Theta (4–8 Hz) and gamma (30–80 Hz) rhythms in the brain are commonly associated with memory and learning (Kahana in J Neurosci 26:1669–1672, 2006; Quilichini et al. in J Neurosci 30:11128–11142, 2010). The precision of co-firing between neurons and incoming inputs is critical in these cognitive functions. We consider an inhibitory neuron model with M-current under forcing from gamma pulses and a sinusoidal current of theta frequency. The M-current has a long time constant (∼90 ms) and it has been shown to generate resonance at theta frequencies (Hutcheon and Yarom in Trends Neurosci 23:216–222, 2000; Hu et al. in J Physiol 545:783–805, 2002). We have found that this slow M-current contributes to the precise co-firing between the network and fast gamma pulses in the presence of a slow sinusoidal forcing. The M-current expands the phase-locking frequency range of the network, counteracts the slow theta forcing, and admits bistability in some parameter range. The effects of the M-current balancing the theta forcing are reduced if the sinusoidal current is faster than the theta frequency band. We characterize the dynamical mechanisms underlying the role of the M-current in enabling a network to be entrained to gamma frequency inputs using averaging methods, geometric singular perturbation theory, and bifurcation analysis.

中文翻译：

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M-Current扩展了神经元目标所夹带的伽马频率输入的范围。

大脑中的Theta（4–8 Hz）和γ（30–80 Hz）节律通常与记忆和学习有关（Kahana in J Neurosci 26：1669–1672，2006; Quilichini et al。in J Neurosci 30：11128– 11142，2010）。在这些认知功能中，神经元和传入输入之间的共同射击的精度至关重要。我们考虑在伽马脉冲和theta频率的正弦电流强迫下具有M电流的抑制性神经元模型。M电流具有很长的时间常数（〜90 ms），并且已证明会在theta频率处产生共振（Hutcheon和Yarom在Trends Neurosci 23：216–222，2000中； Hu等人在《 J Physiol 545：783》中–805，2002年）。我们发现，在存在缓慢正弦强迫的情况下，这种缓慢的M电流有助于网络与快速伽马脉冲之间的精确共点火。M电流扩大了网络的锁相频率范围，抵消了缓慢的θ强迫，并在某些参数范围内允许了双稳态。如果正弦电流比θ频带快，则M电流平衡θ强迫的影响会减小。我们描述了使用平均方法，几何奇异摄动理论和分叉分析使M电流在使网络能够被引入伽马频率输入中的动力学机制的特征。