ArticlePhysical review. E, Statistical, nonlinear, and soft matter physics2011
Stochastic differential equation models for ion channel noise in Hodgkin-Huxley neurons.
Article in Physical review. E, Statistical, nonlinear, and soft matter physics, 2011. The graph could read no effect estimate from its abstract, so it casts no vote on the map. An erratum has been issued. Cited by 33 papers.
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33 citing papers in PubMed.
- Effect of Ion Channel Randomness on Sensitivity of Neurons to External Electromagnetic Fields: Computational Study.Entropy (Basel, Switzerland) · 2026Article
- Evaluating the predictive accuracy of ion-channel models using data from multiple experimental designs.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2025Article
- Parameter inference for stochastic reaction models of ion channel gating from whole-cell voltage-clamp data.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2025Article
- Power spectral analysis of voltage-gated channels in neurons.Frontiers in neuroinformatics · 2024Article
- Empirical Quantification of Predictive Uncertainty Due to Model Discrepancy by Training with an Ensemble of Experimental Designs: An Application to Ion Channel Kinetics.Bulletin of mathematical biology · 2023Article
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- Can neuron modeling constrained by ultrafast imaging data extract the native function of ion channels?Frontiers in computational neuroscience · 2023Article
- Mean-return-time phase of a stochastic oscillator provides an approximate renewal description for the associated point process.Biological cybernetics · 2022Review
- A simple model considering spiking probability during extracellular axon stimulation.PloS one · 2022Article
- Toward Robust Cognitive 3D Brain-Inspired Cross-Paradigm System.Frontiers in neuroscience · 2021Article
- Efficient exact inference for dynamical systems with noisy measurements using sequential approximate Bayesian computation.Bioinformatics (Oxford, England) · 2020Article
- Statistical Approaches for the Analysis of Dependency Among Neurons Under Noise.Entropy (Basel, Switzerland) · 2020Article
- Data-driven inference for stationary jump-diffusion processes with application to membrane voltage fluctuations in pyramidal neurons.Journal of mathematical neuroscience · 2019Article
- Synchronization of stochastic mean field networks of Hodgkin-Huxley neurons with noisy channels.Journal of mathematical biology · 2019Article
- Control of clustered action potential firing in a mathematical model of entorhinal cortex stellate cells.Journal of theoretical biology · 2018Article
- Spike timing precision of neuronal circuits.Journal of computational neuroscience · 2018Article
- Plasmodium knowlesi: a superb in vivo nonhuman primate model of antigenic variation in malaria.Parasitology · 2018Review
- Stimulation Strategies for Tinnitus Suppression in a Neuron Model.Computational and mathematical methods in medicine · 2018Article
- Methodology of Recurrent Laguerre-Volterra Network for Modeling Nonlinear Dynamic Systems.IEEE transactions on neural networks and learning systems · 2017Article
- Kölliker-Fuse nuclei regulate respiratory rhythm variability via a gain-control mechanism.American journal of physiology. Regulatory, integrative and comparative physiology · 2017Article
Corrections and comments
- Erratum issued
Authors and funding
4 authors.
Funding
Abstract
The random transitions of ion channels between conducting and nonconducting states generate a source of internal fluctuations in a neuron, known as channel noise. The standard method for modeling the states of ion channels nonlinearly couples continuous-time Markov chains to a differential equation for voltage. Beginning with the work of R. F. Fox and Y.-N. Lu [Phys. Rev. E 49, 3421 (1994)], there have been attempts to generate simpler models that use stochastic differential equation (SDEs) to approximate the stochastic spiking activity produced by Markov chain models. Recent numerical investigations, however, have raised doubts that SDE models can capture the stochastic dynamics of Markov chain models.We analyze three SDE models that have been proposed as approximations to the Markov chain model: one that describes the states of the ion channels and two that describe the states of the ion channel subunits. We show that the former channel-based approach can capture the distribution of channel noise and its effects on spiking in a Hodgkin-Huxley neuron model to a degree not previously demonstrated, but the latter two subunit-based approaches cannot. Our analysis provides intuitive and mathematical explanations for why this is the case. The temporal correlation in the channel noise is determined by the combinatorics of bundling subunits into channels, but the subunit-based approaches do not correctly account for this structure. Our study confirms and elucidates the findings of previous numerical investigations of subunit-based SDE models. Moreover, it presents evidence that Markov chain models of the nonlinear, stochastic dynamics of neural membranes can be accurately approximated by SDEs. This finding opens a door to future modeling work using SDE techniques to further illuminate the effects of ion channel fluctuations on electrically active cells.
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