Cyclic transitions between higher order motifs underlie sustained activity in asynchronous sparse recurrent networks

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.nnAuthor summaryHere we address two questions. First, it remains unclear how activity propagates stably through a network since neurons are leaky and connectivity is sparse and weak. Second, higher order patterns abound in neocortex, hinting at potential functional relevance for their presence. Several lines of evidence suggest that higher-order network interactions may be instrumental for spike propagation. For example, excitatory synaptic connectivity shows a prevalence of local neuronal cliques and patterns, and propagating activity in vivo displays elevated clustering dominated by specific triplet motifs. In this study we demonstrate a mechanistic link between activity propagation and higher-order motifs at the level of individual neurons and across networks. We algorithmically build spiking neural network (SNN) models to mirror the topological and dynamical statistics of neocortex. Using a combination of graph theory, information theory, and probabilistic tools, we show that higher order coordination of synapses is necessary for sustaining activity. Coordination takes the form of cyclic transitions between specific triangle motifs. The results of our model are consistent with numerous experimental observations in neuroscience, and their generalizability to other weakly and sparsely connected networks is predicted.