Jensen’s force and the statistical mechanics of cortical asynchronous states

Abstract

Cortical networks are shaped by the combined action of excitatory and inhibitory interactions. Among other important functions, inhibition solves the problem of the all-or-none type of response that comes about in purely excitatory networks, allowing the network to operate in regimes of moderate or low activity, between quiescent and saturated regimes. Here, we elucidate a noise-induced effect that we call “Jensen’s force” –stemming from the combined effect of excitation/inhibition balance and network sparsity– which is responsible for generating a phase of self-sustained low activity in excitation-inhibition networks. The uncovered phase reproduces the main empirically-observed features of cortical networks in the so-called asynchronous state, characterized by low, un-correlated and highly-irregular activity. The parsimonious model analyzed here allows us to resolve a number of long-standing issues, such as proving that activity can be self-sustained even in the complete absence of external stimuli or driving. The simplicity of our approach allows for a deep understanding of asynchronous states and of the phase transitions to other standard phases it exhibits, opening the door to reconcile, asynchronous-state and critical-state hypotheses, putting them within a unified framework. We argue that Jensen’s forces are measurable experimentally and might be relevant in contexts beyond neuroscience.

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, PLOS COMPUTATIONAL BIOLOGY [36][37][38], our findings suggest that the same cortical network could be tuned from criticality to asynchrony, by tuning inhibition and excitation appropriately.…”

“…Since stronger synapses are more effective for propagating activity, we suspect our work points to a different mechanism than that discussed by Priesemann and colleagues. Buendia et al focused on the 'low-activity intermediate' (LAI) regime, which had small fluctuations similar asynchronous regimes [37]. Their LAI regime emerged when they reduced the density of connections to a sufficiently sparse level (less than 0.01).…”

“…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][37][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].…”

“…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]. Although very useful, this model was too abstract to identify specific biological mechanisms that might be responsible for changing m. Buendia et al studied networks of excitatory and inhibitory neurons and found that, for sufficiently sparse networks, a new regime emerges near criticality with weak flucutations around a moderate mean firing rate, reminiscent of some asynchronous activity [37]. 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].…”

Spontaneous neuronal avalanches as a correlate of access consciousness

“…However, while SOC provides a candidate framework for a unified theory of Consciousness (Melloni et al, 2021), a critical state is not strictly required for explaining the presence of spontaneous scale-free neuronal avalanches (e.g., Buendía et al, 2020aBuendía et al, , 2022. For example, it was suggested that during deep sleep or under anesthesia, the brain self-organizes at the edge of bistability (SOB, a first order phase transition Buendía et al, 2020b), rather than SOC (Priesemann et al, 2013). Furthermore, other bursting phenomena such as EEG micro states (Britz et al, 2009;Michel and Koenig, 2018) and neuronal assemblies (Papadimitriou et al, 2020) have been linked to cognition and perception.…”