Permeation through an open channel: Poisson-Nernst-Planck theory of a synthetic ionic channel

The synthetic channel [acetyl-(LeuSerSerLeuLeuSerLeu)(3)-CONH2](6) (pore diameter similar to 8 Angstrom, length similar to 30 Angstrom) is a bundle of six alpha-helices with blocked termini. This simple channel has complex properties, which are difficult to explain, even qualitatively, by traditional theories: its single-channel currents rectify in symmetrical solutions and its selectivity (defined by reversal potential) is a sensitive function of bathing solution. These complex properties can be fit quantitatively if the channel has fixed charge at its ends, forming a kind of macrodipole, bracketing a central charged region, and the shielding of the fixed charges is described by the Poisson-Nernst-Planck (PNP) equations. PNP fits current voltage relations measured in 15 solutions with an r.m.s. error of 3.6% using four adjustable parameters: the diffusion coefficients in the channel's pore D-K = 2.1 x 10(-6) and D-Cl = 2.6 x 10(-7) cm(2)/s; and the fixed charge at the ends of the channel of +/-0.12e (with unequal densities 0.71 M = 0.021e/Angstrom on the N-side and -1.9 M = -0.058e/Angstrom on the C-side). The fixed charge in the central region is 0.31e (with density P-2 = 0.47 M = 0.014e/Angstrom). In contrast to traditional theories, PNP computes the electric field in the open channel from all of the charges in the system, by a rapid and accurate numerical procedure. In essence, PNP is a theory of the shielding of fixed (i.e., permanent) charge of the channel by mobile charge and by the ionic atmosphere in and near the channel's pore. The theory fits a wide range of data because the ionic contents and potential profile in the channel change significantly with experimental conditions, as they must, if the channel simultaneously satisfies the Poisson and Nernst-Planck equations and boundary conditions. Qualitatively speaking, the theory shows that small changes in the ionic atmosphere of the channel (i.e., shielding) make big changes in the potential profile and even bigger changes in flux, because potential is a sensitive function of charge and shielding, and flux is an exponential function of potential.