From the statistics of connectivity to the statistics of spike times in neuronal networks
An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad principles underlying collective spiking activity in neural circuits. The first is that local features of network connectivity can be surprisingly effective in predicting global statistics of activity across a network. The second is that, for the important case of large networks with excitatory-inhibitory balance, correlated spiking persists or vanishes depending on the spatial scales of recurrent and feedforward connectivity. We close by showing how these ideas, together with plasticity rules, can help to close the loop between network structure and activity statistics.\n\nHighlightsO_LIRemarkable new data on connectivity and activity raise the promise and raise the bar for linking structure and dynamics in neural networks.\nC_LIO_LIRecent theories aim at a statistical approach, in which the enormous complexity of wiring diagrams is reduced to key features of that connectivity that drive coherent, network-wide activity.\nC_LIO_LIWe provide a unified view of three branches of this work, tied to a broadly useful \"neural response\" formula that explicitly relates connectivity to spike train statistics.\nC_LIO_LIThis isolates a surprisingly systematic role for the local structure and spatial scale of connectivity in determining spike correlations, and shows how the coevolution of structured connectivity and spiking statistics through synaptic plasticity can be predicted self-consistently.\nC_LI