a B S TRAC T A literature review reveals many lines of evidence that both delayed rectifier and inward rectifier potassium channels are multi-ion pores. These include unidirectional flux ratios given by the 2-2.5 power of the electrochemical activity ratio, very steeply voltage-dependent block with monovalent blocking ions, relief of block by permeant ions added to the side opposite from the blocking ion, rectification depending on E -EK, and a minimum in the reversal potential or conductance as external K + ions are replaced by an equivalent concentration of TI + ions. We consider a channel with a linear sequence of energy barriers and binding sites. The channel can be occupied by more than one ion at a time, and ions hop in single file into vacant sites with rate constants that depend on barrier heights, membrane potential, and interionic repulsion. Such multi-ion models reproduce qualitatively the special flux properties of potassium channels when the barriers fi~r hopping out of the pore are larger than for hopping between sites within the pore and when there is repulsion between ions. These conditions also produce multiple maxima in the conductance-ion activity relationship. In agreement with Armstrong's hypothesis (1969.J. Gen. Physiol. 54:553-575), inward rectification may be understood in terms of block by an internal blocking cation. Potassium channels must have at least three sites and often contain at least two ions at a time.Evidence has accumulated, for the sodium channel and for several types of potassium channels of electrically excitable cells, that ions interact with the channel and with other ions in it while diffusing across the membrane (French and Adelman, 1976). An earlier paper of Hille (1975 b) discussed a model of the sodium channel in which the permeating ion must pass across a sequence of four energy barriers to cross the membrane. Inasmuch as the model assumed that no more than one ion could be in the channel at a time, it was called a oneion pore. In this paper we consider a similar type of linear, multibarrier model for a multi-ion pore where more than one ion may be in a channel at a time, and the ions are not permitted to pass by each other as they move through the channel. These assumptions lead to phenomena commonly referred to as "single-file diffusion" or the "long pore effect" which have been reported in measurements of the passive movement of ions in potassium channels of nerve, muscle, and other cell membranes. Our goal is to show that the major transport properties of potassium channels may be accounted for by this class of multi-ion channel models. For practical reasons, only a qualitative agreement is demonstrated here. An attempt to make more realistic models would need many more J. GEN. PHYSIOL. 9 The Rockefeller University Press .
