For decades, neuroscientists have observed that the brain operates at a critical state, where information states and propagation are optimized in the form of neural avalanches. A great deal of this behavior is made possible because of the connectivity of the individual neurons in the brain, in a structure called the connectome. Recently, there have been great strides in deepening our understanding of the individual neuronal connections that form various connectomes of different species. 

In a 2025 study published in Scientific Reports by researchers Michelle T. Cirunay, Rene C. Batac, and Géza Ódor, the connection between the critical dynamics of the brain and its connectome structure is investigated. They observed that, by running sandpile-like dynamics in a baseline hierarchical modular network (HMN) and imposing learning mechanisms that aid/inhibit the formation of stronger connections, the statistical properties of connectomes naturally emerge. 

The researchers started with an HMN, and introduced triggering at random neuronal locations every time step. The network responds by following the rules of the sandpile to simulate how neurons interact: When a local neuron reaches a threshold value, it relaxes by distributing its entire state to all of its connections. This, in turn, may lead to a cascade of relaxations, wherein other connected neurons are also activated to their maximum possible states and relaxed by local redistributions. When the authors looked at the statistical distributions of the number of such neurons activated during a single triggering event, they observed a decaying power-law behavior with scaling exponents close to 3/2, for a broad range of baseline HMN sizes and configurations. Interestingly, this decay exponent is akin to those observed for actual neuronal avalanches in actual brains and in neuronal cultures grown in the lab. 

The breakthrough in this study comes from the introduction of Hebbian learning—the famous principle that "neurons that fire together, wire together." In the model, every time two neurons are driven to their maximal state, they create or strengthen their connection. Additionally, inhibitory mechanisms were introduced by random weakenings of unused connections during instances without avalanches. The interplay between these two mechanisms allowed the simulated brain to grow a connectome network in a way that mirrors real biological data. Without any central "master plan" or external tuning, the model spontaneously reproduced the same structural patterns found in the connectomes of fruit flies and humans, including the specific way synaptic weights and connection strengths are distributed.

The model therefore not only validates the criticality hypothesis through the use of a paradigm model of self-organized criticality in the sandpile; it also highlights the role of an initial modular structure, and the balance between excitory and inhibitory learning mechanisms in the origin of connectome structure. The work is one of the additions to literature to close the loop between experimental, theoretical, and computational approaches to brain modeling.◼