Self-organized critical neuronal networks: Structural determinants and directed information transfer

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 biological neuronal networks is supported by recent neurophysiological studies; these studies additionally associate critical neuronal network dynamics with several appealing properties, including optimized information transfer. Here we systematically seek the structural determinants of self-organized critical neuronal dynamics and quantify directed information transfer at criticality, in neurobiologically realistic neuronal networks. We study dynamics in hierarchically modular networks of leaky integrate-and-fire neurons with spike-timing-dependent synaptic plasticity and axonal conduction delays. We characterize emergent dynamics in our networks by distributions of active neuronal ensemble modules (neuronal avalanches) and rigorously assess these distributions for power-law scaling. We define three novel transfer-entropy based measures of directed information transfer; these measures compute the amount of predictive information present in neuronal avalanche properties (avalanche size, avalanche duration and inter-avalanche period) of the source region about avalanche properties of the destination region. We find that synaptic plasticity enables a rapid phase transition from random subcritical dynamics to ordered supercritical dynamics. Importantly, modular connectivity and low wiring cost broaden this transition, and enable a regime indicative of self-organized criticality. The critical regime is associated with maximized directed information transfer on all three computed measures. We hence infer a novel association between self-organized critical neuronal dynamics and several neurobiologically realistic features of structural connectivity, and find quantitative evidence for maximized directed information transfer at criticality.