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The Dielectric Boundary Force in Ion Channels: The Case of Gramicidin

B. Nadler, U. Hollerbach and R.S. Eisenberg
Yale University, US

Keywords: dielectric boundary force, ion channels, gramicidin

Abstract:
In an electrostatic problem with different dielectric regions, a charge in one region induces surface charges at all dielectric boundaries, which, in turn, exert an often neglected force on the charge that induced them. This dielectric boundary force (DBF) is absent in continuum theories such as Poisson-Boltzmann or Poisson-Nernst-Planck (PNP). The DBF, however, is important in problems involving charged particles near dielectric boundaries, as in ionic permeation through biological ion channels. Recently, Schuss et al. derived a modified PNP system that includes the DBF. In this paper we define the DBF and present its importance for ion permeation through the gramicidin channel. Our main result is that the permeation characteristics of gramicidin, permeability to monovalent positive ions but not to negative or double charged ions, are explained by comparison of the DBF and the force formed by the permanent charges of gramicidin. While the DBF depends on the geometry and dielectric values of the problem, it is independent of the permanent charges of the channel. The fact that gramicidin produces a force that cancels out the DBF for a positive ion is characteristic of a device. This natural device might suggest design principles for man-made nanopores.

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