A Paradox Concerning Ion Permeation of the Delayed Rectifier Potassium Ion Channel in Squid Giant Axons

1. The fully activated current-voltage relation (I-V) of the delayed rectifier potassium ion channel in squid giant axons has a non-linear dependence upon the driving force, V-EK, as I have previously demonstrated, where V is membrane potential and EK is the equilibrium potential for potassium ions. 2. The non-linearity of the I-V relation and its dependence upon external potassium ion concentration are both well described, phenomenologically, by the Goldman-Hodgkin-Katz (GHK) flux equation, as I have also previously demonstrated. As illustrated below, this result can be modelled using the Eyring rate theory of single-file diffusion of ions through a channel in the low-occupancy limit of the theory. 3. The GHK equation analysis and the low-occupancy limit of the Eyring rate theory are both consistent with the independence principle for movement of ions through the channel, which is at odds with tracer flux ratio results from the delayed rectifier, published elsewhere. Those results suggest that the channel is multiply occupied by two, or perhaps three, ions. 4. The resolution of this paradox is provided by a triple-binding site, multiple-occupancy model in which only one vacancy, at most, is allowed in the channel. This model predicts current-voltage relations which are consistent with the data (and with the phenomenological prediction of the GHK flux equation). The model is also consistent, approximately, with the tracer flux ratio results.