Total charge movement per channel - The relation between gating charge displacement and the voltage sensitivity of activation

One measure of the voltage dependence of ion channel conductance is the amount of gating charge that moves during activation and vice versa. The limiting slope method, introduced by Almers (Almers, W. 1978. Rev. Physiol. Biochem. Pharmacol. 82:96-190), exploits the relationship of charge movement and voltage sensitivity, yielding a lower limit to the range of single channel gating charge displacement. In practice, the technique is plagued by low experimental resolution due to the requirement that the logarithmic voltage sensitivity of activation be measured at very low probabilities of opening. In addition, the linear sequential models to which the original theory was restricted needed to be expanded to accommodate the complexity of mechanisms available for the activation of channels. In this communication, we refine the theory by developing a relationship between the mean activation charge displacement (a measure of the voltage sensitivity of activation) and the gating charge displacement (the integral of gating current). We demonstrate that recording the equilibrium gating charge displacement as an adjunct to the limiting slope technique greatly improves accuracy under conditions where the plots of mean activation charge displacement and gross gating charge displacement versus voltage can be superimposed. We explore this relationship for a wide variety of channel models, which include those having a continuous density of states, nonsequential activation pathways, and subconductance states. We introduce new criteria for the appropriate use of the limiting slope procedure and provide a practical example of the theory applied to low resolution simulation data.