The Journal of Membrane Biology

, Volume 82, Issue 3, pp 221–239 | Cite as

Slow potential changes due to transport number effects in cells with unstirred membrane invaginations or dendrites

  • Peter H. Barry


Many neurones are extremely invaginated and possess branching processes, axons and dendrites. In general, they are surrounded by a restricted diffusion space. Many of these cells exhibit large, slow potential changes during the passage of current across their membranes. Whenever currents cross membranes separating aqueous solutions, differences in transport numbers of the major permeant ions give rise to local concentration changes of these ions adjacent to the membranes, which will result in various electrical and osmotic effects. These transport number effects are expected to be enhanced by the presence of membrane invaginations. Dendrites are equivalent to reversed invaginations and there should be significant changes in concentrations of permeant ions within them. In general, the effects of such changes on the electrical response of a cell will be greater when the concentration of a major permeant ion is low. The effects have been modelled in terms of two nondimensional parameters: the invagination transport number parameter β and the relative area occupied by the invaginations δA. If these two parameters are known, the magnitudes and time course of the slow potential changes can immediately be estimated and the time course converted to real time, if the length of the invaginations (l) and ionic diffusion coefficient (D) within them are also known. Both analytical and numerical solutions have been given and predictions compared. It is shown that in the case of large currents and potentials the analytical solution predictions will underestimate the magnitudes and rates of onset of the voltage responses. The relative magnitude of the transport number effect within the invaginations (or dendrites) and other transport number contributions to slow potential changes have also been assessed and order-of-magnitude values of these are estimated for some biological data.

