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

Soudry Soudry

doi:10.3389/fncom.2010.00003

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 timescales 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.

Highlights

Many recent experiments have demonstrated that the timescale of adaptation of a single neuron in response to periodic stimuli slows down as the period of stimulation increases (Fairhall et al, 2001; Lundstrom et al, 2008; Wark et al, 2009)
At a sub-neuronal level, experiments on sodium (Toib et al, 1998; Melamed-Frank and Marom, 1999; Ellerkmann et al, 2001) and calcium (Uebachs et al, 2006) ion channel populations have shown that the timescale of the recovery from inactivation following a long duration of membrane depolarization increased with the length of the depolarization period
Patch clamp experiments on single ion channels have hinted at the existence of a large inactivation state space within a single ion channel (Liebovitch and Sullivan, 1987; Millhauser et al, 1988; Marom, 1998 and the references therein)

Summary

Introduction

Many recent experiments have demonstrated that the timescale of adaptation of a single neuron in response to periodic stimuli slows down as the period of stimulation increases (Fairhall et al, 2001; Lundstrom et al, 2008; Wark et al, 2009). At a sub-neuronal level, experiments on sodium (Toib et al, 1998; Melamed-Frank and Marom, 1999; Ellerkmann et al, 2001) and calcium (Uebachs et al, 2006) ion channel populations have shown that the timescale of the recovery from inactivation following a long duration of membrane depolarization increased with the length of the depolarization period. We refer to this type of behavior as history-dependence. How are the behaviors observed at the different levels related (e.g., Lowen et al, 1999)? is there a connection between the history-dependent timescale of adaptation in the neuron to the history-dependent behavior of ion channels? Does a multitude of inactivation states create the observed channel behavior? What is the functional significance of this history-dependent behavior (e.g., Wark et al, 2009)?

Methods

Results

Conclusion