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

Abolfazl Ziaeemehr,Aida Sheshbolouki,Mina Zarei

doi:10.1038/s41598-020-60205-0

Abstract

The collective behaviour of neural networks depends on the cellular and synaptic properties of the neurons. The phase-response curve (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 is delivered to that neuron. The neuronal PRCs can be classified as having either purely positive values (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 unidirectional synapses. Performing the linear stability analysis and the numerical simulation of the extended Kuramoto model, we show that feedforward loop motifs favour synchronization of type I excitatory and inhibitory neurons, while feedback loop motifs destroy their synchronization tendency. Moreover, large directed networks, either without feedback motifs or with many of them, have been constructed from the same undirected backbones, and a high synchronization level is observed for directed acyclic graphs with type I neurons. It has been shown that, the synchronizability of type I neurons depends on both the directionality of the network connectivity and the topology of its undirected backbone. The abundance of feedforward motifs enhances the synchronizability of the directed acyclic graphs.

Highlights

For several decades, there has been a continuing research interest in the synchronization phenomenon due to its widespread application in natural and artificial systems ranging from neural dynamics[1,2,3], cardiac pacemaker cells[4], and power grid networks[5] to social networks[6]
It has been found that brain neurons have different types of intrinsic dynamics that close to threshold, they may be grouped into two excitability classes: Type I and Type II
We focus on two distinct categories: (I) feedback loops (FBL) and (II) feedforward loop motifs (FFL)

Summary

Introduction

There has been a continuing research interest in the synchronization phenomenon due to its widespread application in natural and artificial systems ranging from neural dynamics[1,2,3], cardiac pacemaker cells[4], and power grid networks[5] to social networks[6]. Different profiles of the neuronal phase response curve arise for different types of neurons in that in type I neurons, any excitatory perturbation causes an acceleration of the spike, while in type II neurons, perturbations cause acceleration or delay of the spike depending on the phase at which the perturbation is delivered to that neuron These qualitatively different responses to stimulation lead to dramatically different synchronization patterns in neural networks. Regarding the underlying network connectivity, Master Stability Function is a well-known formalism providing estimation of the synchronization stability in the networks of coupled identical oscillators[22]. According to this formalism, the spread of the eigenvalues of the Laplacian matrix is a synchronizability index. It can be shown that complete graphs and directed acyclic graphs with identical node in-degrees are optimal networks provided that they embed an oriented spanning tree[23,24]

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Conclusion