Yujia Zhou, Theodore Vo, Horacio G Rotstein, Michelle M McCarthy, Nancy Kopell
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引用次数: 9
摘要
大脑中的Theta (4- 8hz)和gamma (30- 80hz)节律通常与记忆和学习有关(Kahana in J Neurosci 26:1669-1672, 2006;Quilichini et al. journal of Neurosci, 2010)。在这些认知功能中,神经元和输入信号之间共放电的准确性至关重要。我们考虑了一个抑制性神经元模型,该模型具有伽马脉冲强迫下的m电流和频率为θ的正弦电流。m电流具有很长的时间常数(~ 90 ms),并且已被证明在θ频率上产生共振(Hutcheon和Yarom in Trends Neurosci 23:16 -222, 2000;Hu et al. in J Physiol 545:783-805, 2002)。我们发现,在慢正弦强迫存在的情况下,这种慢m电流有助于网络和快速伽马脉冲之间的精确共烧。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双稳。当正弦波电流大于θ频带时,m电流平衡θ强迫的作用减弱。我们利用平均方法、几何奇异摄动理论和分岔分析,描述了m电流在使网络被夹带到伽马频率输入中的作用的动力机制。
M-Current Expands the Range of Gamma Frequency Inputs to Which a Neuronal Target Entrains.
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.
期刊介绍:
The Journal of Mathematical Neuroscience (JMN) publishes research articles on the mathematical modeling and analysis of all areas of neuroscience, i.e., the study of the nervous system and its dysfunctions. The focus is on using mathematics as the primary tool for elucidating the fundamental mechanisms responsible for experimentally observed behaviours in neuroscience at all relevant scales, from the molecular world to that of cognition. The aim is to publish work that uses advanced mathematical techniques to illuminate these questions.
It publishes full length original papers, rapid communications and review articles. Papers that combine theoretical results supported by convincing numerical experiments are especially encouraged.
Papers that introduce and help develop those new pieces of mathematical theory which are likely to be relevant to future studies of the nervous system in general and the human brain in particular are also welcome.