PDF(Pubmed)
Abstract：
Cyclic AMP controls neuronal ion channel activity. For example hyperpolarization-activated cyclic nucleotide-gated (HCN) and M-type K+ channels are activated by cAMP. These effects have been suggested to be involved in astrocyte control of neuronal activity, for example, by controlling the action potential firing frequency. In cortical neurons, cAMP can induce mixed-mode oscillations (MMOs) consisting of small-amplitude, subthreshold oscillations separating complete action potentials, which lowers the firing frequency greatly. We extend a model of neuronal activity by including HCN and M channels, and show that it can reproduce a series of experimental results under various conditions involving and inferring with cAMP-induced activation of HCN and M channels. In particular, we find that the model can exhibit MMOs as found experimentally, and argue that both HCN and M channels are crucial for reproducing these patterns. To understand how M and HCN channels contribute to produce MMOs, we exploit the fact that the model is a three-time scale dynamical system with one fast, two slow, and two super-slow variables. We show that the MMO mechanism does not rely on the super-slow dynamics of HCN and M channel gating variables, since the model is able to produce MMOs even when HCN and M channel activity is kept constant. In other words, the cAMP-induced increase in the average activity of HCN and M channels allows MMOs to be produced by the slow-fast subsystem alone. We show that the slow-fast subsystem MMOs are due to a folded node singularity, a geometrical structure well known to be involved in the generation of MMOs in slow-fast systems. Besides raising new mathematical questions for multiple-timescale systems, our work is a starting point for future research on how cAMP signalling, for example resulting from interactions between neurons and glial cells, affects neuronal activity via HCN and M channels.
摘要：
环AMP控制神经元离子通道活性。例如,超极化激活的环核苷酸门控(HCN)和M型K+通道被cAMP激活。这些作用已被认为与神经元活动的星形胶质细胞控制有关，例如,通过控制动作电位激发频率。在皮质神经元中，cAMP可以诱发由小振幅组成的混合模式振荡(MMO)，分离完整动作电位的亚阈值振荡，这大大降低了发射频率。我们通过包括HCN和M通道来扩展神经元活动的模型，并表明它可以在涉及和推断cAMP诱导的HCN和M通道激活的各种条件下再现一系列实验结果。特别是,我们发现该模型可以表现出实验发现的MMO，并认为HCN和M通道对于再现这些模式至关重要。要了解M和HCN通道如何有助于产生MMO，我们利用了这样一个事实，即该模型是一个具有一个快速的三时间尺度动力系统，两个慢，和两个超慢变量。我们表明，MMO机制不依赖于HCN和M通道门控变量的超慢动力学，因为即使当HCN和M通道活动保持恒定时，该模型也能够产生MMO。换句话说,cAMP诱导的HCN和M通道平均活性的增加允许仅通过慢-快子系统产生MMOs。我们证明了慢速-快速子系统MMO是由于折叠节点奇点，一种众所周知的几何结构，涉及慢-快系统中MMOs的生成。除了为多时间尺度系统提出新的数学问题之外，我们的工作是未来研究cAMP信号，例如，由于神经元和神经胶质细胞之间的相互作用，通过HCN和M通道影响神经元活动。
