Andrzej Fuliński and I. D. Kosińska
Modelling ionic transport through nanochannels
Transport of ions through nanochannels exhibits several untypical modes of behaviour of the diffusional and conduction currents, absent in the normal (electro-)diffusion. Biological and synthetic nanochannels exhibit two essential biophysical properties: selective ion conduction and the ability to gate open in response to appropriate stimulus. The asymmetric channels rectify the electric currents: the relation I vs. U is asymmetric, moreover, for U=0 the magnitude of purely diffusional currents depends on the direction of the concentration gradient. Synthetic nanochannels under oscillating electric fields are able to pump ions against concentration gradients. All these phenomena can be described by a model based on the continuous description starting from the Smoluchowski equation, and are caused by asymmetries of the channel's geometry and of its internal electric fields.
Gating results, among others, in the appearance of the flicker noise in the power spectra of ionic currents measured both in very narrow biological and (some) synthetic channels. The results of Brownian Dynamics simulations are presented of the motion of K+ ions of the single-file type through a model channel with the gate which opens and closes under influence of both random noise (Wiener process), and interactions with ions present inside the channel. We found that there is a range of the parameters, in which the power spectrum has the characteristics of the flicker noise. Essential for the appearance of the flicker noise is the condition of single-file motion of ions through the channel (the single-file motion is also the condition for the appearance of subdiffusion). 1/f noise is accompanied by the long-tail distributions of the dwell times in open and closed states. Moreover, in the long runs, the K+ currents are self-similar, and the open-channel currents scale over the range of of Δt's as Io = Io,0 (Δt/Δ0 t)β with β=1 ±0.07.

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