Electrostatic control of occupancy and valence selectivity in a charged nanometer‐sized cylindrical pore

Abstract

Simple analytical calculations of the electrostatic energy for systems composed of positive charges confined to the axis of a negatively charged cylindrical pore are used to explore the role of electrostatic forces in the problems of ion permeation, ion occupancy and valence selectivity in biological ion channels. Considering the effect of finite length of the charged pore as an alternative to fixed charged residue representations, we show that ion occupancy and ion configurations in the pore are governed by two parameters: (i) the magnitude of the uniform surface charge density of the pore and (ii) the pore (diameter-to-length) aspect ratio through the interplay between favorable interaction of the mobile ions with the pore interior and unfavorable interaction among the ions themselves. The pore with an overall surface charge of -2e (representing a potassium channel) is found to favor occupancy by three K + ions over two K + ions at low aspect ratio but not at high. The pore with surface charge -4e (representing a calcium channel) favors occupancy by two lateral Ca 2+ ions and one central Na + ion over two symmetrically positioned Ca 2+ ions at a low aspect ratio, but this preference is reversed at a higher aspect ratio. These results allow us to speculate that Ca 2+ block of sodium current in the calcium channel is due to lower electrostatic energy for the Na + -Ca 2+ -Na + configuration than for the Na + -Na + -Na + configuration, and that the yet lower energy of the