Potirakis Stelios M, Diakonos Fotios K, Contoyiannis Yiannis F
Department of Electrical and Electronics Engineering, University of West Attica, Ancient Olive Grove Campus, 12241 Egaleo, Greece.
Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, Metaxa and Vasileos Pavlou, Penteli, 15236 Athens, Greece.
Entropy (Basel). 2025 Mar 4;27(3):267. doi: 10.3390/e27030267.
Spike structures appear in several phenomena, whereas spike trains (STs) are of particular importance, since they can carry temporal encoding of information. Regarding the STs of the biological neuron type, several models have already been proposed. While existing models effectively simulate spike generation, they fail to capture the dynamics of high-frequency spontaneous membrane potential fluctuations observed during relaxation intervals between consecutive spikes, dismissing them as random noise. This is eventually an important drawback because it has been shown that, in real data, these spontaneous fluctuations are not random noise. In this work, we suggest an ST production mechanism based on the appropriate coupling of two specific intermittent maps, which are nonlinear first-order difference equations. One of these maps presents small variation in low amplitude values and, at some point, bursts to high values, whereas the other presents the inverse behavior, i.e., from small variation in high values, bursts to low values. The suggested mechanism proves to be able to generate the above-mentioned spontaneous membrane fluctuations possessing the associated dynamical properties observed in real data. Moreover, it is shown to produce spikes that present spike threshold, sharp peak and the hyperpolarization phenomenon, which are key morphological characteristics of biological spikes. Furthermore, the inter-spike interval distribution is shown to be a power law, in agreement with published results for ST data produced by real biological neurons. The use of the suggested mechanism for the production of other types of STs, as well as possible applications, are discussed.
尖峰结构出现在多种现象中，而尖峰序列（STs）尤为重要，因为它们可以携带信息的时间编码。关于生物神经元类型的尖峰序列，已经提出了几种模型。虽然现有模型有效地模拟了尖峰的产生，但它们未能捕捉到在连续尖峰之间的弛豫间隔期间观察到的高频自发膜电位波动的动态，将其视为随机噪声而忽略。这最终是一个重要的缺点，因为已经表明，在实际数据中，这些自发波动并非随机噪声。在这项工作中，我们提出了一种基于两个特定间歇映射适当耦合的尖峰序列产生机制，这两个映射是非线性一阶差分方程。其中一个映射在低幅值时变化较小，在某一点会突然跃升至高值，而另一个映射则呈现相反的行为，即从高值时的小变化突然跃降至低值。所提出的机制被证明能够产生上述具有在实际数据中观察到的相关动态特性的自发膜波动。此外，它还能产生具有尖峰阈值、尖锐峰值和超极化现象的尖峰，这些是生物尖峰的关键形态特征。此外，尖峰间隔分布显示为幂律分布，这与真实生物神经元产生的尖峰序列数据的已发表结果一致。还讨论了所提出的机制用于产生其他类型尖峰序列的用途以及可能的应用。