Key Words

transport number effects membrane invaginations dendrites restricted diffusion space slow potential changes slow conductance changes neurones solute polarization membrane infoldings 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Almers, W. 1972. Potassium conductance changes in skeletal muscle and the potassium concentration in the transverse tubules.J. Physiol. (London) 225:33–56Google Scholar
  2. Andrews, S. 1977. A Study of Neurones in Aplysia Abdominal Ganglia. M. Sc. Thesis. University of New South Wales. Sydney, AustraliaGoogle Scholar
  3. Barry, P.H. 1977. Transport number effects in the transverse tubular system and their implications for low frequency impedance measurement of capacitance of skeletal muscle fibers.J. Membrane Biol. 34:383–408Google Scholar
  4. Barry, P.H. 1983. The effects of unstirred-layers on the movement of ions across cell membranes.Proc. Aust. Physiol. Pharmacol. Soc. 14:152–169Google Scholar
  5. Barry, P.H., 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. 14:243–292Google Scholar
  6. Barry, P.H., Diamond, J.M. 1984. Effects of unstirred layers on membrane phenomena.Physiol. Rev. 64:763–872Google Scholar
  7. Barry, P.H., Dulhunty, A.F. 1984. Slow potential changes in mammalian muscle fibres during prolonged hyperpolarization: Transport number effects and chloride depletion.J. Membrane Biol. 78:235–248Google Scholar
  8. Barry, P.H., Hope, A.B. 1969a. Electroosmosis in membranes: Effects of unstirred layers and transport numbers. I. Theory.Biophys. J. 9:700–728Google Scholar
  9. Barry, P.H., Hope, A.B. 1969b. Electroosmosis in membranes: Effects of unstirred layers and transport numbers. II. Experimental.Biophys. J. 9:729–757Google Scholar
  10. Bullock, T.H., Orkand, R., Grinell, A. 1977. Introduction to the Nervous System. W.H. Freeman, San FranciscoGoogle Scholar
  11. Carslaw, H.S., Jaeger, J.C. 1959. Conduction of Heat in Solids. 2nd Edition. Clarendon, OxfordGoogle Scholar
  12. Coggeshall, R.E. 1967. A light and electron microscope study of the abdominal ganglion ofAplysia californica.J. Neurophysiol. 13:1263–1287Google Scholar
  13. Dewhurst, D.J. 1960. Concentration polarization in plane membrane-solution systems.Trans. Faraday Soc. 56:599–609Google Scholar
  14. Eaton, D.C. 1972. Potassium ion accumulation near a pace-making cell ofAplysia.J. Physiol. (London) 224:421–440Google Scholar
  15. Fenwick, E., Marty, A., Neher, E. 1982. Sodium and calcium channels in bovine chromaffin cells.J. Physiol. (London) 331:599–635Google Scholar
  16. Frankenheuser, B., Hodgkin, A.L. 1956. The after-effects of impulses in the giant nerve fibres ofLoligo.J. Physiol. (London) 131:341–376Google Scholar
  17. Gorman, A.L.F., Mirolli, M. 1972. The passive electrical properties of the membrane of a molluscan neurone.J. Physiol. (London) 227:35–49Google Scholar
  18. Graubard, K. 1975. Voltage attenuation withinAplysia neurons: The effect of branching pattern.Brain Res. 88:325–332Google Scholar
  19. Jaeger, J.C. 1961. An Introduction to the Laplace Transformation. 2nd Edition. Methuen, LondonGoogle Scholar
  20. Johnston, D., Brown, T.H. 1983. Interpretation of voltage-clamp measurements in hippocampal neurons.J. Neurophysiol. 50:464–486Google Scholar
  21. Kostyuk, P.G. 1981. Calcium channels in the neuronal membrane.Biochim. Biophys. Acta 650:128–150Google Scholar
  22. Lakshminarayanaiah, N. 1967. Water transport through cation exchange membranes.Desalination 3:97–105Google Scholar
  23. MacDonald, R.C. 1976. Effects of unstirred layers or transport number discontinuities on the transient and steady-state current-voltage relationships of membranes.Biochim. Biophys. Acta 448:199–219Google Scholar
  24. MacLachlan, N.W. 1953. Complex Variable Theory and Transform Calculus. Cambridge University Press, CambridgeGoogle Scholar
  25. Mirolli, M., Talbott, S.R. 1972. The geometrical factors determining the electrotonic properties of a molluscan neurone.J. Physiol. (London) 227:19–34Google Scholar
  26. Neher, E., Lux, H.D. 1973. Rapid changes of potassium concentration at the outer surface of exposed single neurons during membrane current flow.J. Gen. Physiol. 61:385–399Google Scholar
  27. Noyes, D.H., Rehm, W.S. 1971. Unstirred layer model for the long time-constant transient voltage response to current in epithelial tissue.J. Theor. Biol. 32:25–45Google Scholar
  28. Orkand, R.K. 1980. Symposium on: Functional Consequences of Ionic Changes Resulting from Electrical Activity.Fed. Proc. 39:1514–1542Google Scholar
  29. Robinson, R.A., Stokes, R.H. 1965. Electrolyte Solutions. Butterworths, LondonGoogle Scholar
  30. Segal, J.R. 1967. Electrical capacitance of ion-exchanger membranes.J. Theor. Biol. 14:11–34Google Scholar
  31. Smith, J.R. 1977. Electrical Characteristics, of Biological Membranes in Different Environments. Ph.D. Thesis. University of New South Wales, Sydney, AustraliaGoogle Scholar
  32. Tsien, R.W. 1983. Calcium channels in excitable cell membranes.Annu. Rev. Physiol. 45:341–358Google Scholar
  33. Valdiosera, R., Clausen, C., Eisenberg, R.S. 1974. Impedance of frog skeletal muscle fibers in various solutions.J. Gen. Physiol. 63:460–491Google Scholar
  34. Wedner, H.J., Diamond, J.M. 1969. Contributions of unstirredlayer effects to apparent electrokinetic phenomena in the gall bladder.J. Membrane Biol. 1:92–108Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Peter H. Barry
    • 1
  1. 1.Nerve-Muscle Research Centre, School of Physiology and PharmacologyUniversity of New South WalesKensingtonAustralia

Personalised recommendations