The dielectric boundary force in ion channels: the case of gramicidin

The dielectric boundary force (DBF) is the force that induced charges at dielectric boundaries exert on the charge that induced them. The DBF is present in any electrostatic problem with a non-uniform dielectric constant, and is important in the case of charged particles near dielectric boundaries. Yet, it is absent in common continuum theories of charge distribution and of charge transport, such as Poisson-Boltzmann and Poisson-Nernst-Planck. In this paper we define the DBF, formulate it as a solution of a partial differential equation, and present its crucial importance for ionic permeation through the gramicidin channel. The main permeation characteristics of gramicidin can be explained in terms of a delicate balance between the DBF and the force formed by the permanent charges of the gramicidin polypeptide. This balance, characteristic of a device, might suggest design principles for man-made nanopores.