论文标题
突触耦合的二次集成和开火神经元网络中的跨尺度兴奋性
Cross-scale excitability in networks of synaptically-coupled quadratic integrate-and-fire neurons
论文作者
论文摘要
从神经元和心脏细胞的作用电位到卵母细胞中钙信号的扩增，兴奋性是许多生物信号过程的标志。近年来，单个细胞的兴奋性与通过大型解决方案进行了多个时间表的动力学有关，这些解决方案确定了全有或不响应的有效阈值。但是，大量人群中兴奋性的出现仍然是一个开放的问题。在这里，我们表明，大型网络中的兴奋性机理以及耦合二次集成和开火（QIF）细胞的平均场描述反映了单个组件的。我们最初利用Ott-Antonsen Ansatz来得出耦合网络的低维动力学，并使用它通过慢速周期性强迫来描述Canards的结构。我们证明，可以以与单个单元格的方式相同的方式找到人口射击的发作和抵消阈值。我们将理论分析和数值计算结合在一起，以开发一个新颖的综合框架，以实现大量人群的兴奋性，不仅适用于可降低Ott-Antonsen的模型，还适用于没有封闭形式的均值范围限制的网络，特别是稀疏网络。
From the action potentials of neurons and cardiac cells to the amplification of calcium signals in oocytes, excitability is a hallmark of many biological signalling processes. In recent years, excitability in single cells has been related to multiple-timescale dynamics through canards, special solutions which determine the effective thresholds of the all-or-none responses. However, the emergence of excitability in large populations remains an open problem. Here, we show that the mechanism of excitability in large networks and mean-field descriptions of coupled quadratic integrate-and-fire (QIF) cells mirrors that of the individual components. We initially exploit the Ott-Antonsen ansatz to derive low-dimensional dynamics for the coupled network and use it to describe the structure of canards via slow periodic forcing. We demonstrate that the thresholds for onset and offset of population firing can be found in the same way as those of the single cell. We combine theoretical analysis and numerical computations to develop a novel and comprehensive framework for excitability in large populations, applicable not only to models amenable to Ott-Antonsen reduction, but also to networks without a closed-form mean-field limit, in particular sparse networks.
