Interactions between distinct populations of excitatory (E) and inhibitory (I) neurons can produce complex dynamical landscapes, featuring multistability, oscillations, and paradoxical perturbation responses. By employing an elementary model, the threshold-linear network (TLN), we indicate mathematical conditions for each dynamical regime across fundamental microcircuit architectures, thereby mapping previously unrelated systems neuroscience hypotheses to a common reference space and obtaining novel insights on inputs and connectivity. Namely, we compare balancing strategies in inhibition-stabilized E-I networks, we interpret experiments on gamma oscillations in a canonical neocortical E-I-I circuit, and we discuss bistability in hippocampal E-I-I networks. Then, we show that connectivity determines three fundamentally different kinds of interactions between assemblies in E-E-I circuits. Moreover in, E-E-I-I circuits we find that balanced clustering hinders lateral inhibition, while opponent clustering can produce different bistable configurations, even between completely unstructured assemblies. We conclude that TLNs allow to grasp deep and universal aspects of microcircuit dynamics.
Masserini, S., Kempter, R.
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