Research Center for Advanced Science and Technology, The University of Tokyo, Tokyo, Japan.
PLoS One. 2024 Jul 5;19(7):e0306605. doi: 10.1371/journal.pone.0306605. eCollection 2024.
Delays in nerve transmission are an important topic in the field of neuroscience. Spike signals fired or received by the dendrites of a neuron travel from the axon to a presynaptic cell. The spike signal then triggers a chemical reaction at the synapse, wherein a presynaptic cell transfers neurotransmitters to the postsynaptic cell, regenerates electrical signals via a chemical reaction through ion channels, and transmits them to neighboring neurons. In the context of describing the complex physiological reaction process as a stochastic process, this study aimed to show that the distribution of the maximum time interval of spike signals follows extreme-order statistics. By considering the statistical variance in the time constant of the leaky Integrate-and-Fire model, a deterministic time evolution model for spike signals, we enabled randomness in the time interval of the spike signals. When the time constant follows an exponential distribution function, the time interval of the spike signal also follows an exponential distribution. In this case, our theory and simulations confirmed that the histogram of the maximum time interval follows the Gumbel distribution, one of the three forms of extreme-value statistics. We further confirmed that the histogram of the maximum time interval followed a Fréchet distribution when the time interval of the spike signal followed a Pareto distribution. These findings confirm that nerve transmission delay can be described using extreme value statistics and can therefore be used as a new indicator of transmission delay.
神经传递延迟是神经科学领域的一个重要课题。神经元树突接收或发出的尖峰信号从轴突传输到突触前细胞。然后，尖峰信号在突触处引发化学反应，其中突触前细胞将神经递质转移到突触后细胞，通过离子通道通过化学反应再生电信号，并将其传递到相邻的神经元。在将复杂的生理反应过程描述为随机过程的背景下，本研究旨在表明尖峰信号的最大时间间隔分布遵循极值统计。通过考虑漏电积分和触发模型（一种确定性的尖峰信号时间演化模型）的时间常数的统计方差，我们使尖峰信号的时间间隔具有随机性。当时间常数遵循指数分布函数时，尖峰信号的时间间隔也遵循指数分布。在这种情况下，我们的理论和模拟证实了最大时间间隔直方图遵循极值统计的三种形式之一的 Gumbel 分布。当尖峰信号的时间间隔遵循帕累托分布时，我们进一步证实了最大时间间隔直方图遵循 Fréchet 分布。这些发现证实了神经传递延迟可以使用极值统计来描述，因此可以用作传输延迟的新指标。
