Correlated firing and oscillations in spiking networks with global delayed inhibition

Neural population densities shape network correlations

The way sensory microcircuits manage cellular response correlations is a crucial question in understanding how such systems integrate external stimuli and encode information. Most sensory systems exhibit heterogeneities in terms of population sizes and features, which all impact their dynamics. This work addresses how correlations between the dynamics of neural ensembles depend on the relative size or density of excitatory and inhibitory populations. To do so, we study an apparently symmetric system of coupled stochastic differential equations that model the evolution of the populations' activities. Excitatory and inhibitory populations are connected by reciprocal recurrent connections, and both receive different stimuli exhibiting a certain level of correlation with each other. A stability analysis is performed, which reveals an intrinsic asymmetry in the distribution of the fixed points with respect to the threshold of the nonlinearities. Based on this, we show how the cross correlation between the population responses depends on the density of the inhibitory population, and that a specific ratio between both population sizes leads to a state of zero correlation. We show that this so-called asynchronous state subsists, despite the presence of stimulus correlation, and most importantly, that it occurs only in asymmetrical systems where one population outnumbers the other. Using linear approximations, we derive analytical expressions for the root of the cross-correlation function and study how the asynchronous state is impacted by the model's parameters. This work suggests a possible explanation for why inhibitory cells outnumber excitatory cells in the visual system.