A Multi-Scale Approach to Model K⁺ Permeation Through the KcsA Channel

K⁺ channels allow a very efficient passage of K⁺ ions through the membrane while excluding Na⁺ ions, and these properties are essential for life. The 3D structure of the KcsA K⁺ channel, solved more than 20 years ago, allows to address many relevant aspects of K⁺ permeation and selectivity mechanisms at the molecular level. Recent crystallographic data and molecular dynamics (MD) studies suggest that no water is normally present inside the selectivity filter (SF), which can instead accommodate four adjacent K⁺ ions. Using a multi-scale approach, whereby information taken from a low-level simulation approach is used to feed a high-level model, we studied the mechanism of K⁺ permeation through KcsA channels. More specifically, we used MD to find stable ion configurations under physiological conditions. They were characterized by two adjacent K⁺ ions occupying the more central positions of the SF (sites S2 and S3), while the other two K⁺ ions could be found at the external and internal entrances to the SF. Sites S1 and S4 were instead not occupied by K⁺. A continuum Bikerman-Poisson-Boltzmann model that takes into account the volume of the ions and their dehydration when entering the SF fully confirmed the MD results, showing peaks of K⁺ occupancy at S2, S3, and the external and internal entrances, with S1 and S4 sites being virtually never occupied by K⁺. Inspired by the newly found ion configuration in the SF at equilibrium, we developed a simple kinetic permeation model which, fed with kinetic rate constants assessed from molecular meta-dynamics, reproduced the main permeation properties of the KcsA channel found experimentally, including sublinear current-voltage and saturating conductance-concentration relationships. This good agreement with the experimental data also implies that the ion configuration in the SF we identified at equilibrium would also be a key configuration during permeation.