Synaptic shot-noise triggers fast and slow global oscillations in balanced neural networks

TL;DR

This paper develops a mean-field theory for neural networks that incorporates synaptic shot-noise, revealing new dynamical regimes with global oscillations not predicted by traditional diffusion models, and links these to observed brain rhythms.

Contribution

The authors introduce a rigorous mean-field framework that accounts for synaptic shot-noise, uncovering novel oscillatory behaviors in sparse balanced neural networks.

Findings

Identifies new regimes of self-sustained global oscillations at low connectivity.

Shows oscillation frequencies can be tuned from slow to fast by adjusting network parameters.

Links low-in-degree oscillations to gamma rhythms observed in cortex and hippocampus.

Abstract

Neural dynamics is determined by the transmission of discrete synaptic pulses (synaptic shot-noise) among neurons. However, the neural responses are usually obtained within the diffusion approximation modeling synaptic inputs as continuous Gaussian noise. Here, we present a rigorous mean-field theory that encompasses synaptic shot-noise for sparse balanced inhibitory neural networks driven by an excitatory drive. Our theory predicts new dynamical regimes, in agreement with numerical simulations, which are not captured by the classical diffusion approximation. Notably, these regimes feature self-sustained global oscillations emerging at low connectivity (in-degree) via either continuous or hysteretic transitions and characterized by irregular neural activity, as expected for balanced dynamics. For sufficiently weak (strong) excitatory drive (inhibitory feedback) the transition line displays a peculiar re-entrant shape revealing the existence of global oscillations at low and high in-degrees, separated by an asynchronous regime at intermediate levels of connectivity. The mechanisms leading to the emergence of these global oscillations are distinct: drift-driven at high connectivity and cluster activation at low connectivity. The frequency of these two kinds of global oscillations can be varied from slow (around 1 Hz) to fast (around 100 Hz), without altering their microscopic and macroscopic features, by adjusting the excitatory drive and the synaptic inhibition strength in a prescribed way. Furthermore, the cluster-activated oscillations at low in-degrees could correspond to the gamma rhythms reported in mammalian cortex and hippocampus and attributed to ensembles of inhibitory neurons sharing few synaptic connections [G. Buzsaki and X.-J. Wang, Annual Review of Neuroscience 35, 203 (2012)].