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.

中文翻译：

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小脑深核神经元开/关转换的模型：解释潜在的离子机制

小脑深层神经元（DCNn）的神经元代表小脑皮层与其余中枢神经系统之间的主要功能联系。因此，了解DCNn的电生理特性对了解小脑的整体功能至关重要。实验数据表明DCNn可以可逆地在两种状态之间切换：尖峰发射（F状态）和稳定的去极化状态（SD状态）。我们引入了DCNn膜电响应的新生物物理模型，以研究DCNn中确定的已记录电导之间的相互作用如何引起这些状态。在该模型中，F状态显示为极限环的孤立变量，即与SD固定点的分支断开的周期解的闭环。这种分叉结构使模型具有再现由超极化电流脉冲触发的$ \ text {F} \到\ text {SD} $过渡的能力。该模型还重现了由阻塞Ca电流引起的$ \ text {F} \到\ text {SD} $过渡，并将此过渡归因于高阈值Ca电流的阻断。该模型表明，细胞内电流注入可以触发完全可逆的$ \ text {F} \ leftrightarrow \ text {SD} $转换。对低维简化模型的研究表明，依赖于电压的Na电流对于这些动力学特征非常重要。最后，对该模型的仿真表明，生理性突触输入可能触发$ \ text {F} \ leftrightarrow \ text {SD} $转换。