Institute of Advanced Studies in Basic Sciences (IASBS), Department of Physics, Zanjan, 45137-66731, Iran.
Institute for Research in Fundamental Sciences (IPM), School of Computer Science, Tehran, 19395-5531, Iran.
Sci Rep. 2020 Feb 24;10(1):3306. doi: 10.1038/s41598-020-60205-0.
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.
神经网络的集体行为取决于神经元的细胞和突触特性。相位反应曲线（PRC）是一种可通过实验获得的细胞特性测量方法，它量化了刺激施加到神经元时，神经元下一个尖峰时间相对于相位的偏移。神经元 PRC 可以分为具有纯正值（I 型）或明显的正、负值区域（II 型）。具有 I 型 PRC 的网络往往不会通过相互兴奋性突触连接而同步。我们研究了相同 I 型和 II 型神经元的同步特性，假设存在单向突触。通过对扩展 Kuramoto 模型进行线性稳定性分析和数值模拟，我们表明前馈环模式有利于 I 型兴奋性和抑制性神经元的同步，而反馈环模式则破坏它们的同步趋势。此外，还从相同的无向主干构建了具有大量无反馈模式或具有许多反馈模式的大型有向网络，并观察到具有 I 型神经元的有向无环图具有较高的同步水平。已经表明，I 型神经元的同步能力取决于网络连接的方向性和无向主干的拓扑结构。前馈模式的丰富性增强了有向无环图的同步能力。
