Statistic thermodynamics of the selectivity of KcsA channel to Na+, K+ and Rb+ ions

Potassium is at least 10 000 times more permeant than Na+, remaining to be an open question of K+ channels. To elucidate the mechanism of ion selectivity at atomic level, the density functional theory was used to calculate the potential on the basis of the X-ray structure of the KcsA K+ channel. In the viewpoint of statistic. thermodynamics, the two most readily permeant ions, K+ and Rb+ ions, can pass through the selectivity filter. In contrast, Na+ ions, which prefer staying in site 2, can not pass through the channel. The energy barrier difference between the K+ and Na+ is 27.4 kJ/mol which induced the permeant ratio of 15 000. The energy barrier difference of Rb+ ions is higher than that of K+ ions which is corresponding to the lower permeant of Rb+ ions. The results are qualitatively consistent with the experimental data. It is remarkable that the system, involved in 269 atoms, is much lower than the MD simulation which is about 41 000 atoms.