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Ionic motion in the bulk solution away from the mouth of a biological ion channel, and inside the channel, is analyzed using Poisson-Nernst-Planck (PNP) equation. The one-dimensional method allows us to connect in a self-consistent way ion dynamics in the bulk solution and inside the channel by taking into account access resistance to the channel. In order to glue the PNP solution in the bulk to that inside the channel, a continuity condition is used for the concentration and the current near the channel mouth at the surface of the hemisphere. The resulting one dimensional (1D) current-voltage characteristics are compared with the Kurnikova(16) results which are in good agreement with experimental measurement on the channel, by using a filling factor as the only fitting parameter. The filling factor compensates the fact that the radial charge distribution is non-uniform in a real channel as compared to the cylindrically symmetrical channel used in the 1D approximation

Self-consistent analytic solution for the current and access resistance in open ionic channels.