Elementary Dynamics of Neural Microcircuits

Abstract

In neural circuits with multiple excitatory (E) and inhibitory (I) cell types, qualitatively new dynamics arise when one population is silenced by the others, an effect linear theories cannot capture. Using threshold-linear networks, the simplest nonlinear population model, we derive closed-form conditions for multistability, oscillations, and paradoxical responses across microcircuits. In E-I circuits, strengthening E-to-I rather than I-to-E connections controls runaway excitation without silencing E cells. In a canonical neocortical circuit, two distinct gamma-oscillation mechanisms reproduce optogenetic silencing experiments, reconciling conflicting models. In hippocampal E-I-I circuits, cross-inhibition determines whether transitions between gamma rhythms are gradual, abrupt, or non-oscillatory. Two E populations or assemblies can cooperate, compete, or suppress each other depending on cross- versus self-excitation. Balanced inhibition prevents competition between E-I assemblies, unless I-to-I connections are more specialized than I-to-E ones, whereas lateral inhibition yields winner-take-all dynamics even without assemblies. These testable conditions link connectivity to dynamics across brain areas.