Physical origin of selectivity in ionic channels of biological membranes

This paper shows that the selectivity properties of monovalent cation channels found in biological membranes can originate simply from geometrical properties of the inner core of the channel without any critical contribution from electrostatic interactions between the permeating ions and charged or polar groups. By using well-known techniques of statistical mechanics, such as the Langevin equations and Kramer theory of reaction rates, a theoretical equation is provided relating the permeability ratio PB/PA between ions A and B to simple physical properties, such as channel geometry, thermodynamics of ion hydration, and electrostatic interactions between the ion and charged (or polar) groups. Diffusive corrections and recrossing rates are also considered and evaluated. It is shown that the selectivity found in usual K+, gramicidin, Na+, cyclic nucleotide gated, and end plate channels can be explained also in the absence of any charged or polar group. If these groups are present, they significantly change the permeability ratio only if the ion at the selectivity filter is in van der Waals contact with them, otherwise these groups simply affect the channel conductance, lowering the free energy barrier of the same amount for the two ions, thus explaining why single channel conductance, as it is experimentally observed, can be very different in channels sharing the same selectivity sequence. The proposed theory also provides an estimate of channel minimum radius for K+, gramicidin, Na+, and cyclic nucleotide gated channels.