同宿发放神经元双稳态放电统计
Firing statistics in the bistable regime of neurons with homoclinic spike generation
摘要：
有规律放电的神经元的神经元电压动力学通常有一个稳定的吸引子：固定点（如在阈下状态）或限定动作电位的强直放电的极限环（在阈上状态）。然而，在已知引起全或无类型动作电位的三个尖峰起始分叉序列中的两个中，静息状态不动点和极限环尖峰可以共存于中间状态，从而导致双稳态动力学。这里，噪声可以引起吸引子之间的切换，即，之间的休息和尖峰，并因此增加了脉冲序列的变化相比，只有一个稳定的吸引神经元。由此产生的尖峰统计的定性特征取决于尖峰发作分叉。本研究的重点是通过鞍同宿轨道（HOM）分岔的尖峰极限环的创建，并推导出基于电导的神经元模型在双稳态制度的峰间期（ISI）密度。双稳态同宿神经元的ISI密度是单峰的，但不同于与鞍结不变环（SNIC）分叉相关的逆高斯分布。它表明，HOM分叉之间的过渡休息和尖峰主要是确定沿下行的动作电位-一个动态的功能，是不被常用的复位神经元模型捕获。推导出的尖峰统计量可以帮助识别实验数据中的HOM动力学。
英文摘要：
Neuronal voltage dynamics of regularly firing neurons typically has one stable attractor: either a fixed point (like in the subthreshold regime) or a limit cycle that defines the tonic firing of action potentials (in the suprathreshold regime). In two of the three spike onset bifurcation sequences that are known to give rise to all-or-none type action potentials, however, the resting-state fixpoint and limit cycle spiking can coexist in an intermediate regime, resulting in bistable dynamics. Here, noise can induce switches between the attractors, i.e., between rest and spiking, and thus increase the variability of the spike train compared to neurons with only one stable attractor. Qualitative features of the resulting spike statistics depend on the spike onset bifurcations. This study focuses on the creation of the spiking limit cycle via the saddle-homoclinic orbit (HOM) bifurcation and derives interspike interval (ISI) densities for a conductance-based neuron model in the bistable regime. The ISI densities of bistable homoclinic neurons are found to be unimodal yet distinct from the inverse Gaussian distribution associated with the saddle-node-on-invariant-cycle (SNIC) bifurcation. It is demonstrated that for the HOM bifurcation the transition between rest and spiking is mainly determined along the downstroke of the action potential -- a dynamical feature that is not captured by the commonly used reset neuron models. The deduced spike statistics can help to identify HOM dynamics in experimental data.
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