Grid cells, in entorhinal cortex (EC) and related structures, signal animal location relative to hexagonal tilings of 2D space. A number of modeling papers have addressed the question of how grid firing behaviors emerge using (for example) ideas borrowed from dynamical systems (attractors) or from coupled oscillator theory. Here we use a different approach: instead of asking how grid behavior emerges, we take as a given the experimentally observed intracellular potentials of superficial medial EC neurons during grid firing. Employing a detailed neural circuit model modified from a lateral EC model, we then ask how the circuit responds when group of medial EC principal neurons exhibit such potentials, simultaneously with a simulated theta frequency input from the septal nuclei. The model predicts the emergence of robust theta-modulated gamma/beta oscillations, suggestive of oscillations observed in an in vitro medial EC experimental model (Cunningham, M.O., Pervouchine, D.D., Racca, C., Kopell, N.J., Davies, C.H., Jones, R.S.G., Traub, R.D., and Whittington, M.A. (2006). Neuronal metabolism governs cortical network response state. Proc. Natl. Acad. Sci. U S A 103: 5597–5601). Such oscillations result because feedback interneurons tightly synchronize with each other – despite the varying phases of the grid cells – and generate a robust inhibition-based rhythm. The lack of spatial specificity of the model interneurons is consistent with the lack of spatial periodicity in parvalbumin interneurons observed by Buetfering, C., Allen, K., and Monyer, H. (2014). Parvalbumin interneurons provide grid cell-driven recurrent inhibition in the medial entorhinal cortex. Nat. Neurosci. 17: 710–718. If in vivo EC gamma rhythms arise during exploration as our model predicts, there could be implications for interpreting disrupted spatial behavior and gamma oscillations in animal models of Alzheimer’s disease and schizophrenia. Noting that experimental intracellular grid cell potentials closely resemble cortical Up states and Down states, during which fast oscillations also occur during Up states, we propose that the co-occurrence of slow principal cell depolarizations and fast network oscillations is a general property of the telencephalon, in both waking and sleep states.

中文翻译：

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由网格单元输出近似引起的振荡动力学仿真

内嗅皮层 (EC) 和相关结构中的网格细胞指示动物相对于二维空间六边形平铺的位置。许多建模论文已经解决了网格激发行为如何出现的问题，例如使用从动力系统（吸引子）或耦合振荡器理论借用的思想。在这里，我们使用不同的方法：我们不询问网格行为如何出现，而是将实验观察到的浅层内侧 EC 神经元在网格放电期间的细胞内电位作为给定。采用从外侧 EC 模型修改而来的详细神经回路模型，然后我们询问当内侧 EC 主要神经元组表现出这种电位时，电路如何响应，同时输入来自隔膜核的模拟 θ 频率。体外内侧 EC 实验模型（Cunningham, MO、Pervouchine, DD、Racca, C.、Kopell, NJ、Davies, CH、Jones, RSG、Traub, RD 和 Whittington, MA (2006)。神经元代谢控制皮质网络反应状态。美国国家科学院院刊 103：5597–5601）。产生这种振荡的原因是反馈中间神经元彼此紧密同步（尽管网格细胞的相位不同），并产生强大的基于抑制的节律。模型中间神经元缺乏空间特异性与 Buetfering, C.、Allen, K. 和 Monyer, H. (2014) 观察到的小白蛋白中间神经元缺乏空间周期性是一致的。小清蛋白中间神经元在内侧内嗅皮层提供网格细胞驱动的反复抑制。纳特。神经科学。17：710-718。如果体内正如我们的模型预测的那样，EC 伽马节律在探索过程中出现，这可能对解释阿尔茨海默病和精神分裂症动物模型中的空间行为破坏和伽马振荡产生影响。注意到实验性细胞内网格细胞电位与皮质向上状态和向下状态非常相似，在向上状态期间也发生快速振荡，我们提出缓慢的主细胞去极化和快速网络振荡的同时发生是端脑的一般属性，在清醒和睡眠状态下。