Synaptic-resolution network connectomics has revealed that brain circuits feature fine-scale structural connectivity, such as pairs of correlated synaptic couplings known as second-order motifs. Large-scale recordings of neuronal activity in networks containing nonlinear neurons reveal macroscopic heterogeneous population dynamics throughout the brain. These findings rekindle the inquiry into this intriguing question: Can microscale synaptic structures contribute to macroscopic heterogeneous dynamics and computations in ways that canonical brain circuit models cannot? To answer this question, we construct random RNNs with various cell types, nonlinear non-negative neural responses, and arbitrary marginal and second-order correlated synaptic statistics. We derive low-rank mean-field equations for \(P\)-population networks in which the pre- and postsynaptic neuronal population identities determine the synaptic and motif strengths. Our framework requires \(2P\) latent dynamic variables with \(P\) variables describing mean population activity and \(P\) variables capturing within-population variability. Theoretical and numerical results demonstrate that chain motifs induce correlations in synaptic variability, coupling within-population variability to population mean dynamics through nonlinear gain. We use this framework to construct network models constrained by experimentally observed motif statistics that reproduce key population activity patterns in the mouse primary visual cortex. By explicitly linking synaptic organization to coupled mean-variability dynamics, our results provide a testable framework for studying the relationship between fine-scale connectivity, heterogeneous dynamics, and task-related responses.

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