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.

Recent experimental results on spike avalanches measured in the urethane-anesthetized rat cortex have revealed scaling relations that indicate a phase transition at a specific level of cortical firing rate variability. The scaling relations point to critical exponents whose values differ from those of a branching process, which has been the canonical model employed to understand brain criticality. This suggested that a different model, with a different phase transition, might be required to explain the data. Here we show that this is not necessarily the case. By employing two different models belonging to the same universality class as the branching process (mean-field directed percolation) and treating the simulation data exactly like experimental data, we reproduce most of the experimental results. We find that subsampling the model and adjusting the time bin used to define avalanches (as done with experimental data) are sufficient ingredients to change the apparent exponents of the critical point. Moreover, experimental data is only reproduced within a very narrow range in parameter space around the phase transition.

No abstract

No abstract

Neuronal avalanches and asynchronous irregular (AI) firing patterns have been thought to represent distinct frameworks to understand the brain spontaneous activity. The former is typically present in systems where there is a balance between the slow accumulation of tension and its fast dissipation, whereas the latter is accompanied by the balance between synaptic excitation and inhibition (E/I). Here, we develop a new theory of E/I balance that relies on two homeostatic adaptation mechanisms: the short-term depression of inhibition and the spike-dependent threshold increase. First, we turn off the adaptation and show that the so-called static system has a typical critical point commonly attributed to self-organized critical models. Then, we turn on the adaptation and show that the network evolves to a dynamic regime in which: (I) E/I synapses balance regardless of any parameter choice; (II) an AI firing pattern emerges; and (III) neuronal avalanches display visually accurate power laws. This is the first time that these three phenomena appear simultaneously in the same network activity. Thus, we show that the once thought opposing frameworks may be unified into a single dynamics, provided that adaptation mechanisms are in place. In our model, the AI firing pattern is a direct consequence of the hovering close to the critical line where external inputs are compensated by threshold growth, creating synaptic balance for any E/I weight ratio.Author summaryTwo competing frameworks are employed to understand the brain spontaneous activity, both of which are backed by computational and experimental evidence: globally asynchronous and locally irregular (AI) activity arises in excitatory/inhibitory balanced networks subjected to external stimuli, whereas avalanche activity emerge in excitable systems on the critical point between active and inactive states. Here, we develop a new theory for E/I networks and show that there is a state where synaptic balance coexists with AI firing and power-law distributed neuronal avalanches. This regime is achieved through the introducing of short-time depression of inhibitory synapses and spike-dependent threshold adaptation. Thus, the system self-organizes towards the balance point, such that its AI activity arises from quasicritical fluctuations. The need for two independent adaptive mechanisms explains why different dynamical states are observed in the brain.