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Episodic activity in a heterogeneous excitatory network, from spiking neurons to mean field. (English) Zbl 1412.92005
Summary: Many developing neural systems exhibit spontaneous activity [the third author, “The origin of spontaneous activity in developing networks of the vertebrate nervous system”, Curr. Opinion Neurobiology 9, No. 1, 94–104 (1999; doi:10.1016/S0959-4388(99)80012-9); M. B. Feller, “Spontaneous correlated activity in developing neural circuits”, Neuron 22, No. 4, 653–656 (1999; doi:10.1016/S0896-6273(00)80724-2)] 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.

MSC:
92B20 Neural networks for/in biological studies, artificial life and related topics
92C20 Neural biology
92B25 Biological rhythms and synchronization
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