Electrochemistry of Symmetrical Ion Channel: A Three-Dimensional Nernst-Planck- Poisson Model

Ion channels are of major interest for their important function in living organisms. It has been demonstrated that nanofabricated channels can mimictransport properties of biological ones [1].The fluctuations and rectification effects in conical nano-channels are of interest [2]. Although modeling of ionic transport throughout open channel, known as “selective filter”, presents a difficult task it is of major importance in the understanding of fundamental processes in the cell  physiology. The so called voltage-gated ion channels have charged domains that make their structure and behavior sensitive to the variation of the applied field. The ion gating is driven by conformal protein changes, that are due to the variation of the electric field. For a particular range of membrane potentials the proteins adopt a conformation with a central narrow hole permeable for chosen ions. Such open channel pores, known as “selective filters”, present  a difficult task of major importance in the understanding of fundamental processes in the cell  physiology.

Here, the stationary behavior is studied of the different symmetrical channels showing complex geometry. The rigid channel wall is assumed to be locally charged. The ion transport is described by the nonequilibrium steady-state solution in cylindrical geometry of the 3DNernst-Planck-Poisson system. The total flux includes drift (convection) and diffusion terms. The solution of the coupled differential drift-diffusion equations is achieved by finite element method. The essential importance of the asymmetry in the potential distribution at the channel ends on the selectivity effect is demonstrated. The model satisfactorily describes the regime of small-to-moderate ionic currents. For various boundary conditions that are key parameters controlling the selectivity of the channel, it allows determining the flow characteristic, calculating the local concentration across the channel showing cylindrical symmetry and potential distribution. The model gives understanding of the mechanism of ion selectivity by channels but it can be also applied to simulate transport in polymer membranes and nanopores which might be useful in designing biosensors and nanodevices.

[1] Z. Siwy, Y. Gu, H. A. Spohr, D. Baur, A. Wolf-Reber, R. Spohr, P. Apel and Y. E. Korchev, Europhys. Lett. 60 (2002) 349.

[2] I. D. Kosińska, I. Goychuk, M. Kostur, and G. Schmid, Phys. Rev. E 77 (2008) 031131.