Resolving molecular contributions of ion channel noise to interspike interval variability through stochastic shielding
Resolving molecular contributions of ion channel noise to interspike interval variability through stochastic shielding
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DOI：
10.1007/s00422-021-00877-7
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发表时间：
2021-05-22
影响因子：
1.9
通讯作者：
Thomas，Peter J.
中科院分区：
文献类型：
--
作者：
Pu，Shusen;Thomas，Peter J.
分子波动可以导致宏观可观察到的效应。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。之前尚未在基于电导的模型离子态图中的分子转变水平上研究过独立噪声源对动作电位时序变化的贡献。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，即 (Pu and Thomas in Neural Computation 32(10):1775–1835, 2020) 中介绍的“D 模型”。我们展示了如何解决离子通道图中每个转变对峰间间隔 (ISI) 方差的单独贡献。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) 相位缩减扩展到从 MRT 等时线到自身的返回时间的第二个时刻。由于固定电压尖峰检测触发器不对应于 MRT 等时线，因此相间间隔 (IPI) 方差仅近似于 ISI 方差。我们发现，当 IPI 方差和 ISI 方差都可以计算时，两者的一致性在几个百分点之内。此外，我们严格证明并以数值方式表明，我们的 IPI 方差表达式在小噪声（大系统规模）情况下是准确的；我们的理论在小噪声的限制下是准确的。通过选择性地包括与导致大部分 ISI 方差的少数转换相关的噪声，我们的分析将随机屏蔽 (SS) 范式（Schmandt 和 Galán in Phys Rev Lett 109(11):118101, 2012）从固定电压钳情况扩展到电流钳情况。我们通过数值表明，即使对于较大的、生理相关的噪声水平，SS 近似也具有很高的准确性。最后，我们证明 ISI 方差不是一个明确定义的量，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迹线，ISI 方差略有但显着增加，尖峰检测电压越高。相反，IPI 方差对于用作计数“尖峰”触发器的等时线的选择是不变的。
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 “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, theinter-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.”