Model of the Current-Voltage Relation for a Skin Pore

Abstract

Using a Nernst-Planck model, we show that the current density in a membrane’s pore as a function of voltage has three types of behavior: a quasi-ohmic behavior at low voltages, with a small slope, a non-ohmic linear dependence at large voltages, with a large slope, and a nonlinear transition region at intermediate voltages. The magnitude of the quasi-ohmic current from low voltages depends mainly on the height of energy barrier inside the pore, w, through an exponential term, e^w. The low voltages domain is experimentally accessible and almost unexplored, despite the fact that it can offer direct information about the energy barrier inside a pore. The model has only two assumed parameters, the energy barrier height, w, and the relative size of the entrance region of the pore, r, with a clear physical meaning, an important advantage for fitting and interpreting experimental data. This simple model for the current-voltage nonlinearity is a good starting point for explaining the electrical behavior of the skin at low voltages.