Emergence of global synchronization in directed excitatory networks of type I neurons

Collective behavior of neural networks depends on the cellular and synaptic properties of the neurons. The phase-response curve (\textit{PRC}) is an experimentally obtainable measure of cellular properties that quantifies the shift in the next spike time of a neuron as a function of the phase at which stimulus delivered to that neuron. The neuronal \textit{PRC}s can be classified as having either purely positive value (type I) or distinct positive and negative regions (type II). Networks of type 1 PRCs tend not to synchronize via mutual excitatory synaptic connections. We study the synchronization properties of identical type I and type II neurons, assuming excitatory unidirectional synapses. Performing the linear stability analysis and the numerical simulation of the extended Kuramoto model, we show that Feedforward loops favour synchronization of type I neurons, while feedback loops destroy their synchronization tendency. The results are robust to large directed networks constructed from only feedforward or mostly feedback loops, and high synchronization level observed for directed acyclic graphs with type I neurons. The synchronizability of type I neurons depends on both the directionality of the connectivity network and the topology of its undirected backbone. The abundance of feedforward motifs enhances the synchronizability of the directed acyclic graphs.