Theoretical relation between axon initial segment geometry and excitability

  1. Sarah Goethals
  2. Romain Brette  Is a corresponding author
  1. Sorbonne Université, INSERM, CNRS, France


In most vertebrate neurons, action potentials are triggered at the distal end of the axon initial segment (AIS). Both position and length of the AIS vary across and within neuron types, with activity, development and pathology. What is the impact of AIS geometry on excitability? Direct empirical assessment has proven difficult because of the many potential confounding factors. Here we carried a principled theoretical analysis to answer this question. We provide a simple formula relating AIS geometry and sodium conductance density to the somatic voltage threshold. A distal shift of the AIS normally produces a (modest) increase in excitability, but we explain how this pattern can reverse if a hyperpolarizing current is present at the AIS, due to resistive coupling with the soma. This work provides a theoretical tool to assess the significance of structural AIS plasticity for electrical function.

Data availability

Code to generate all figures is available on GitHub: data analyzed in Fig. 2 has been uploaded on Zenodo: (DOI: 10.5281/zenodo.3539296), on behalf of Prof. Bean (Data from Hu & Bean, 2018).Digitized data used in Fig. 3 have been uploaded on GitHub (link above).

The following previously published data sets were used

Article and author information

Author details

  1. Sarah Goethals

    Institut de la Vision, Sorbonne Université, INSERM, CNRS, Paris, France
    Competing interests
    The authors declare that no competing interests exist.
  2. Romain Brette

    Institut de la Vision, Sorbonne Université, INSERM, CNRS, Paris, France
    For correspondence
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-0110-1623


Agence Nationale de la Recherche (ANR-14-CE13-0003)

  • Sarah Goethals
  • Romain Brette

Ecole des Neurosciences de Paris (N/A)

  • Sarah Goethals
  • Romain Brette

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Reviewing Editor

  1. Frances K Skinner, Krembil Research Institute, University Health Network, Canada

Publication history

  1. Received: November 7, 2019
  2. Accepted: March 30, 2020
  3. Accepted Manuscript published: March 30, 2020 (version 1)
  4. Version of Record published: April 20, 2020 (version 2)


© 2020, Goethals & Brette

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.


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  1. Sarah Goethals
  2. Romain Brette
Theoretical relation between axon initial segment geometry and excitability
eLife 9:e53432.
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