A model of on/off transitions in neurons of the deep cerebellar nuclei: deciphering the underlying ionic mechanisms

Hugues Berry,Stéphane Genet

doi:10.1186/s13408-021-00105-3

Abstract

The neurons of the deep cerebellar nuclei (DCNn) represent the main functional link between the cerebellar cortex and the rest of the central nervous system. Therefore, understanding the electrophysiological properties of DCNn is of fundamental importance to understand the overall functioning of the cerebellum. Experimental data suggest that DCNn can reversibly switch between two states: the firing of spikes (F state) and a stable depolarized state (SD state). We introduce a new biophysical model of the DCNn membrane electro-responsiveness to investigate how the interplay between the documented conductances identified in DCNn give rise to these states. In the model, the F state emerges as an isola of limit cycles, i.e. a closed loop of periodic solutions disconnected from the branch of SD fixed points. This bifurcation structure endows the model with the ability to reproduce the text{F}to text{SD} transition triggered by hyperpolarizing current pulses. The model also reproduces the text{F}to text{SD} transition induced by blocking Ca currents and ascribes this transition to the blocking of the high-threshold Ca current. The model suggests that intracellular current injections can trigger fully reversible text{F}leftrightarrow text{SD} transitions. Investigation of low-dimension reduced models suggests that the voltage-dependent Na current is prominent for these dynamical features. Finally, simulations of the model suggest that physiological synaptic inputs may trigger text{F}leftrightarrow text{SD} transitions. These transitions could explain the puzzling observation of positively correlated activities of connected Purkinje cells and DCNn despite the former inhibit the latter.

Highlights

The connectivity of the cerebellum places deep cerebellar nuclei neurons (DCNn) in a strategic position
These experimental results hint at the coexistence of two different stable electric states in the DCNn phase space: a silent depolarized state and an active state characterized by low frequency firing of large-amplitude spikes
The silent depolarized (SD) state is stable as evidenced by the fact that, once settled in this state, the model remains in this state despite small depolarizing or hyperpolarizing pulses of current (Fig. 1A3)

Summary

Introduction

The connectivity of the cerebellum places deep cerebellar nuclei neurons (DCNn) in a strategic position. Reversible transitions between spontaneous firing and a silent depolarized state were reported later by Raman et al [4] in patch-clamp recordings of DCNn, ruling out the possibility that these transitions are artifacts resulting from experimental membrane leaks created by sharp electrodes used by Jahnsen. While sparse, these experimental results hint at the coexistence of two different stable electric states in the DCNn phase space: a silent depolarized state (stable fixed point, sFP) and an active state characterized by low frequency firing of large-amplitude spikes (stable limit cycle, sLC)

Methods

Results

Conclusion