Role of the dielectric constants of membrane proteins and channel water in ion permeation

Using both analytical solutions obtained from simplified systems and numerical results from more realistic cases, we investigate the role played by the dielectric constant of membrane proteins ε_p and pore water ε_w in permeation of ions across channels. We show that the boundary and its curvature are the crucial factors in determining how an ion's potential energy depends on the dielectric constants near an interface. The potential energy of an ion outside a globular protein has a dominant 1/ε_w dependence, but this becomes 1/ε_p for an ion inside a cavity. For channels, where the boundaries are in between these two extremes, the situation is more complex. In general, we find that variations in ε_w have a much larger impact on the potential energy of an ion compared to those in ε_p. Therefore a better understanding of the effective ε_w values employed in channel models is desirable. Although the precise value of ε_p is not a crucial determinant of ion permeation properties, it still needs to be chosen carefully when quantitative comparisons with data are made.