Many studies have demonstrated the prominence of higher-order patterns in excitatory synaptic connectivity as well as activity in neocortex. Surveyed as a whole, these results suggest that there may be an essential role for higher-order patterns in neocortical function. In order to stably propagate signal within and between regions of neocortex, the most basic - yet nontrivial - function which neocortical circuitry must satisfy is the ability to maintain stable spiking activity over time. Here we algorithmically construct spiking neural network models comprised of 5000 neurons using topological statistics from neocortex and a set of objective functions that identify networks which produce naturalistic low-rate, asynchronous, and critical activity. We find that the same network topology can exhibit either sustained activity under one set of initial membrane voltages or truncated activity under a different set. Yet these two outcomes are not readily differentiated by rate or criticality. By summarizing the statistical dependencies in the pairwise activity of neurons as directed weighted functional networks, we examined the transient manifestations of higher-order motifs in the functional networks across time. We find that stereotyped low variance cyclic transitions between three isomorphic triangle motifs, quantified as a Markov process, are required for sustained activity. If the network fails to engage the dynamical regime characterized by a recurring stable pattern of motif dominance, spiking activity ceased. Motif cycling generalized across manipulations of synaptic weights and across topologies, demonstrating the robustness of this dynamical regime for sustained spiking in critical asynchronous network activity. Our results point to the necessity of higher-order patterns amongst excitatory connections for sustaining activity in sparse recurrent networks. They also provide a possible explanation as to why such excitatory synaptic connectivity and activity patterns have been prominently reported in neocortex.
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