Single neurons can dynamically change the gain of their spiking responses to take into account shifts in stimulus variance. Moreover, gain adaptation can occur across multiple timescales. Here, we examine the ability of a simple statistical model of spike trains, the generalized linear model (GLM), to account for these adaptive effects. The GLM describes spiking as a Poisson process whose rate depends on a linear combination of the stimulus and recent spike history. The GLM successfully replicates gain scaling observed in Hodgkin-Huxley simulations of cortical neurons that occurs when the ratio of spike-generating potassium and sodium conductances approaches one. Gain scaling in the GLM depends on the length and shape of the spike history filter. Additionally, the GLM captures adaptation that occurs over multiple timescales as a fractional derivative of the stimulus envelope, which has been observed in neurons that include long timescale afterhyperpolarization conductances. Fractional differentiation in GLMs requires long spike history that span several seconds. Together, these results demonstrate that the GLM provides a tractable statistical approach for examining single-neuron adaptive computations in response to changes in stimulus variance.

中文翻译：

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使用广义线性模型捕获适应二阶统计的多个时间尺度：增益缩放和分数微分

单个神经元可以动态地改变其尖峰响应的增益，以考虑刺激方差的变化。此外，增益适应可以跨多个时间尺度发生。在这里，我们检查了一个简单的尖峰列车统计模型，即广义线性模型 (GLM)，以解释这些自适应效应的能力。GLM 将尖峰描述为泊松过程，其速率取决于刺激和最近尖峰历史的线性组合。GLM 成功地复制了在皮层神经元的 Hodgkin-Huxley 模拟中观察到的增益缩放，当产生尖峰的钾和钠电导的比率接近 1 时，就会发生这种情况。GLM 中的增益缩放取决于尖峰历史滤波器的长度和形状。此外，GLM 捕获在多个时间尺度上发生的适应，作为刺激包络的分数导数，这已在包含长时间超极化后电导的神经元中观察到。GLM 中的分数微分需要跨越几秒钟的长尖峰历史。总之，这些结果表明 GLM 提供了一种易于处理的统计方法，用于检查响应刺激方差变化的单神经元自适应计算。