On the theory of interfacial double-layer potential differences and periaxonal accumulation of potassium in squid giant axons

The steady state potassium conductance as a function of measured membrane potential difference (p.d.) ? of the squid giant axon is corrected for the effect of accumulation of potassium in the periaxonal space. This correction is made on the assumption that several mathematical models of the axon are valid. These are (i) the McIlroy (1975), McIlroy-Hahn (1978) model of membrane conductanceg _i(i=K, Na) which is a detailed model of passive transport of ions across the axonal membrane with the aid of mobile, negatively-charged carriers, (ii) the Adelmanet al. (1973) compartmental model of the periaxonal and external bathing-solution spaces, (iii) the enzymatic theory of nervous conduction due to McIlroy (1970 a, b, c), (iv) the Wien dissociative effect of the axolemmic electric field on the weak membrane buffer proposed by Bass and Moore (1968) as a trigger mechanism in nervous excitation and (v) the model (McIlroy, 1979) of the interfacial double-layer p.d.s. which are assumed to exist at the membrane’s surfaces because of the presence of a fixed surface charge. From the correctedg _k (?) curves the values of the double-layer p.d.s. of model (v) are deduced and these are shown to lead to a consistent, physically reasonable solution for the distance (approx. 6.8Å) between the fixed surface charges and for the dissociation constants of these sites in their interactions with the ions of the extra-membrane electrolytes. Assuming that the selectivity coefficint of the potassium conducting system for the squid giant axon is approx. 52 it is deduced that the potassium permeability,P _ks , of the periaxonal barrier ≈1.37(±0.5)×10^?4 cm sec^?1 and the thickness of the periaxonal space ≈451±159Å.