Unidirectional fluxes in saturated single-file pores of biological and artificial membranes I. Pores containing no more than one vacancy

A theoretical treatment of isotope fluxes in filled single-file pores is given. The treatment is confined to pores permitting only one vacancy at a time. Tracer flux, unidirectional fluxes and net flux are calculated. The exponent n which is obtained by representing the ratio of unidirectional fluxes as a power of the electrochemical activity-ratio proves to be closely related with m, the number of sites per pore. The minimum and maximum values of n are m?1 and m. It is shown that measurement of n provides sufficient information to determine m if the energetic properties of sites and barriers do not change too much with varying concentrations. Unlike the unidirectional fluxes, the net fluxes yield no direct information about the number of sites. The concentration dependence of the net fluxes, however, can be used to discriminate between the two limiting cases, n = m?1 and n = m. It is interesting with regard to the instantaneous potassium currents of nerve membranes that a suitable choice of the energetic parameters of a filled pore leads to a quasi-linearity of the net flux-voltage curves, which is only slightly affected by variation of the external concentration.