Biologically realistic mean field model of spiking neural networks with fast and slow inhibitory synapses

We present a mean field model for a spiking neural network of excitatory and inhibitory neurons with fast GABAA and nonlinear slow GABAB inhibitory conductance-based synapses. This mean field model can predict the spontaneous and evoked response of the network to external stimulation in asynchronous irregular regimes. The model displays theta oscillations for sufficiently strong GABAB conductance. Optogenetic activation of interneurons and an increase of GABAB conductance caused opposite effects on the emergence of gamma oscillations in the model. In agreement with direct numerical simulations of neural networks and experimental data, the mean field model predicts that an increase of GABAB conductance reduces gamma oscillations. Furthermore, the slow dynamics of GABAB synapses regulates the appearance and duration of transient gamma oscillations, namely gamma bursts, in the mean field model. Finally, we show that nonlinear GABAB synapses play a major role to stabilize the network from the emergence of epileptic seizures.