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Action Potential Initiation in the Hodgkin-Huxley Model

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  • Lucy J Colwell
  • Michael P Brenner

Abstract

A recent paper of B. Naundorf et al. described an intriguing negative correlation between variability of the onset potential at which an action potential occurs (the onset span) and the rapidity of action potential initiation (the onset rapidity). This correlation was demonstrated in numerical simulations of the Hodgkin-Huxley model. Due to this antagonism, it is argued that Hodgkin-Huxley-type models are unable to explain action potential initiation observed in cortical neurons in vivo or in vitro. Here we apply a method from theoretical physics to derive an analytical characterization of this problem. We analytically compute the probability distribution of onset potentials and analytically derive the inverse relationship between onset span and onset rapidity. We find that the relationship between onset span and onset rapidity depends on the level of synaptic background activity. Hence we are able to elucidate the regions of parameter space for which the Hodgkin-Huxley model is able to accurately describe the behavior of this system.Author Summary: In 1952, Hodgkin and Huxley described the underlying mechanism for the firing of action potentials through which information is propagated in the nervous system. Hodgkin and Huxley's model relies on the opening and closing of channels, selectively allowing ions to move across the membrane. In the original picture, the channels open independently of one another. A recent paper argues that this model is incapable of modeling a set of action potential data recorded in the cortical neurons of cats. Instead the authors suggest that to model their data it is necessary to conclude that ion channels open cooperatively, so that opening one channel increases the chance that another channel opens. We analyze the initiation of action potentials using a method from theoretical physics, the path integral. We demonstrate that deviations of the data from the predictions of the Hodgkin-Huxley model hinge on measurement of the noise strength.

Suggested Citation

  • Lucy J Colwell & Michael P Brenner, 2009. "Action Potential Initiation in the Hodgkin-Huxley Model," PLOS Computational Biology, Public Library of Science, vol. 5(1), pages 1-7, January.
    • Handle: RePEc:plo:pcbi00:1000265
    DOI: 10.1371/journal.pcbi.1000265
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    References listed on IDEAS

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    1. Björn Naundorf & Fred Wolf & Maxim Volgushev, 2006. "Unique features of action potential initiation in cortical neurons," Nature, Nature, vol. 440(7087), pages 1060-1063, April.
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    Cited by:

    1. Jonathan Platkiewicz & Romain Brette, 2010. "A Threshold Equation for Action Potential Initiation," PLOS Computational Biology, Public Library of Science, vol. 6(7), pages 1-16, July.

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