A mean-field model of neural networks with PV and SOM interneurons reveals connectivity-based mechanisms of gamma oscillations

Classic theoretical models of cortical oscillations are based on the interactions between two populations of excitatory and inhibitory neurons. Nevertheless, experimental studies and network simulations suggest that interneuron subclasses such as parvalbumin (PV) and somatostatin (SOM) exert distinct control over oscillatory dynamics. Yet, we lack a theoretical understanding of the mechanisms underlying oscillations in E-PV-SOM circuits and of the differences with respect to the classical mechanisms for oscillations in simpler E–I networks. Here, we derive a biologically realistic mean-field model of a canonical three-population E-PV-SOM circuit. This model robustly generates oscillations whose features are consistent with experimental observations, including the relative timing of PV and SOM activity and the effects of optogenetic perturbations. By reducing the model to a linear analytical form, we demonstrate that gamma oscillations emerge directly from the cell-specific connectivity of the three-population circuit. This connectivity motif alone accounts for experimentally observed phase relationships, with PV activity consistently leading that of SOM neurons. Together, this mean field model identifies a distinct structural mechanism giving rise to oscillations in canonical E–PV–SOM circuits and provides theoretical primitives for constructing large-scale, cell-type-specific models of cortical dynamics.Author summary: In this work, we develop a computational mean field model that predicts the collective electrical activity of populations of neurons composed of two main types of inhibitory cells, parvalbumin-positive (PV) and somatostatin-positive (SOM) neurons. We compare the predictions of this mean field model with simulations of large spiking neural networks composed of thousands of sparsely connected neurons. We show that this mean field model captures key features of the network, including how different inhibitory cell types shape rhythmic activity. In particular, we find that these inhibitory neurons play distinct roles in generating and controlling oscillatory rhythms at multiple frequencies. Using a linear approximation of the model, we show analytically that oscillations emerge from the specific connectivity scheme between these inhibitory cell types, rather than requiring precise tuning of signal delays or time constants. Because of its simplicity, this mean field model can be studied analytically and used as a building block for constructing large-scale brain models with area-specific interneuron composition and structured layers of inhibitory neurons.