Molecular fluctuations can lead to macroscopically observable effects. The random gating of ion channels in the membrane of a nerve cell provides an important example. The contributions of independent noise sources to the variability of action potential timing have not previously been studied at the level of molecular transitions within a conductance-based model ion-state graph. Here we study a stochastic Langevin model for the Hodgkin–Huxley (HH) system based on a detailed representation of the underlying channel state Markov process, the “\(14\times 28\)D model” introduced in (Pu and Thomas in Neural Computation 32(10):1775–1835, 2020). We show how to resolve the individual contributions that each transition in the ion channel graph makes to the variance of the interspike interval (ISI). We extend the mean return time (MRT) phase reduction developed in (Cao et al. in SIAM J Appl Math 80(1):422–447, 2020) to the second moment of the return time from an MRT isochron to itself. Because fixed-voltage spike detection triggers do not correspond to MRT isochrons, the inter-phase interval (IPI) variance only approximates the ISI variance. We find the IPI variance and ISI variance agree to within a few percent when both can be computed. Moreover, we prove rigorously, and show numerically, that our expression for the IPI variance is accurate in the small noise (large system size) regime; our theory is exact in the limit of small noise. By selectively including the noise associated with only those few transitions responsible for most of the ISI variance, our analysis extends the stochastic shielding (SS) paradigm (Schmandt and Galán in Phys Rev Lett 109(11):118101, 2012) from the stationary voltage clamp case to the current clamp case. We show numerically that the SS approximation has a high degree of accuracy even for larger, physiologically relevant noise levels. Finally, we demonstrate that the ISI variance is not an unambiguously defined quantity, but depends on the choice of voltage level set as the spike detection threshold. We find a small but significant increase in ISI variance, the higher the spike detection voltage, both for simulated stochastic HH data and for voltage traces recorded in in vitro experiments. In contrast, the IPI variance is invariant with respect to the choice of isochron used as a trigger for counting “spikes.”

分子波动会导致宏观上可观察到的效应。神经细胞膜中离子通道的随机门控提供了一个重要的例子。独立噪声源对动作电位时间可变性的贡献以前没有在基于电导的模型离子状态图中的分子跃迁水平上进行过研究。在这里，我们研究了霍奇金-赫胥黎 (HH) 系统的随机朗之万模型，该模型基于底层通道状态马尔可夫过程的详细表示，“ \(14\times 28\)D 模型”（Pu 和 Thomas in Neural Computation 32(10):1775–1835, 2020）中介绍。我们展示了如何解决离子通道图中每个跃迁对尖峰间隔 (ISI) 方差的影响。我们将 (Cao et al. in SIAM J Appl Math 80(1):422–447, 2020) 中开发的平均返回时间 (MRT) 相位减少扩展到从 MRT 等时线到自身的返回时间的第二时刻。由于固定电压尖峰检测触发器不对应于 MRT 等时线，相间间隔(IPI) 方差仅近似于 ISI 方差。当两者都可以计算时，我们发现 IPI 方差和 ISI 方差在百分之几内一致。此外，我们严格证明并以数字方式表明，我们对 IPI 方差的表达在小噪声（大系统规模）情况下是准确的；我们的理论在小噪声的限度内是准确的。通过选择性地包括仅与负责大部分 ISI 方差的少数跃迁相关的噪声，我们的分析扩展了随机屏蔽 (SS) 范式（Schmandt 和 Galán in Phys Rev Lett 109(11):118101, 2012）从固定电压夹盒到当前夹盒。我们从数值上表明，即使对于更大的生理相关噪声水平，SS 近似也具有高度的准确性。最后，我们证明了 ISI 方差不是一个明确定义的数量，而是取决于设置为尖峰检测阈值的电压电平的选择。我们发现，对于模拟随机 HH 数据和体外实验中记录的电压轨迹，ISI 方差都有一个小但显着的增加，尖峰检测电压越高。相比之下，IPI 方差对于用作计数“峰值”的触发器的等时线的选择是不变的。