Ion exchange phase transitions in "doped" water--filled channels

Ion transport through narrow water--filled channels is impeded by a high electrostatic barrier. The latter originates from the large ratio of the dielectric constants of the water and a surrounding media. We show that ``doping'', i.e. immobile charges attached to the walls of the channel, substantially reduces the barrier. This explains why most of the biological ion channels are ``doped''. We show that at rather generic conditions the channels may undergo ion exchange phase transitions (typically of the first order). Upon such a transition a finite latent concentration of ions may either enter or leave the channel, or be exchanged between the ions of different valences. We discuss possible implications of these transitions for the Ca-vs.-Na selectivity of biological Ca channels. We also show that transport of divalent Ca ions is assisted by their fractionalization into two separate excitations.