Many developing neural systems exhibit spontaneous activity (O'Donovan, Curr Opin Neurobiol 9:94-104, 1999; Feller, Neuron 22:653-656, 1999) characterized by episodes of discharge (active phases) when many cells are firing, separated by silent phases during which few cells fire. Various models exhibit features of episodic behavior by means of recurrent excitation for supporting an episode and slow activity-dependent depression for terminating one. The basic mechanism has been analyzed using mean-field, firing-rate models. Firing-rate models are typically formulated ad hoc, not derived from a spiking network description, and the effects of substantial heterogeneity amongst the units are not usually considered. Here we develop an excitatory network of spiking neurons (N-cell model) with slow synaptic depression to model episodic rhythmogenesis. This N-cell model displays episodic behavior over a range of heterogeneity in bias currents. Important features of the episodic behavior include orderly recruitment of individual cells during silent phases and existence of a dynamical process whereby a small critical subpopulation of intermediate excitability conveys synaptic drive from active to silent cells. We also derive a general self-consistency equation for synaptic drive that includes cell heterogeneity explicitly. We use this mean-field description to expose the dynamical bistability that underlies episodic behavior in the heterogeneous network. In a systematic numerical study we find that the robustness of the episodic behavior improves with increasing heterogeneity. Furthermore, the heterogeneity of depression variables (imparted by the heterogeneity in cellular firing thresholds) plays an important role in this improvement: it renders the network episodic behavior more robust to variations in excitability than if depression is uniformized. We also investigate the effects of noise vs. heterogeneity on the robustness of episodic behavior, especially important for the developing nervous system. We demonstrate that noise-induced episodes are very fragile, whereas heterogeneity-produced episodic rhythm is robust.

中文翻译：

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异质兴奋网络中的情节活动，从尖峰神经元到平均场。

许多发育中的神经系统表现出自发活动（O'Donovan, Curr Opin Neurobiol 9:94-104, 1999; Feller, Neuron 22:653-656, 1999），其特征是当许多细胞放电时出现放电（活动期），分离通过沉默阶段，在此期间很少有细胞放电。各种模型通过反复兴奋来支持情节和缓慢的活动依赖性抑郁来终止情节，从而表现出情节行为的特征。已使用平均场、发射率模型分析了基本机制。发射率模型通常是临时制定的，而不是从尖峰网络描述中推导出来的，并且通常不考虑单元之间的实质性异质性的影响。在这里，我们开发了具有缓慢突触抑制的尖峰神经元（N 细胞模型）的兴奋性网络，以模拟情节节律。该 N 单元模型在偏置电流的一系列异质性范围内显示偶发行为。情节行为的重要特征包括在沉默阶段有序地招募单个细胞，以及存在一个动态过程，其中中间兴奋性的小关键亚群将突触驱动从活跃细胞传递到沉默细胞。我们还推导出了突触驱动的一般自洽方程，其中明确包括细胞异质性。我们使用这种平均场描述来揭示作为异构网络中情节行为基础的动态双稳态。在系统的数值研究中，我们发现情节行为的稳健性随着异质性的增加而提高。此外，抑郁变量的异质性（由细胞放电阈值的异质性赋予）在这种改进中起着重要作用：它使网络情节行为对兴奋性变化的影响比抑郁统一时更稳健。我们还研究了噪声与异质性对情节行为稳健性的影响，这对神经系统发育尤其重要。我们证明噪声引起的情节非常脆弱，而异质性产生的情节节奏是稳健的。