Referenced in: none

Automatically associated channels: Slo1

Title: Channel-noise-induced critical slowing in the subthreshold Hodgkin-Huxley neuron.

Authors: Alex Bukoski, D A Steyn-Ross, Moira L Steyn-Ross

Journal, date & volume: Phys Rev E Stat Nonlin Soft Matter Phys, 2015 Mar , 91, 032708

PubMed link: http://www.ncbi.nlm.nih.gov/pubmed/25871145

Abstract
The dynamics of a spiking neuron approaching threshold is investigated in the framework of Markov-chain models describing the random state-transitions of the underlying ion-channel proteins. We characterize subthreshold channel-noise-induced transmembrane potential fluctuations in both type-I (integrator) and type-II (resonator) parametrizations of the classic conductance-based Hodgkin-Huxley equations. As each neuron approaches spiking threshold from below, numerical simulations of stochastic trajectories demonstrate pronounced growth in amplitude simultaneous with decay in frequency of membrane voltage fluctuations induced by ion-channel state transitions. To explore this progression of fluctuation statistics, we approximate the exact Markov treatment with a 12-variable channel-based stochastic differential equation (SDE) and its Ornstein-Uhlenbeck (OU) linearization and show excellent agreement between Markov and SDE numerical simulations. Predictions of the OU theory with respect to membrane potential fluctuation variance, autocorrelation, correlation time, and spectral density are also in agreement and illustrate the close connection between the eigenvalue structure of the associated deterministic bifurcations and the observed behavior of the noisy Markov traces on close approach to threshold for both integrator and resonator point-neuron varieties.