COMPARISON OF NERNST-PLANCK AND REACTION-RATE MODELS FOR MULTIPLY OCCUPIED CHANNELS

Abstract

The Nernst-Planck continuum equation for a channel that can be occupied by at most 2 ions is solved for 2 different physical cases. The first case is for the assumption that the water and ion cannot get around each other anywhere in the channel, so that if there are 2 ions in the channel the distance between them is fixed by the number of water molecules between them. The second case is for the assumption that there are regions at the ends of the channel where the ion and water can get around each other. For these 2 cases, the validity of the simple 2-site reaction-rate approximation when there is a continuously varying central energy barrier was evaluted by comparing it with the exact Nernst-Planck solution. For the first continuum case, the kinetics for the continuum and reaction-rate models are nearly identical. For the second case, the agreement depends on the strength of the ion-ion interaction energy. For a low interaction energy (large channel diameter) at high ion concentrations, there is a large difference in the flux as a function of voltage for the 2 models-with the continuum flux becoming more than 4 times larger at 250 mV. Simple analytical expressions are derived for the 2-ion continuum channel for the case where the ends are in equilibrium with the bulk solution and for the case where ion mobility becomes zero when there are 2 ions in the channel. The implications of these results for biological channels are discussed.