Inhibitory cell type heterogeneity in a spatially structured mean-field model of V1

Inhibitory interneurons in the cortex are classified into cell types differing in their morphology, electrophysiology, and connectivity. Although it is known that parvalbumin (PV), somatostatin (SST), and vasoactive intestinal polypeptide-expressing neurons (VIP), the major inhibitory neuron subtypes in the cortex, have distinct modulatory effects on excitatory neurons, how heterogeneous spatial connectivity properties relate to network computations is not well understood. Here, we study the implications of heterogeneous inhibitory neurons on the dynamics and computations of spatially structured neural networks. We develop a mean-field model of the system in order to systematically examine excitation-inhibition balance, dynamical stability, and cell-type specific gain modulations. The model incorporates three inhibitory cell types and excitatory neurons with distinct connectivity probabilities and recent evidence of long-range spatial projections of SST neurons. Position-dependent firing-rate predictions are validated against simulations, and balanced solutions under Gaussian assumptions are derived from scaling arguments. Stability analysis shows that while long-range inhibitory projections in E-I circuits with a homogeneous inhibitory population result in instability, the heterogeneous network maintains stability with long-range SST projections. This suggests that a mixture of short- and long-range inhibitions may be key to providing diverse computations while maintaining stability. We further find that conductance-based synaptic transmissions are necessary to reproduce experimentally observed cell-type-specific gain modulations of inhibition by PV and SST neurons. These gain modulations are distance dependent, and a linear response analysis suggested that shifts in the excitation-inhibition balance of the network underlie these effects. Our theoretical approach offers insight into the computational function of cell-type-specific and distance-dependent network structure.