Synchronous firing frequency dependence in unidirectional coupled neuronal networks with chemical synapses

Rhythmic brain waves caused by the synchronous firing activity of neurons are believed to be relevant for higher brain functions such as the attention and sleep-wake state switching. In the brain, cortical neurons, including interneurons, are anatomically and functionally diverse and can fire at different frequencies. However, it still remains unclear how such cortical networks that comprise a variety of neurons create synchronous activity. The present study examined entrainments of firing activity in cortical networks. To explore how cortical networks causes synchronous firing and to elucidate the mechanism for synchronous activity, we performed numerical simulations of synchronous firing behaviors observed in a unidirectional coupled neuron model, mimicking one of the minimum motifs in cortical networks. Furthermore, we observed bifurcations of periodic oscillations, which cause various phase locking states, in the coupled neuron model. We analyzed these bifurcations to investigate the effects of differences in membrane excitability, synaptic properties, and model structural complexity on the synchronous firing frequency. We found that the post-synaptic neuron could more readily attain a phase locking state at higher or lower frequencies than the intrinsic firing frequency of the pre-synaptic neuron for excitatory and inhibitory synaptic inputs, respectively. This finding suggests that synaptic coupling properties might determine the entrainable frequency range (phase-locked range) of the synchronous firing behavior. Thus, the specific rhythmic waves evoked by brain activity may be attributable to the synaptic coupling properties constituting local circuits.