History dependent dynamics in a generic model of ion channels - an analytic study

TL;DR

This paper introduces a simple, analytical model of ion channel dynamics that explains history-dependent relaxation phenomena and predicts conditions under which such effects can or cannot occur, with implications for neuronal behavior.

Contribution

It provides a minimal, generic model for ion channel inactivation dynamics that explains experimental observations and predicts voltage dependence and activity thresholds for history effects.

Findings

Explains exponential history-dependent relaxation in sodium channels.

Shows recovery rate from inactivation depends on voltage.

Predicts history effects are absent with sparse spiking activity.

Abstract

Recent experiments have demonstrated that the timescale of adaptation of single neurons and ion channel populations to stimuli slows down as the length of stimulation increases; in fact, no upper bound on temporal time-scales seems to exist in such systems. Furthermore, patch clamp experiments on single ion channels have hinted at the existence of large, mostly unobservable, inactivation state spaces within a single ion channel. This raises the question of the relation between this multitude of inactivation states and the observed behavior. In this work we propose a minimal model for ion channel dynamics which does not assume any specific structure of the inactivation state space. The model is simple enough to render an analytical study possible. This leads to a clear and concise explanation of the experimentally observed exponential history-dependent relaxation in sodium channels in a voltage clamp setting, and shows that their recovery rate from slow inactivation must be voltage dependent. Furthermore, we predict that history-dependent relaxation cannot be created by overly sparse spiking activity. While the model was created with ion channel populations in mind, its simplicity and genericalness render it a good starting point for modeling similar effects in other systems, and for scaling up to higher levels such as single neurons which are also known to exhibit multiple time scales.