Hysteretic Conductance in Ion Channel Gating

Hysteresis seems to play a critical role in the generation and modulation of electrical signal events in neurons, muscles, and other excitable tissues. In voltage-gated ion channels, hysteretic conductance manifests under cycling changes in transmembrane voltage when conductance is delayed in response to voltage changes. Such dynamic behavior emerges naturally when the frequency of the oscillatory voltage becomes comparable to the characteristic relaxation time associated with transitions between channel conductance states and is reminiscent of hysteresis observed in transistors, memristors or solar cells. To investigate this delayed response, various discrete-state Markov models have been proposed. In these frameworks, an ion channel is represented as a finite set of states-typically corresponding to closed and open conformations-with transitions governed by voltage-dependent rates. As an alternative, the progress of activation and transition between opening and closing states of a channel is described in terms of a diffusive, collective "reaction coordinate" which fulfills a Langevin equation and the Smoluchowski-Fokker-Planck equation associated with it. Here we review this approach in modeling dynamic memory of ion channels.