Abstract
Recent experiments suggested that homeostatic regulation of synaptic balance leads the visual system to recover and maintain a regime of power-law avalanches. Here we study an excitatory/inhibitory (E/I) mean-field neuronal network that has a critical point with power-law avalanches and synaptic balance. When short term depression in inhibitory synapses and firing threshold adaptation are added, the system hovers around the critical point. This homeostatically self-organized quasi-critical (SOqC) dynamics generates E/I synaptic current cancellation in fast time scales, causing fluctuation-driven asynchronous-irregular (AI) firing. We present the full phase diagram of the model without adaptation varying external input versus synaptic coupling. This system has a rich dynamical repertoire of spiking patterns: synchronous regular (SR), asynchronous regular (AR), synchronous irregular (SI), slow oscillations (SO) and AI. It also presents dynamic balance of synaptic currents, since inhibitory currents try and compensate excitatory currents over time, resulting in both of them scaling linearly with external input. Our model thus unifies two different perspectives on cortical spontaneous activity: both critical avalanches and fluctuation-driven AI firing arise from SOqC homeostatic adaptation, and are indeed two sides of the same coin.
Highlights
Experimental and theoretical evidence suggests that spontaneous cortical activity happens in the form of asynchronous irregular firing patterns (AI)
This could be generated by the balance of excitatory/inhibitory (E/I) synaptic currents entering individual neurons: inhibition has to nearly compensate excitation, such that cells remain near their firing threshold and fire sporadically, generating a fluctuation-driven regime [2]
Two important issues remain: (i) how to self-organize a neuronal network close to a critical point and (ii) could a network display an AI firing pattern through this selforganization? Concerning the first point, it has been shown that simple local homeostatic mechanisms, such as dynamical synapses [9,10,11,12,13] and dynamical neuronal gains [14,15,16], are sufficient to drive networks towards the so-called selforganized quasicritical state (SOqC as defined by Bonachela and Muñoz [10,17])
Summary
Mauricio Girardi-Schappo ,1,*,† Ludmila Brochini, Ariadne A. When shortterm depression in inhibitory synapses and firing threshold adaptation are added, the system hovers around the critical point This homeostatically self-organized quasicritical (SOqC) dynamics generates E/I synaptic current cancellation in fast timescales, causing fluctuation-driven asynchronous-irregular (AI) firing. Experimental and theoretical evidence suggests that spontaneous cortical activity happens in the form of asynchronous irregular firing patterns (AI) This could be generated by the balance of excitatory/inhibitory (E/I) synaptic currents entering individual neurons Without SOqC, we have a static system presenting the typical synchronicity states of E/I networks exemplified by Brunel’s model [25]: synchronous regular (SR), asynchronous regular (AR), synchronous irregular (SI), and asynchronous irregular (AI) This system has a directed percolation (DP) critical point with power-law avalanches, and dynamic balance of E/I currents, since inhibitory inputs follow excitatory ones over time. Even though the E/I neuron ratio is 80%:20% from cortical data [26], our model predicts that the ratio of coupling strengths of inhibitory to excitatory synapses does not need to be 4:1 to achieve the critical balanced state
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