Quantifying activation delay and the Cole-More shift via current derivatives

The kinetics of ion channels arise from transitions through multiple closed and open states. An example is the sigmoidal activation kinetics exhibited by voltage-gated potassium channels upon depolarization. This activation sigmoidicity or delay is commonly attributed to the number of closed states that the channel needs to traverse before opening. The Cole-Moore shift refers to the change in this delay upon the magnitude of the hyperpolarization before the activation, and it is empirically obtained by extrapolation of an exponential fit to the time of zero current or by calculating a time shift of the activation kinetics in comparison to a reference trace. However, these methods require selecting analysis windows, determining fitting parameters, or choosing alignment thresholds and do not provide a closed form expression for the Cole-Moore shift or activation delay, complicating the integration of delay measurements into kinetic modeling of ion channels. Here we propose the use of the time derivative of the current (dI/dt) as a straightforward way to obtain the delay before opening and characterize the Cole-Moore shift. In the presence of sigmoidal activation kinetics, the derivative of the current shows a maximum that corresponds to the inflection point (where the second derivative of open probability with respect to time is zero), offering a generalizable descriptor of activation delay. The derivative is useful when obtaining the delay even in the presence of inactivation or multicomponent kinetics as shown in experiments with the Shaker voltage-gated potassium channel. We propose that measuring the maximum of the current derivative provides a simple, quantitative, and broadly applicable tool for analyzing the activation delay and Cole-Moore shift, and we demonstrate its application to voltage-gated channels in systems with different activation and inactivation properties.