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Journal article
Resolving molecular contributions of ion channel noise to interspike interval variability through stochastic shielding
Biological cybernetics, Vol.115(3), pp.267-302
06/01/2021
PMID: 34021802
Web of Science ID: WOS:000652923600001
Abstract
Molecular fluctuations can lead to macroscopically observable effects. The random gating of ion channels in themembrane 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 stateMarkov process, the "14x28D 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 Galan 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."
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Details
- Title
- Resolving molecular contributions of ion channel noise to interspike interval variability through stochastic shielding
- Publication Details
- Biological cybernetics, Vol.115(3), pp.267-302
- Resource Type
- Journal article
- Publisher
- Springer Nature
- Grant note
- Oberlin College Department of Mathematics DMS-2052109; DEB-1654989; DMS-1440386 / National Science Foundation; National Science Foundation (NSF) Mathematical Biosciences Institute
- Copyright
- © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature
- Identifiers
- WOS:000652923600001; 99380499097306600
- Academic Unit
- Mathematics and Statistics; Hal Marcus College of Science and Engineering
- Language
- English