Title: Effect of Synaptic Heterogeneity on Neuronal Coordination

Abstract: Recent advancements in measurement techniques have resulted in an increasing amount of data on neural activities recorded in parallel, revealing largely heterogeneous correlation patterns across neurons. Yet, the mechanistic origin of this heterogeneity is largely unknown because existing theoretical approaches linking structure and dynamics in neural circuits are restricted to population-averaged connectivity and activity. Here we present a systematic inclusion of heterogeneity in network connectivity to derive quantitative predictions for neuron-resolved covariances and their statistics in spiking neural networks. Our study shows that the heterogeneity in covariances is not a result of variability in single-neuron firing statistics but stems from the ubiquitously observed sparsity and variability of connections in brain networks. Linear-response theory maps these features to the effective connectivity between neurons, which in turn determines neuronal covariances. Beyond-mean-field tools reveal that synaptic heterogeneity modulates the variability of covariances and thus the complexity of neuronal coordination across many orders of magnitude.