Unified modeling of conductance kinetics for low- and high-conductance potassium ion channels

A kinetics model is proposed for the description of ion conductance of low- and high-conductance potassium ion channels. The model describes ion permeation through the selectivity filter, which is assumed to be the only conductance determining part of the open channel. The filter occupancy can vary from zero to three ions, affecting the ion entry and exit rates. Ion motion between the binding sites inside the filter is assumed fast compared to the latter rates allowing averaging the equilibrium entry and exit rate constants over the possible ion configurations in the filter with a particular occupancy. Averaged rate constants related to a pair of adjacent occupancy states characterize a particular ion permeation mechanism. An expression for the channel conductance as a function of the symmetrical external ion concentration is derived. It comprises a sum of concentration independent conductance amplitudes for different ion permeation mechanisms weighted by the equilibrium filter occupancy probabilities. It is shown that each amplitude (i.e., maximum contribution to the channel conductance from each conductance mechanism) is proportional to an averaged exit rate constant and to quantities characterizing the effect of the applied electric field on the rate constants and the equilibrium ion distribution in the filter. The conductance expression derived provides a good description of the experimentally observed conductance-concentration curves for low-conductance (e.g., Kir2.1) and high-conductance (e.g., KcsA) potassium channels. It enables one to obtain equilibrium ion binding constants at different filter occupancies and to calculate the average number of ions in the selectivity filter for a given external ion concentration. For KcsA this number (2.0 at 200 mM) is in a good agreement with the available experimental value (2.1 at 200 mM). For the high-conductance potassium channels the net negative electrical charge around the selectivity filter increases the ion binding constants, thereby causing the larger occupancy probabilities to occur at smaller external ion concentrations compared to the low-conductance channels. This substantially increases the contributions of the two- and three-ion permeation mechanisms, with the larger conductance amplitudes leading to increased channel conductance compared to the low-conductance channels.