Spatial arrangement of inhibitory connections shapes brain network criticality

In neuroscience, the brain criticality hypothesis proposes that neurons in the brain are arranged in such a way that neural activity lies at or near a transition point between two extremes: an ordered state where neural activity dies out quickly and a disordered state where neural activity tends to spread quickly and potentially grow uncontrollably. This transition point is known as criticality, while the two activity regimes on either side of it are known as subcritical and supercritical, respectively. A useful analogy is a pile of sand. When a grain of sand is dropped into this pile, it might cause nothing, or it might trigger small or large avalanches. Similarly, near criticality, a small burst of neural activity can sometimes remain local, while at other times it can spread through much of the network, producing neural avalanches of many different sizes. 

Criticality can provide several computational advantages to neural networks. Specifically, near this state, neural networks can exhibit maximum computational and information-transmission capacities. Furthermore, they can exhibit high information storage capacity and a maximum dynamic range, making them highly sensitive to external stimuli. How the brain develops into a critical state, however, has long been an open question. Previous studies have revealed that network structure, long-term synaptic plasticity rules, and homeostatic mechanisms, which are feedback loops that stabilize neural activity, can drive networks to criticality. In addition, studies have also found that an important parameter for maintaining criticality is the balance of excitation and inhibition (E/I balance) in a network. 

In a recent study, a research team led by Associate Professor Zenas C. Chao from the International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo, Japan, explored brain criticality from a new perspective. "Most previous models of criticality in neural networks typically assume random or fully connected networks. However, real neurons in the brain occupy physical space, and the distance between neurons significantly influences neural connectivity and how much time signals take to travel," explains Dr. Chao. He adds, "In this study, we computationally explored how the spatial distribution of inhibitory connections interacts with synaptic plasticity to shape the development of critical activity." The team also included Dr. Felix Benjamin Kern and Dr. Takahisa Date, also from The University of Tokyo. Their study was published in the journal PLOS Computational Biology on October 1, 2026. 

The researchers first developed a computational neural network model in which 80 excitatory and 20 inhibitory neurons were scattered randomly across a two-dimensional disk with a radius of 2 mm. In this model, the spatial and connectivity parameters for excitatory connectivity were fixed, while the maximum distance and probability of inhibitory connections were systematically varied across a 5-by-5 grid, resulting in 25 different inhibitory connectivity conditions. The researchers independently generated and simulated 10 network prototypes, each with the same 25 inhibitory conditions, for analysis. Each network was simulated for 15 hours, starting with zero synaptic weights. 

The researchers focused on the final 2 hours of the simulation, after the networks reached a steady state, to explore criticality. Across most parameter settings, they found supercritical behavior to be the most common. Criticality was relatively scarce but was most frequently observed at intermediate-to-high inhibitory connectivity densities. At the highest inhibitory connectivity densities, subcritical behavior dominated. This result is consistent with previous studies demonstrating that criticality typically emerges under conditions where E/I balance is maintained. 

Importantly, the simulations revealed that the physical distance of inhibitory connections can influence whether a neural network settles below, near, or above criticality, independent of the connection density. The researchers found that networks with longer inhibitory connections tend to become more supercritical compared to networks with a similar number of shorter-range inhibitory connections. This was attributed to the presence of synaptic delays in the longer-range connections, caused by signals taking a longer time to reach target neurons. These delays make the longer inhibitory connections weaker compared to shorter-range connections. This weak inhibition allows larger neural avalanches, pushing the network towards a supercritical state. 

"Our results show that not only the number of inhibitory connections, but also their spatial arrangement and transmission delays, shape network criticality," notes Dr. Chao. "Understanding how spatial arrangement and delays influence neural dynamics could help inform the design of stable and adaptable artificial neural systems. Additionally, it could eventually help researchers investigate how genetic or developmental factors that alter inhibitory connectivity affect brain function," he concludes. 

While further research is required, this study offers key insights into how the spatial arrangement of inhibitory connections influences neural activity and could help in the development of advanced brain models, eventually enhancing our understanding of how the brain works.