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

BMC Neuroscience200910 (Suppl 1) :P40

  • Published:


  • Firing Rate
  • Applied Current
  • Firing Behavior
  • Channel Density
  • Fast Spike


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.


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 [24]. Since this is computationally expensive, we also consider directly adding multiplicative noise to the original equations that model channel dynamics following [58]. We also explore the behavior of neurons with different applied currents.


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.

Authors’ Affiliations

Department of Mathematics, University of Michigan, Ann Arbor, 48109, MI, USA


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


© Bodova and Forger; licensee BioMed Central Ltd. 2009

This article is published under license to BioMed Central Ltd.