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

Abstract

A model for current-voltage nonlinearity and asymmetry is a good starting point for explaining the electrical behavior of nanopores in synthetic or biological membranes. Using a Nernst-Planck model, we found three behaviors for the calculated 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 the energy barrier inside the pore, w, through an exponential term, e w . The magnitude of the non-ohmic linear current is controlled by the potential energy gradient at the pore entrance, w/r. The current-voltage relationship 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.

Changes in the electrical properties of the electrode–skin–underlying tissue composite during a week-long programme of neuromuscular electrical stimulation

“…Strong inverse relationships were found between: the stratum corneum resistance and the minimum current, and the series resistance and the peak current. The inverse relationship between the minimum current and stratum corneum resistance observed, has been previously reported (van Boxtel 1977, Yamamoto and Yamamoto 1981, Kuhn et al 2006 and modelled (Dorgan andReilly 1999, Bîrlea andBîrlea 2012). It was first reported by van Boxtel (1977) who noticed a drop in stratum corneum resistance from 26 k at 1 mA to 4 k at 10 mA (using 2 round Ni-Ag electrodes, 15 mm diameter).…”

Ionic transport through a protein nanopore: a Coarse-Grained Molecular Dynamics Study

“…In general, these approaches require a choice between the amount of computational resources and the microscopic level of accuracy. Among continuum approaches, the Poisson–Nernst Planck theory (PNP) 11–16 is useful to study ion transport at a relatively small computational cost, although not very accurate for narrow pores. At the same level, Brownian or Langevin dynamics methods (BD) 12,17–19 can be an alternative.…”