Critical behaviors of modular networks under local excitatory-inhibitory fluctuations

Numerous physiological observations have shown that the brain operates at the edge of a critical state between order and disorder. Meanwhile, brain structures at different scales, from cortical columns to the entire brain, are organized in a modular manner. However, whether modular brain networks represent the optimized structure shaped for criticality and in what ways, have not been fully answered. In this study, a modular network with dense intra-module links but sparse inter-module links is established, and the behavior of each neuron is governed by the Kinouchi-Copelli model. Moreover, randomized surrogate networks with identical degree distribution are introduced to illustrate the significance of modular structures for criticality. Results suggest that the modular network requires fewer synaptic resources and lower firing costs to achieve criticality. More importantly, smaller avalanches indicate that the modular structures can enhance network resilience, facilitating rapid recovery from perturbations. Furthermore, by testing the sensitivity of the network state to local excitatory-inhibitory fluctuations, it is found that the efficiency of excitatory and inhibitory regulation is closely related to the 2-level excitatory input density. In addition, inhibitory regulation targeting modules with larger maximum real eigenvalues can more effectively suppress hyperexcitatory activities to achieve balance. When local excitation is greatly enhanced, even if the modular network is adjusted to the critical state, the size-to-duration ratio of module-level avalanches can effectively capture abnormalities. The properties also manifest in clinical recordings from patients with temporal lobe epilepsy, which may provide a promising method for epileptogenic zone localization.