Dynamical Mechanism of Hyperpolarization-Activated Non-specific Cation Current Induced Resonance and Spike-Timing Precision in a Neuronal Model.

Zhiguo Zhao,Li Li,Huaguang Gu

doi:10.3389/fncel.2018.00062

Zhiguo Zhao, Li Li + Show 1 more

Open Access

https://doi.org/10.3389/fncel.2018.00062

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Abstract

Hyperpolarization-activated cyclic nucleotide-gated cation current (Ih) plays important roles in the achievement of many physiological/pathological functions in the nervous system by modulating the electrophysiological activities, such as the rebound (spike) to hyperpolarization stimulations, subthreshold membrane resonance to sinusoidal currents, and spike-timing precision to stochastic factors. In the present paper, with increasing gh (conductance of Ih), the rebound (spike) and subthreshold resonance appear and become stronger, and the variability of the interspike intervals (ISIs) becomes lower, i.e., the enhancement of spike-timing precision, which are simulated in a conductance-based theoretical model and well explained by the nonlinear concept of bifurcation. With increasing gh, the stable node to stable focus, to coexistence behavior, and to firing via the codimension-1 bifurcations (Hopf bifurcation, saddle-node bifurcation, saddle-node bifurcations on an invariant circle, and saddle homoclinic orbit) and codimension-2 bifurcations such as Bogdanov-Takens (BT) point related to the transition between saddle-node and Hopf bifurcations, are acquired with 1- and 2-parameter bifurcation analysis. The decrease of variability of ISIs with increasing gh is induced by the fast decrease of the standard deviation of ISIs, which is related to the increase of the capacity of resisting noisy disturbance due to the firing becomes far away from the bifurcation point. The enhancement of the rebound (spike) with increasing gh builds up a relationship to the decrease of the capacity of resisting disturbance like the hyperpolarization stimulus as the resting state approaches the bifurcation point. The “typical”-resonance and non-resonance appear in the parameter region of the stable focus and node far away from the bifurcation points, respectively. The complex or “strange” dynamics, such as the “weak”-resonance for the stable node near the transition point between the stable node and focus and the non-resonance for the stable focus close to the codimension-1 and −2 bifurcation points, are discussed.

Highlights

The experimental studies found that Ih can induce subthreshold membrane resonance and enhance spike-timing precision characterized by the standard deviation (STD) or coefficient variation (CV) of the interspike intervals (ISIs) (Zemankovics et al, 2010; Gastrein et al, 2011; Pavlov et al, 2011; Borel et al, 2013; Gonzalez et al, 2015)
The results show that the enhancement of the spike-timing precision is mainly caused by the fast decrease of standard deviation of ISIs with increasing gh, which obeys the bifurcation theory wherein a stable dynamical behavior far away from the bifurcation point exhibits stronger capability of resisting disturbance such as noise
Experimental studies found that Ih contributes to the voltage sag and rebound to the inhibitory square current, resonance to sinusoidal current input, and more spike-timing precision

Summary

Introduction

The hyperpolarization-activated current (Ih) mediated by hyperpolarization-activated cyclic nucleotide-gated (HCN) cation ion channels have been identified to contribute to many physiological and pathological functions in the nervous systems, such as neocortical spiny interneurons, cerebellar Purkinje cells, rod photoreceptors, hippocampal pyramidal neurons, inspiratory neurons, motor neurons, and thalamic relay neurons (Pape, 1996; Wahl-Schott and Biel, 2009; He et al, 2014; DiFrancesco and DiFrancesco, 2015). The dysregulation of HCN channels in the nervous system may lead to pathological conditions such as epilepsy (DiFrancesco et al, 2011; Reid et al, 2012), neuropathic pain (Emery et al, 2012; Schnorr et al, 2014), and Parkinsonian disease (Good et al, 2011; Masi et al, 2013) These physiological or pathological functions related to Ih are achieved by modulating the electrophysiological activities, such as the resting membrane potential, neuronal excitability, rhythmic activity, dendritic integration, and synaptic transmission (He et al, 2014; DiFrancesco and DiFrancesco, 2015). Hippocampal interneurons exhibit precise firing when Theta and Gamma oscillations appear in the hippocampus and neocortex (Hájos et al, 2004; Somogyi and Klausberger, 2005; Klausberger et al, 2006; Vida et al, 2006)

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