Electrostatic screening and energy barriers of ions in low-dielectric membranes

We present exact solutions of the linear Poisson-Boltzmann equation for several problems relevant for ion translocation across low-dielectric membranes. Our results are obtained for a finite Debye screening length, and they generalize the classical results for pure Coulombic electrostatics (Parsegian, A. Nature (London) 1969, 221, 844). We calculate the electrostatic self-energy of an ion in the middle of a low-dielectric slab, its energy inside a cylindrical high-dielectric pore, and its energy inside a high-dielectric spherical jacket. We consider also the influence of negative charges distributed on the walls of the cylindrical pore. We show that ion self-energy barriers are considerably reduced due to screening of electrolyte. We compare our results with some numerical results for screened electrostatics of ion channels and wide pores.