Shot noise generated by subpopulations of neural networks

While the so-called next-generation neural mass models provide exact descriptions of densely coupled neural populations in the thermodynamic limit, finite-size effects introduce stochastic fluctuations whose power spectrum we derived in our previous work. However, coupling between different populations in the brain is typically sparse, meaning that only a subset of neurons from one population actually projects connections to another. This necessitates the study of shot noise generated by subpopulations within densely coupled neural populations. In the present work, we perform such an analysis and show that the shot noise of subpopulations differs from that of the whole population in both intensity and spectral properties, depending non-trivially on subpopulation size. Generalizing the previously introduced nesting method, we derive an analytical expression for the power spectrum of subpopulation shot noise, which shows excellent agreement with direct numerical simulations. Importantly, our approach accounts for realistic, non-Lorentzian distributions of local neuron parameters using a previously developed reduction technique. Thus, our results constitute an important step toward a new class of stochastic mean-field models suited for hierarchical neural networks with dense local connectivity and sparse inter-population connectivity.