Miller Jennifer, Ryu Hwayeon, Wang Xueying, Booth Victoria, Campbell Sue Ann
Mathematics Department, Bellarmine University, Louisville, KY, United States.
Department of Mathematics and Statistics, Elon University, Elon, NC, United States.
Front Comput Neurosci. 2022 Aug 16;16:903883. doi: 10.3389/fncom.2022.903883. eCollection 2022.
Neural firing in many inhibitory networks displays synchronous assembly or clustered firing, in which subsets of neurons fire synchronously, and these subsets may vary with different inputs to, or states of, the network. Most prior analytical and computational modeling of such networks has focused on 1D networks or 2D networks with symmetry (often circular symmetry). Here, we consider a 2D discrete network model on a general torus, where neurons are coupled to two or more nearest neighbors in three directions (horizontal, vertical, and diagonal), and allow different coupling strengths in all directions. Using phase model analysis, we establish conditions for the stability of different patterns of clustered firing behavior in the network. We then apply our results to study how variation of network connectivity and the presence of heterogeneous coupling strengths influence which patterns are stable. We confirm and supplement our results with numerical simulations of biophysical inhibitory neural network models. Our work shows that 2D networks may exhibit clustered firing behavior that cannot be predicted as a simple generalization of a 1D network, and that heterogeneity of coupling can be an important factor in determining which patterns are stable.
许多抑制性网络中的神经放电表现出同步组合或成簇放电，即神经元的子集同步放电，并且这些子集可能会随着网络的不同输入或状态而变化。此前，对此类网络的大多数分析和计算建模都集中在一维网络或具有对称性（通常为圆对称性）的二维网络上。在这里，我们考虑一个一般环面上的二维离散网络模型，其中神经元在三个方向（水平、垂直和对角）与两个或更多最近邻耦合，并允许在所有方向上有不同的耦合强度。使用相位模型分析，我们建立了网络中不同成簇放电行为模式稳定性的条件。然后，我们应用我们的结果来研究网络连通性的变化和异质耦合强度的存在如何影响哪些模式是稳定的。我们用生物物理抑制性神经网络模型的数值模拟来证实和补充我们的结果。我们的工作表明，二维网络可能表现出成簇放电行为，这种行为不能作为一维网络的简单推广来预测，并且耦合的异质性可能是决定哪些模式稳定的一个重要因素。
