Synchronization induced by signal propagation delays in inhibitory networks

Abstract

It is generally accepted that inhibitory neurons play an important role in the generation of synchronous brain rhythms. A number of theoretical studies have been conducted over last decade to determine the properties of the inhibitory neuronal networks that can result in stable network synchrony and much work has focused on synaptic properties of GABA inhibition (the decay time of the synapse and the reversal potential), the heterogeneity in the intrinsic neuron firing rates and the architecture of the underlying networks. Very few studies, however, have focused on the role for explicit signal propagation delays in modulating synchrony in inhibitory networks. One reason for the paucity of work in this area stems for the fact that mathematical studies of a general network of coupled nonlinear delaydifferential equations resulting from the presence of signal propagation delays is a formidable task. Here our goal is to systematically investigate, in the setting of computer simulations, the role of signal propagation delays in the synchronization of inhibitory networks. We consider a random network G of N=10 interacting inhibitory neurons (Type-1 parvalbumin positive interneurons) with the following network constraints: (1) Unidirectional neuronal interaction (2) Mean in-degree for each node of the network is k=3. In order to systematically investigate how neuronal synchrony in this random network changes as a function of signal propagation delay τs, 1000 instances of G were generated and each network was simulated 100 times with random initial conditions. All simulations were performed for fixed