论文标题

神经元兴奋性的概括允许识别与实验可测量值联系的兴奋性变化参数

Generalisation of neuronal excitability allows for the identification of an excitability change parameter that links to an experimentally measurable value

论文作者

Broek, Jantine A. C., Drion, Guillaume

论文摘要

神经元兴奋性是描述由于刺激输入引起的动作电位产生的现象。通常,神经元兴奋性分为两类:I型和II型,既有影响信息处理的不同属性,例如阈值和增益缩放。可以使用广义现象学模型(例如Fitzhugh-Nagumo模型和镜像FHN)对这些特性进行数学研究。 FHN模型显示,每种兴奋性类型对应于相位平面中的一种特定类型的分叉类型:I类型I是不变循环分叉上的鞍节点的基础,而II型A HOPF分叉。建模I型兴奋性的难度在于,它不仅由其基础分叉表示,而且还应能够在保持较小的去极化电流的同时产生频率。使用MFHN模型,我们证明这种情况是可能的,而无需修改相肖像,这是由于结合了缓慢的再生变量。我们表明,在MFHN模型的奇异极限中,可以选择时间尺度的分离,以使经典相位肖像具有构型,该肖像允许SNIC分叉,零频率发作和去极性电流,例如在I型兴奋性中观察到的。使用缓慢电导的定义G_S,我们表明这些用于兴奋性变化的数学发现可以转换为基于电导的模型减少,并且还与实验可测量的数量有关。这不仅允许衡量兴奋性变化,而且还将数学参数指示了I型I型兴奋性与在实验过程中可以调整的参数。

Neuronal excitability is the phenomena that describes action potential generation due to a stimulus input. Commonly, neuronal excitability is divided into two classes: Type I and Type II, both having different properties that affect information processing, such as thresholding and gain scaling. These properties can be mathematically studied using generalised phenomenological models, such as the Fitzhugh-Nagumo model and the mirrored FHN. The FHN model shows that each excitability type corresponds to one specific type of bifurcation in the phase plane: Type I underlies a saddle-node on invariant cycle bifurcation, and Type II a Hopf bifurcation. The difficulty of modelling Type I excitability is that it is not only represented by its underlying bifurcation, but also should be able to generate frequency while maintaining a small depolarising current. Using the mFHN model, we show that this situation is possible without modifying the phase portrait, due to the incorporation of a slow regenerative variable. We show that in the singular limit of the mFHN model, the time-scale separation can be chosen such that there is a configuration of a classical phase portrait that allows for SNIC bifurcation, zero-frequency onset and a depolarising current, such as observed in Type I excitability. Using the definition of slow conductance, g_s, we show that these mathematical findings for excitability change are translatable to reduced conductance based models and also relates to an experimentally measurable quantity. This not only allows for a measure of excitability change, but also relates the mathematical parameters that indicate a physiological Type I excitability to parameters that can be tuned during experiments.

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