Spectator-ion effect on the passage of ions through membranes

In this paper, we investigate the interplay between geometric and dielectric factors in influencing the image force acting on an ion passing through a membrane, for a system having the approximate dimensions of Escherichia coli. We also study the effect of one ion in a membrane on the passage of a second ion through the membrane, by calculating the radial and angular forces experienced by the second ion due to the presence of the "spectator ion." Our conclusions follow from numerical studies on expressions obtained by solving (exactly) Laplace's equation for the model assumed in this paper. The conclusions are: (i) small changes in the dielectric constant of the membrane are far more significant in determining the image force acting on an ion in a membrane than dramatic changes in the dielectric character of the regions interior and/or exterior to the cell; (ii) a spectator ion in a membrane situated near a boundary may influence in a significant way the passage of a second ion through the middle third of the membrane. We suggest that this latter result should be taken into account in discussing the mechanism of ion migration across membranes.