. McGraw-Hill Book Co., New York and London.
Hodgkin, A. L., Huxley, A. F. 1952a. Currents carried by sodium and potassium ions through the membrane of the giant axon ofLoligo.J. Physiol. 116:449.
—— 1952b. The components of membrane conductance in the giant axon ofLoligo.J. Physiol. 116:472.
—— 1952c. The dual effect of membrane potential on sodium conductance in the giant axon ofLoligo.J. Physiol. 116:497.
—— 1952d. A quantitative description of membrane current and its application to conduction and excitation in nerve.J. Physiol. 117:500.
——, Katz, B. 1952. Measurement of current-voltage relations in the membrane of the giant axon ofLoligo.J. Physiol. 116:424.
Jost, W. 1960. Theory of diffusion in solids.In: Diffusion in Solids, Liquids and Gases. E. M. Loebl, editor. p. 135. Academic Press Inc., New York.
Roy, G. 1969. A model for electrical conductivity of the squid axon: conducting channel approach. Ph. D. Thesis. University of California, Berkeley, Calif.
Shewmon, P. G. 1963. Atomic theory of diffusion.In: Diffusion in Solids, R. F. Mehl, Senior Advisor editor. p. 40. McGraw-Hill Book Company Inc. U.S.A., Canada, U.K.
Tsein, R. W., Noble, D. 1969. A transition state theory approach to the kinetics of conductance changes in excitable membranes.J. Membrane Biol. 1:248.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Roy, G. Ionic diffusion in membranes. J. Membrain Biol. 6, 329–352 (1971). https://doi.org/10.1007/BF02116578
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02116578