The current-voltage relation of a pore and its asymptotic behavior in a Nernst-Planck model

A model for current-voltage nonlinearity and asymmetry is a good starting point for explaining the electrical behavior of the nanopores in synthetic or biological membranes. Using a Nernst-Planck model, we found three behaviors for the current density in a membrane's pore as a function of voltage: a quasi-ohmic, slow rising linear current at low voltages, a nonlinear current at intermediate voltages, and a non-ohmic, fast rising linear current at large voltages. The slope of the quasi-ohmic current depends mainly on the height of energy barrier inside the pore, w, through an exponential term, ew. The magnitude of the non-ohmic linear current is controlled by the potential energy gradient at the pore entrance, w/r. The current-voltage relation is asymmetric if the ion's potential energy inside the pore has an asymmetric triangular profile. The model has only two assumed parameters, the energy barrier height, w, and the relative size of the entrance region of the pore, r, which is a useful feature for fitting and interpreting experimental data.