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Model Reduction Captures Stochastic Gamma Oscillations on Low-Dimensional Manifolds.
Frontiers in Computational Neuroscience ( IF 3.2 ) Pub Date : 2021-08-17 , DOI: 10.3389/fncom.2021.678688
Yuhang Cai 1 , Tianyi Wu 2, 3 , Louis Tao 3, 4 , Zhuo-Cheng Xiao 5
Affiliation  

Gamma frequency oscillations (25-140 Hz), observed in the neural activities within many brain regions, have long been regarded as a physiological basis underlying many brain functions, such as memory and attention. Among numerous theoretical and computational modeling studies, gamma oscillations have been found in biologically realistic spiking network models of the primary visual cortex. However, due to its high dimensionality and strong non-linearity, it is generally difficult to perform detailed theoretical analysis of the emergent gamma dynamics. Here we propose a suite of Markovian model reduction methods with varying levels of complexity and apply it to spiking network models exhibiting heterogeneous dynamical regimes, ranging from nearly homogeneous firing to strong synchrony in the gamma band. The reduced models not only successfully reproduce gamma oscillations in the full model, but also exhibit the same dynamical features as we vary parameters. Most remarkably, the invariant measure of the coarse-grained Markov process reveals a two-dimensional surface in state space upon which the gamma dynamics mainly resides. Our results suggest that the statistical features of gamma oscillations strongly depend on the subthreshold neuronal distributions. Because of the generality of the Markovian assumptions, our dimensional reduction methods offer a powerful toolbox for theoretical examinations of other complex cortical spatio-temporal behaviors observed in both neurophysiological experiments and numerical simulations.

中文翻译:

模型简化捕获低维流形上的随机伽马振荡。

在许多大脑区域的神经活动中观察到的伽马频率振荡 (25-140 Hz) 长期以来被认为是许多大脑功能(如记忆和注意力)的生理基础。在众多理论和计算建模研究中,已经在初级视觉皮层的生物学逼真的尖峰网络模型中发现了伽马振荡。然而,由于其高维数和强非线性,一般难以对涌现伽马动力学进行详细的理论分析。在这里,我们提出了一套具有不同复杂程度的马尔可夫模型简化方法,并将其应用于表现出异构动态机制的尖峰网络模型,范围从近乎均匀的发射到伽马波段的强同步。简化模型不仅成功地在完整模型中重现了伽马振荡,而且在我们改变参数时也表现出相同的动态特征。最值得注意的是,粗粒度马尔可夫过程的不变测度揭示了状态空间中的二维表面,伽马动力学主要存在于该表面上。我们的结果表明伽马振荡的统计特征强烈依赖于亚阈值神经元分布。由于马尔可夫假设的普遍性,我们的降维方法为神经生理学实验和数值模拟中观察到的其他复杂皮层时空行为的理论检验提供了一个强大的工具箱。粗粒度马尔可夫过程的不变测度揭示了状态空间中的二维表面,伽马动力学主要存在于该表面上。我们的结果表明伽马振荡的统计特征强烈依赖于亚阈值神经元分布。由于马尔可夫假设的普遍性,我们的降维方法为神经生理学实验和数值模拟中观察到的其他复杂皮层时空行为的理论检验提供了一个强大的工具箱。粗粒度马尔可夫过程的不变测度揭示了状态空间中的二维表面,伽马动力学主要存在于该表面上。我们的结果表明伽马振荡的统计特征强烈依赖于亚阈值神经元分布。由于马尔可夫假设的普遍性,我们的降维方法为神经生理学实验和数值模拟中观察到的其他复杂皮层时空行为的理论检验提供了一个强大的工具箱。
更新日期:2021-08-17
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