Biological and synthetic nanochannels exhibit two essential biophysical properties: selective ion conduction and the ability to gate open in response to appropriate stimulus. Both these properties are related to several untypical modes of behaviour of the diffusional and conduction currents, absent in the normal (electro-)diffusion. We present our recent results concerning some of such anomalous phenomena. Selectivity is related to the fact that electrical and diffusive currents exhibit several asymmetries --- the asymmetric channels rectify the electric currents: the relation I versus U is asymmetric (this is related to the pumping effect observed in synthetic nanochannels), moreover, for U=0 the magnitude of purely diffusional currents depends on the direction of the concentration gradient. These phenomena can be described by a model based on the continuous description starting from the Smoluchowski equation. The flicker noise in the power spectra of ionic currents is known to be present both in very narrow biological and (some) synthetic channels. We simulated 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, and interactions with ions present inside the channel. We found that there is a range of the varied parameters, in which the power spectrum has the characteristics of th e flicker noise. Critical for the appearance of the flicker noise are the condition of single-file motion of ions through the channel and the opening/closing of the gate.

PACS numbers: 05.40.Ca, 87.16.Uv, 87.15.Ya, 05.10.Gg