We present a novel recursion method for obtaining theoretical expressions for unidirectional single-file fluxes of ions through narrow membrane channels containing an arbitrary number of ion sites. The theory is applied to experimental tracer fluxes associated with nerve impulses from cephalopod giant axon membranes at various temperatures between 70 and 270. The comparison between the theoretical and experimental one-way fluxes suggests that the potassium channel in nerve membrane contains three ion sites, which is consistent with the deduction by Hodgkin and Keynes that the potassium channel contains two or three sites on the basis of the ratio of tracer influx to tracer efflux. The analytical results in this paper provide a further test of the single-file model for nerve and other membrane preparations.The exchange of K+ across the nerve membrane during nerve impulses is considerably less than that predicted from the Hodgkin-Huxley equations, assuming independent movement of ions (1, 2). One explanation of this discrepancy may be that K+ interact with one another within the membrane. For example, Hodgkin and Keynes (3) demonstrated that the voltage-dependence of the ratio of passive fluxes in resting membrane is consistent with a single-file model in which ions move via "knock-cn" collisions through a narrow channel containing two or three ion sites. A problem with comparing the single-file model to flux data associated with nerve activity has been the lack of theoretical expressions for the one-way fluxes.In this paper we present such expressions for a channel containing an arbitrary number of sites which we use to calculate the unidirectional fluxes during a Hodgkin-Huxley model action potential. The results are compared with the tracer flux data obtained from cephalopod giant axons at various temperatures between 70 and 270 (2). We find the data to be consistent with a model channel containing three ion sites. Description of the model A detailed description of our model of ion translocation has been given in our theoretical work on K+ current noise in nerve membrane (4, 5). We start with the model of Hodgkin and Keynes (3) which consists of a channel having s (s > 1) fully occupied K-selective sites along which K+ move in single file. The ion row moves only when a K+ from the internal or external bathing solution strikes the corresponding end of the channel with sufficient energy to overcome static forces that tend to keep the ions in place. We separate the motion of the channel ions into its temporal and spatial components by describing successful collisions from either side of the membrane with a single probability density function ,6(t). That is, ,t(t)dt is the probability of a successful collision from either side of the membrane within the infinitesimal time interval (t, t + dt).The process represented by f(t) is in general semi-Markovian.The motion of the channel row in response to a successful collision is described by the probability p(/), in which IlI is the distance that the row moves and...