Bulletin of Mathematical Biology

, Volume 41, Issue 3, pp 343–356 | Cite as

Analysis of potassium conductance in squid giant axons

  • Douglas K. McIlroy


Assuming a model of facilitated ionic transport across axonal membranes proposed by McIlroy (1975) and extended by McIlroy and Hahn (1978), it is shown that if the selectivity coefficient, πK, of the potassium conducting system ≃59 the permeabilityP Ks, of the periaxonal barrier of the squid giant axon for K+ ions≃(1.2±0.44)×10−4 cm sec−1 and the thickness of the periaxonal space ≃477±168 Å. Using a value (10−4 cm sec−1) ofP Ks in the foregoing range the experimental curves for the steady state membrane ionic conductance versus measured membrane potential difference (p.d.), ϕ, of Gilbert and Ehrenstein (1969) are corrected for the effect of accumulation of K+ in the periaxonal space. This correction is most marked for the axon immersed in a natural ionic environment, whose conductance curve is shifted ≃70mV along the voltage axis in the hyperpolarization direction.

By assuming that the physico-chemical connection between a depolarization of the axonal membrane and the consequent membrane conductance changes is a Wien dissociative effect of the membrane's electric field on a weak electrolyte situated in the axolemma, the position of the peaks of the corrected conductance versus ϕ curves can be identified with zero membrane electric field and hence with zero p.d.across the axolemma. A set of values for the double-layer p.d.s at the axonal membrane interfaces with the external electrolytes in the vicinity of the K+ conducting pores can therefore be deduced for the various external electrolytes employed by Gilbert and Ehrenstein. A model of these double-layer p.d.s in which the membrane interfaces are assumed to possess fixed monovalent negatively charged sites, at least in the neighbourhood of the K+ conducting pores, is constructed. It is shown that, using the previously deduced values for the doublelayer p.d.s, such a model has a consistent, physically realistic solution for the distance between the fixed charged sites and for the dissociation constants of these sites in their interaction with the ions of the extramembrane electrolytes.


Giant Axon Potassium Conductance Conductance Curve Membrane Interface Axonal Membrane 
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Copyright information

© Society for Mathematical Biology 1979

Authors and Affiliations

  • Douglas K. McIlroy
    • 1
  1. 1.Department of Applied MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa

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