Dynamical response of the Hodgkin-Huxley model in the high-input regime

TL;DR

This paper investigates how the Hodgkin-Huxley neuron model responds to stochastic inputs across different dynamical regimes, revealing coherence resonances, bistability, and spike triggering mechanisms.

Contribution

It provides a detailed analysis of the Hodgkin-Huxley model's response to stochastic inputs in all three fundamental regimes, highlighting coherence resonances and stochastic bistability.

Findings

Coexistence of two coherence resonances at different noise levels.

Bistability explained by stochastic barrier crossing.

Maximized incoherence observed at finite noise in firing regime.

Abstract

The response of the Hodgkin-Huxley neuronal model subjected to stochastic uncorrelated spike trains originating from a large number of inhibitory and excitatory post-synaptic potentials is analyzed in detail. The model is examined in its three fundamental dynamical regimes: silence, bistability and repetitive firing. Its response is characterized in terms of statistical indicators (interspike-interval distributions and their first moments) as well as of dynamical indicators (autocorrelation functions and conditional entropies). In the silent regime, the coexistence of two different coherence resonances is revealed: one occurs at quite low noise and is related to the stimulation of subthreshold oscillations around the rest state; the second one (at intermediate noise variance) is associated with the regularization of the sequence of spikes emitted by the neuron. Bistability in the low noise limit can be interpreted in terms of jumping processes across barriers activated by stochastic fluctuations. In the repetitive firing regime a maximization of incoherence is observed at finite noise variance. Finally, the mechanisms responsible for spike triggering in the various regimes are clearly identified.