Effects of Spatial Constraints of Inhibitory Connectivity on the Dynamical Development of Criticality in Spiking Networks

Neural systems are hypothesized to operate near criticality, enhancing their capacity for optimal information processing, transmission and storage capabilities. Criticality has typically been studied in spiking neural networks and related systems organized in random or full connectivity, with the balance of excitation and inhibition being a key determinant of the critical point of the system. However, given that neurons in the brain are spatially distributed, with their distances significantly influencing connectivity and signal timing, it is unclear how the spatial organization of excitatory and inhibitory connectivity influences the networks self-organization towards criticality. Here, we systematically constrain the distance and density of inhibitory connectivity in two-dimensional spiking networks and allow synaptic weights to self-organize with activity-dependent excitatory and inhibitory plasticity in the presence of a low level of stochastic intrinsic activity. We then investigate the relationship between inhibitory connectivity, synaptic weights, and the resulting network activity during and after development. We find that networks with longer-range inhibitory synapses tend towards more supercritical behavior compared to networks with a similar number of shorter-range inhibitory synapses. We show that this distance dependence is a consequence of weaker long-range synapses after development due to the presence of synaptic delays, which shift most spike pairs outside of the potentiation window of the inhibitory learning rule.