Tuning network dynamics from criticality to the chaotic balanced state

Abstract

According to many experimental observations, neurons in cerebral cortex tend to operate in an asynchronous regime, firing independently of each other. In contrast, many other experimental observations reveal cortical population firing dynamics that are relatively coordinated and occasionally synchronous. These discrepant observations have naturally led to a lively debate surrounding discrepant hypotheses. A commonly hypothesized explanation of asynchronous firing is that excitatory and inhibitory neurons are precisely correlated, nearly canceling each other, resulting in the so-called 'chaotic balanced state'. On the other hand, the 'criticality' hypothesis posits an explanation of the more coordinated state that also requires a certain balance of excitatory and inhibitory interactions. Both hypotheses claim the same qualitative mechanism -properly balanced excitation and inhibition. Thus, a natural question arises: how are the chaotic balanced state and criticality related, how do they differ? Here we propose an answer to this question based on investigation of a simple, network-level computational model. We show that the strength of inhibitory synapses relative to excitatory synapses can be tuned from weak to strong to generate a family of models that spans a continuum from 'criticality' to the 'chaotic balanced state'. Our results bridge two long-standing competing hypotheses and offer a possible explanation of discrepant experimental observations: neuromodulatory mechanisms that tune the strength of excitatory and inhibitory synapses may tune cortical state from criticality to the balanced state, and to intermediate states between these extremes. Author summaryWhat is the dynamical state of cerebral cortex? Are neurons mostly uncorrelated, firing asynchronously with each other? Are synchronous oscillations important? The answers to these questions have fundamental implications for how the cortical neural population encodes and processes information. Here we show that two possible scenarioscriticality and the chaotic balanced state -that are typically considered incompatible can be attained in the same network by maintaining a certain kind of balance, while tuning the strength of inhibition relative to excitation. Introduction 1Mounting experimental evidence supports the hypothesis that the cerebral cortex 2 operates in a dynamical regime near criticality [1][2][3][4][5][6][7][8]. What do we mean by criticality?Often, criticality is described as a boundary in the space of possible dynamical regimes. 4On one side of the boundary population activity tends to be orderly, correlated across 5 the entire network. On the other side, neurons fire more independently of each other. 6At criticality, population dynamics are more diverse, rarely exhibiting synchronization 7 that spans the network, but often showing coordinated firing among groups of neurons 8 at small and intermediate scales [9,10]. Direct evidence that the cerebral cortex may 9 indeed operate near such a boundary comes from experiments and models in which...

Description of spreading dynamics by microscopic network models and macroscopic branching processes can differ due to coalescence

“…This typically involves stochastic processes, such as (probabilistic) cellular automata [8][9][10], contact processes [10,11], or interacting Hawkes processes [12]. In particular, infectious diseases have been modeled by so-called susceptible-infectious models or generalizations thereof [13], whereas spikepropagation in neural networks has been modeled by socalled branching networks [14][15][16][17][18][19][20][21][22], Hawkes processes [23][24][25], or probabilistic integrate-and-fire networks [26,27]. These models can be either constructed as independentinteraction models (static interactions), or as threshold models with interactions depending on the states of the interacting partners [28].…”