Skip to main content
  • Poster presentation
  • Open access
  • Published:

Statistical properties of noise-induced firing and quiescence in a Hodgkin-Huxley model

Introduction

The electrical behavior of neurons can show a significant amount of variability. Three sources of randomness contribute to this variability: fluctuating pre-synaptic inputs, variability in synaptic transmission and stochastic channel dynamics. Here we focus on how stochastic channel dynamics can influence the behavior of a single neuron. Previous work has shown that this variability may induce or suppress firing. This variability is also reflected in the distribution of inter-spike intervals (ISI). We aim to further investigate the effect of channel noise in neuronal dynamics by exhaustive numerical simulation for a wide range of both noise parameters and applied currents.

Methods

To simulate the classical Hodgkin-Huxley model [1] (HH) with stochastic channel dynamics, we use several previously described methods. Our first approach tracks the opening and closing of a fixed number of sodium (each consisting of 3 m gates and 1 h gate) and potassium (each consisting of 4 n gates) channels [2–4]. Since this is computationally expensive, we also consider directly adding multiplicative noise to the original equations that model channel dynamics following [5–8]. We also explore the behavior of neurons with different applied currents.

Results

Regardless of the number of channels, we find that the firing rate always increases as the applied current increases. For low applied currents, we find that stochasticity induces neuronal firing. The firing rate in the presence of low amplitude currents increases as the channel density decreases (more variability). Past a threshold applied current, the deterministic Hodgkin-Huxley equations show repetitive firing. This firing is also captured in our stochastic simulations. However, unlike lower amplitude currents, lower channel densities can cause slower rather than faster spiking in this case. A simplified model can explain how the firing rates depend on the channel density and noise level. We also find that noise from sodium channels has a smaller effect on the firing behavior of the neuron than noise from potassium channels. As the potassium channel density decreases, we find that the shape of the ISI distribution changes from a multi-modal to an exponential-tailed function with each peak roughly symmetrical. On the other hand as the sodium channel density changes, both the shape of the ISI distribution and the spiking frequency remain almost unchanged. As the applied current decreases the tail of the distribution gets heavier and spikes typically occur only after a long waiting time. Our studies show that noise can play significant and counterintuitive roles in determining the firing behavior of a neuron and lead to testable predictions of the real channel density based on the spiking frequency and shape of the inter-spike interval distribution.

References

  1. Hodgkin AL, Huxley AF: A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952, 117: 500-544.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  2. Schneidman E, Freedman B, Segev I: Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural Comput. 1998, 10: 1679-1703. 10.1162/089976698300017089.

    Article  CAS  PubMed  Google Scholar 

  3. White JA, Rubinstein JT, Kay AR: Channel noise in neurons. Trends Neurosci. 2000, 23: 131-137. 10.1016/S0166-2236(99)01521-0.

    Article  CAS  PubMed  Google Scholar 

  4. Rowat P: Interspike interval statistics in the stochastic Hodgkin-Huxley model: Coexistence of gamma frequency bursts and highly irregular firing. Neural Comput. 2007, 19: 1215-1250. 10.1162/neco.2007.19.5.1215.

    Article  PubMed  Google Scholar 

  5. Chow CC, White JA: Spontaneous action potentials due to channel fluctuations. Biophys J. 1996, 71: 3013-3021. 10.1016/S0006-3495(96)79494-8.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  6. Fox RF: Stochastic versions of the Hodgkin – Huxley Equations. Biophys J. 1997, 72: 2068-2074. 10.1016/S0006-3495(97)78850-7.

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  7. Bazso F, Zalanyi L, Csardi G: Channel noise in Hodgkin-Huxley model neurons. Physica A. 2003, 325: 165-175. 10.1016/S0378-4371(03)00195-X.

    Article  Google Scholar 

  8. Schmidt G, Goychuk I, Hanggi P: Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin-Huxley systems. Physical Biol. 2006, 3: 248-254. 10.1088/1478-3975/3/4/002.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Katarina Bodova.

Rights and permissions

Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Bodova, K., Forger, D.B. Statistical properties of noise-induced firing and quiescence in a Hodgkin-Huxley model. BMC Neurosci 10 (Suppl 1), P40 (2009). https://doi.org/10.1186/1471-2202-10-S1-P40

Download citation

  • Published:

  • DOI: https://doi.org/10.1186/1471-2202-10-S1-P40

Keywords