Impact of Local Connectivity Patterns on Excitatory-Inhibitory Network Dynamics

Networks of excitatory and inhibitory (EI) neurons form a canonical circuit in the brain. Seminal theoretical results on the dynamics of such networks are based on the assumption that synaptic strengths depend on the type of neurons they connect, but are otherwise statistically independent. Recent synaptic physiology datasets, however, highlight the prominence of specific connectivity patterns that go well beyond what is expected from independent connections. While decades of influential research have demonstrated the strong role of the basic EI cell type structure, the extent to which additional connectivity features influence dynamics remains to be fully determined. Here we examine the effects of pairwise connectivity motifs on the linear dynamics in excitatory-inhibitory networks using an analytical framework that approximates the connectivity in terms of low-rank structures. This low-rank approximation is based on a mathematical derivation of the dominant eigenvalues of the connectivity matrix, and it predicts the impact on responses to external inputs of connectivity motifs and their interactions with cell-type structure. Our results reveal that a particular pattern of connectivity, namely chain motifs, have a much stronger impact on dominant eigenmodes than other pairwise motifs. In particular, an over-representation of chain motifs induces a strong positive eigenvalue in inhibition-dominated networks, and it generates a potential instability that requires revisiting the classical excitation-inhibition balance criteria. Examining the effects of external inputs, we show that chain motifs can on their own induce paradoxical responses, where an increased input to inhibitory neurons leads to a decrease in their activity due to the recurrent feedback. These findings have direct implications for the interpretation of experiments in which responses to optogenetic perturbations are measured and used to infer the dynamical regime of cortical circuits.