Neurobiologically Realistic Determinants of Self-Organized Criticality in Networks of Spiking Neurons

Self-organized criticality refers to the spontaneous emergence of self-similar dynamics in complex systems poised between order and randomness. The presence of self-organized critical dynamics in the brain is theoretically appealing and is supported by recent neurophysiological studies. Despite this, the neurobiological determinants of these dynamics have not been previously sought. Here, we systematically examined the influence of such determinants in hierarchically modular networks of leaky integrate-and-fire neurons with spike-timing-dependent synaptic plasticity and axonal conduction delays. We characterized emergent dynamics in our networks by distributions of active neuronal ensemble modules (neuronal avalanches) and rigorously assessed these distributions for power-law scaling. We found that spike-timing-dependent synaptic plasticity enabled a rapid phase transition from random subcritical dynamics to ordered supercritical dynamics. Importantly, modular connectivity and low wiring cost broadened this transition, and enabled a regime indicative of self-organized criticality. The regime only occurred when modular connectivity, low wiring cost and synaptic plasticity were simultaneously present, and the regime was most evident when between-module connection density scaled as a power-law. The regime was robust to variations in other neurobiologically relevant parameters and favored systems with low external drive and strong internal interactions. Increases in system size and connectivity facilitated internal interactions, permitting reductions in external drive and facilitating convergence of postsynaptic-response magnitude and synaptic-plasticity learning rate parameter values towards neurobiologically realistic levels. We hence infer a novel association between self-organized critical neuronal dynamics and several neurobiologically realistic features of structural connectivity. The central role of these features in our model may reflect their importance for neuronal information processing. Author Summary: The intricate relationship between structural brain connectivity and functional brain activity is an important and intriguing research area. Brain structure (the pattern of neuroanatomical connections) is thought to strongly influence and constrain brain function (the pattern of neuronal activations). Concurrently, brain function is thought to gradually reshape brain structure, through processes such as activity-dependent plasticity (the “what fires together, wires together” principle). In this study, we examined the relationship between brain structure and function in a biologically realistic mathematical model. More specifically, we considered the relationship between realistic features of brain structure, such as self-similar organization of specialized brain regions at multiple spatial scales (hierarchical modularity) and realistic features of brain activity, such as self-similar complex dynamics poised between order and randomness (self-organized criticality). We found a direct association between these structural and functional features in our model. This association only occurred in the presence of activity-dependent plasticity, and may reflect the importance of the corresponding structural and functional features in neuronal information processing.