Synaptic balance due to homeostatically self-organized quasicritical dynamics

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.

Tuning network dynamics from criticality to an asynchronous state

“…If stronger inhibition balances stronger excitation in a higher “tension” balance, we found that the dynamics are asynchronous and steady. Along with other recent studies [ 24 , 36 – 38 ], our findings suggest that the same cortical network could be tuned from criticality to asynchrony, by tuning inhibition and excitation appropriately.…”

“…These similarities suggest that the asynchronous regime in our model might correspond to “edge of chaos” criticality, but, considering the differences in their model (firing rate) and ours (probabilistic binary neurons), a more careful study would be required to test this possibility. Finally, we note that Girardi-Schappo et al found that a network of probabilistic leaky-and-fire neurons can be tuned from criticality to an ‘asynchronous irregular’ regime (as defined by [ 39 ]) by strengthening inhibition relative to excitation (increasing their g parameter) [ 38 ]. Our model, considered together with the work of Girardo-Schappo et al and Dahmen et al suggests that there may be a general principle governing our models; perhaps increasing the strength of inhibition relative to excitation, while maintaining balance, will always result in a shift away from criticality, towards asynchronous dynamics.…”

“…Recent computational modeling efforts have begun to tackle these questions. They have shown several different ways that tuning one or a few simple parameters can result in a shift from asynchronous dynamics to critical dynamics or vice versa [ 24 , 36 – 38 ]. For example, Priesemann and colleagues showed that tuning the input and an effective branching parameter ( m in their terminology) can generate a family of models ranging from fully asynchronous to critical [ 11 , 36 ].…”

“…Dahmen et al also studied sparse networks of excitatory and inhibitory neurons, highligting how increasing the heterogeneity of synaptic strengths can change the dynamics of a system from traditional criticality (as discussed here) to a different type of critical regime at the “edge of chaos” which manifests with asynchronous dynamics [ 24 ]. Most recently, Girardi-Schappo et al studied a more complex model of probabilistic leaky integrate and fire neurons [ 38 ], showing that Brunel’s classic parameter space [ 39 ] includes a critical point that is adjacent to the ‘asynchronous regular’ regime and nearby the ‘asynchronous irregular’ regime studied by Brunel and others. (Touboul and Destexhe have pointed out that the ‘synchronous irregular’ state in Brunel’s model is not consistent with criticality [ 40 ]).…”

Mechanisms of Self-Organized Quasicriticality in Neuronal Network Models

“…Girardi-Schappo et al [93] examined a network with N E pN 0.8N excitatory and N I qN 0.2N inhibitory stochastic LIF neurons. They found a phase diagram very similar to that of the Brunel model [94], with synchronous regular (SR), asynchronous regular (AR), synchronous irregular (SI), and asynchronous irregular (AI) states.…”