Mathematical relationships between spinal motoneuron properties

  1. Arnault HD Caillet  Is a corresponding author
  2. Andrew TM Phillips
  3. Dario Farina
  4. Luca Modenese
  1. Imperial College London, United Kingdom

Abstract

Our understanding of the behaviour of spinal alpha-motoneurons (MNs) in mammals partly relies on our knowledge of the relationships between MN membrane properties, such as MN size, resistance, rheobase, capacitance, time constant, axonal conduction velocity and afterhyperpolarization period. We reprocessed the data from 40 experimental studies in adult cat, rat and mouse MN preparations, to empirically derive a set of quantitative mathematical relationships between these MN electrophysiological and anatomical properties. This validated mathematical framework, which supports past findings that the MN membrane properties are all related to each other and clarifies the nature of their associations, is besides consistent with the Henneman's size principle and Rall's cable theory. The derived mathematical relationships provide a convenient tool for neuroscientists and experimenters to complete experimental datasets, to explore relationships between pairs of MN properties never concurrently observed in previous experiments, or to investigate inter-mammalian-species variations in MN membrane properties. Using this mathematical framework, modelers can build profiles of inter-consistent MN-specific properties to scale pools of MN models, with consequences on the accuracy and the interpretability of the simulations.

Data availability

Figure 3 - Source Data 1 contains the numerical data used to generate Figure 3.Figure 7 - Source Data 1 and Figure 7 - Source Data 2 contain the numerical data used to generate Figure 7.Table 5 - Source Data 1 contains the numerical data used to compute the mathematical relationships presented in Table 5.Please note that our study used exclusively data from previous investigations, for which public datasets were not available. The data were manually digitised by the authors from published figures and are made available as supplementary materials.

Article and author information

Author details

  1. Arnault HD Caillet

    Department of Civil and Environmental Engineering, Imperial College London, London, United Kingdom
    For correspondence
    arnault.caillet17@imperial.ac.uk
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-6146-1829
  2. Andrew TM Phillips

    Department of Civil and Environmental Engineering, Imperial College London, London, United Kingdom
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-6618-0145
  3. Dario Farina

    Department of Bioengineering, Imperial College London, London, United Kingdom
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-7883-2697
  4. Luca Modenese

    Department of Civil and Environmental Engineering, Imperial College London, London, United Kingdom
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-1402-5359

Funding

No funding

Reviewing Editor

  1. Hugo Merchant, National Autonomous University of Mexico, Mexico

Publication history

  1. Received: December 17, 2021
  2. Accepted: July 13, 2022
  3. Accepted Manuscript published: July 18, 2022 (version 1)

Copyright

© 2022, Caillet et al.

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. Arnault HD Caillet
  2. Andrew TM Phillips
  3. Dario Farina
  4. Luca Modenese
(2022)
Mathematical relationships between spinal motoneuron properties
eLife 11:e76489.
https://doi.org/10.7554/eLife.76489

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