Calculation of the conductance and selectivity of an ion-selective potassium channel (IRK1) from simulation of atomic scale models

We present the equations and methodology for the theoretical prediction of the conductance, permeability and selectivity of a K⁺ channel on the basis of atomic scale models for it. The methodology involves the use of Langevin dynamics and activated trajectories in order to obtain translocation free energies, rate constants and transmission coefficients for an ion going through the channel. The models are for the Inward Rectifier K⁺ channel (IRK1) which is a member of a family of ion-selective K⁺ channels. The IRK1 channel is biologically important because of its role in cardiac pacemaker function. The models we use for the IRK1 channel are developed from a model of the Shaker voltage-gated K⁺ channel. We find that the theoretically predicted conductance is too low by three orders of magnitude. We attribute this underestimate to a specific structural defect in the model used. Perhaps our most significant result is that the computed conductance is tremendously sensitive to the structural details of the so-called ‘P-loop’ that lines the outer half of the permeation pathway of the channel. This sensitivity may be useful in future studies on ion channel proteins for which the structure is not known from X-ray crystallography. In addition, this sensitivity may help determine whether X-ray structures of these proteins correspond to open or closed conformations.