Tuned inhibition explains strong correlations across segregated excitatory subnetworks

Understanding the basis of shared, across trial fluctuations in neural activity in mammalian cortex is critical to uncovering the nature of information processing in the brain. This correlated variability has often been related to the structure of cortical connectivity since variability not accounted for by signal changes likely arises from local circuit inputs. However, recent recordings from segregated networks of excitatory neurons in mouse primary visual cortex (V1) complicate this relationship. These results found that despite weak cross-network connection probability, noise correlations were significantly larger than one would expect. We aim to explore possible circuit mechanisms responsible for these enhanced positive correlations through biologically motivated cortical network models, with the hypothesis that they arise from unobserved inhibitory neurons.
In particular, we consider networks with weakly interconnected excitatory populations, but either global or subpopulation-specific inhibitory populations. We then ask how correlations can be enhanced or marred via the strength of outgoing and incoming connections to these inhibitory populations. By performing a pathway expansion of the covariance matrix, we find that a single inhibitory population with sufficiently strong I to E connections can lead to stronger than expected positive correlations across excitatory populations. However, this result is highly parameter dependent. When considering an inhibition-stabilized network (ISN) the viable parameter regime shrinks dramatically into a narrow band close to the edge of stability. We find that both non-ISN and ISN regimes can recover the ability to robustly explain the experimental results by allowing for two tuned inhibitory populations, meaning that each inhibitory population preferentially connects to one of the two excitatory populations. Our results therefore imply that complexity in excitation should be mirrored by complexity in the structure of inhibition.