Influence of inhibitory autapses on synchronization of inhibitory network gamma oscillations

A recent experimental study showed that inhibitory autapses favor firing synchronization of parvalbumin interneurons in the neocortex during gamma oscillations. In the present paper, to provide a comprehensive and deep understanding to the experimental observation, the influence of inhibitory autapses on synchronization of interneuronal network gamma oscillations is theoretically investigated. Weak, middle, and strong synchronizations of a globally inhibitory coupled network composed of Wang-Buzsaki model without autapses appear at the bottom-left, middle, and top-right of the parameter plane with the conductance (g(syn)) and the decay constant (tau(syn)) of inhibitory synapses taken as the x-axis and y-axis, respectively. After introducing inhibitory autapses, the border between the strong and middle synchronizations in the (g(syn), tau(syn)) plane moves to the top-right with increasing the conductance (g(aut)) and the decay constant (tau(aut)) of autapses, due to that interspike interval of the single neuron becomes longer, leading to that larger tau(syn) is needed to ensure the strong synchronization. Then, the synchronization degree of middle and strong synchronizations around the border in the (g(syn), tau(syn)) plane decreases, while of strong synchronization in the remaining region remains unchanged. The synchronization degree of weak synchronization increases with increasing tau(aut) and g(aut), due to that the inhibitory autaptic current becomes strong and long to facilitate synchronization. The enhancement of weak synchronization modulated by inhibitory autapses is also simulated in the random, small-world, and scale-free networks, which may provide explanations to the experimental observation. These results present complex dynamics of synchronization modulated by inhibitory autapses, which needs future experimental demonstrations.