Large cortical and hippocampal pyramidal neurons are elements of neuronal circuitry that have been implicated in cross-frequency coupling (CFC) during cognitive tasks. We investigate potential mechanisms for CFC within these neurons by examining the role that the hyperpolarization-activated mixed cation current (Ih) plays in modulating CFC characteristics in multicompartment neuronal models. We quantify CFC along the soma-apical dendrite axis and tuft of three models configured to have different spatial distributions of Ih conductance density: (1) exponential gradient along the soma-apical dendrite axis, (2) uniform distribution, and (3) no Ih conductance. We simulated two current injection scenarios: distal apical 4 Hz modulation and perisomatic 4 Hz modulation, each with perisomatic, mid-apical, and distal apical 40 Hz injections. We used two metrics to quantify CFC strength—modulation index and height ratio—and we analyzed CFC phase properties. For all models, CFC was strongest in distal apical regions when the 40 Hz injection occurred near the soma and the 4 Hz modulation occurred in distal apical dendrite. The strongest CFC values were observed in the model with uniformly distributed Ih conductance density, but when the exponential gradient in Ih conductance density was added, CFC strength decreased by almost 50%. When Ih was in the model, regions with much larger membrane potential fluctuations at 4 Hz than at 40 Hz had stronger CFC. Excluding the Ih conductance from the model resulted in CFC either reduced or comparable in strength relative to the model with the exponential gradient in Ih conductance. The Ih conductance also imposed order on the phase characteristics of CFC such that minimum (maximum) amplitude 40 Hz membrane potential oscillations occurred during Ih conductance deactivation (activation). On the other hand, when there was no Ih conductance, phase relationships between minimum and maximum 40 Hz oscillation often inverted and occurred much closer together. This analysis can help experimentalists discriminate between CFC that originates from different underlying physiological mechanisms and can help illuminate the reasons why there are differences between CFC strength observed in different regions of the brain and between different populations of neurons based on the configuration of the Ih conductance.

中文翻译：

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评估 Ih 电导对模型锥体神经元交叉频率耦合的影响

大型皮质和海马锥体神经元是神经元回路的元素，在认知任务期间与交叉频率耦合 (CFC) 有牵连。我们通过检查超极化激活的混合阳离子电流 (Ih) 在调节多室神经元模型中的 CFC 特性中的作用来研究这些神经元内 CFC 的潜在机制。我们沿着体顶枝晶轴和三个模型的簇量化 CFC，这些模型配置为具有不同的 Ih 电导密度空间分布：（1）沿体顶枝晶轴的指数梯度，（2）均匀分布，以及（3）无Ih 电导。我们模拟了两种当前注射场景：远端 4 Hz 调制和 perisomatic 4 Hz 调制，每个都有 perisomatic、mid-apical 和远端心尖 40 Hz 注射。我们使用两个指标来量化 CFC 强度——调制指数和高度比——并分析了 CFC 相特性。对于所有模型，当 40 Hz 注射发生在体细胞附近并且 4 Hz 调制发生在远端根尖树突时，CFC 在远端根尖区域最强。在具有均匀分布的 Ih 电导密度的模型中观察到最强的 CFC 值，但是当加入 Ih 电导密度的指数梯度时，CFC 强度下降了近 50%。当 Ih 在模型中时，4 Hz 下膜电位波动比 40 Hz 大得多的区域具有更强的 CFC。从模型中排除 Ih 电导导致 CFC 相对于具有 Ih 电导指数梯度的模型降低或在强度上相当。Ih 电导还对 CFC 的相位特性施加了顺序，以便在 Ih 电导失活（激活）期间发生最小（最大）振幅 40 Hz 膜电位振荡。另一方面，当没有 Ih 电导时，最小和最大 40 Hz 振荡之间的相位关系经常反转并且发生得更近。这种分析可以帮助实验者区分源自不同潜在生理机制的 CFC，并可以帮助阐明为什么在大脑的不同区域观察到的 CFC 强度之间以及基于 Ih 电导配置的不同神经元群体之间存在差异的原因。