Analysis of Graph Invariants in Functional Neocortical Circuitry Reveals Generalized Features Common to Three Areas of Sensory Cortex

Abstract

Correlations in local neocortical spiking activity can provide insight into the underlying organization of cortical microcircuitry. However, identifying structure in patterned multi-neuronal spiking remains a daunting task due to the high dimensionality of the activity. Using two-photon imaging, we monitored spontaneous circuit dynamics in large, densely sampled neuronal populations within slices of mouse primary auditory, somatosensory, and visual cortex. Using the lagged correlation of spiking activity between neurons, we generated functional wiring diagrams to gain insight into the underlying neocortical circuitry. By establishing the presence of graph invariants, which are label-independent characteristics common to all circuit topologies, our study revealed organizational features that generalized across functionally distinct cortical regions. Regardless of sensory area, random and -nearest neighbors null graphs failed to capture the structure of experimentally derived functional circuitry. These null models indicated that despite a bias in the data towards spatially proximal functional connections, functional circuit structure is best described by non-random and occasionally distal connections. Eigenvector centrality, which quantifies the importance of a neuron in the temporal flow of circuit activity, was highly related to feedforwardness in all functional circuits. The number of nodes participating in a functional circuit did not scale with the number of neurons imaged regardless of sensory area, indicating that circuit size is not tied to the sampling of neocortex. Local circuit flow comprehensively covered angular space regardless of the spatial scale that we tested, demonstrating that circuitry itself does not bias activity flow toward pia. Finally, analysis revealed that a minimal numerical sample size of neurons was necessary to capture at least 90 percent of functional circuit topology. These data and analyses indicated that functional circuitry exhibited rules of organization which generalized across three areas of sensory neocortex.

Author Summary

Information in the brain is represented and processed by populations of interconnected neurons. However, there is a lack of a clear understanding of the structure and organization of circuit wiring, particularly at the mesoscale which spans multiple columns and layers. In this study, we sought to evaluate whether functional circuit architecture generalizes across the neocortex, testing the existence of a functional analogue to the neocortical microcircuit hypothesis. We analyzed the correlational structure of spontaneous circuit activations in primary auditory, somatosensory, and visual neocortex to generate functional topologies. In these graphs, neurons were represented as nodes, and time-lagged firing between neurons were directed edges. Edge weights reflected how many times the lagged firing occurred and was synonymous to the strength of the functional connection between two neurons. The presence of label-independent features, identified by investigating functional circuit topologies under a graph invariant framework, suggest that functionally distinct areas of the neocortex carry features of a generalized functional cortical circuit. Furthermore, our analyses show that the simultaneous recording of large sections of cortical circuitry is necessary to recognize these features and avoid undersampling errors.