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Reply to ‘Only negligible deviations from electroneutrality are expected in dendritic spines’

Nature Reviews Neuroscience volume 21, pages 54–55 (2020)Cite this article

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Our original Opinion piece described our intuitions about novel experimental and theoretical directions to study voltage at a nanoscale from a few to hundreds of nanometres in cellular nanodomains to microdomains (The new nanophysiology: regulation of ionic flow in neuronal subcompartments. Nat. Rev. Neurosci. 16, 685–692 (2015))1. We proposed that a new ‘nanophysiology’ is needed to interpret data that will be recorded in the future for channel–cytoplasm nanodomains, dendritic spines, axonal terminals, mitochondria, glia protrusions, neck–head junctions and other nanostructures with large fluctuations in membrane curvature. As we pointed out, traditional cable theory assumes that concentration changes associated with ionic currents are negligible and, therefore, ignores electrodiffusion (that is, the interaction between electrical fields and ionic diffusion). This assumption, although true for large neuronal compartments such as the original squid giant axon, could be incorrect when applied to femtolitre-sized structures such as dendritic spines. In his correspondence (Only negligible deviations from electroneutrality are expected in dendritic spines. Nat. Rev. Neurosci. https://doi.org/10.1038/s41583-019-0238-x (2019))2, Barbour ignores the wider scope of our argument and the recently published literature and narrowly reduces the focus of our Opinion piece1 to our discussion of electroneutrality, claiming that it is confusing and not relevant. However, the main goal of our article was not to deny electroneutrality but, instead, to explore the possibility that a complete set of electrodiffusion equations might be more suitable to model ion dynamics and voltage inside cellular nanodomains than traditional cable theory. Below, we respond to Barbour’s main criticisms. Note that we have already addressed most of these points in detail in a response that is available online3. Moreover, our recent modelling based on data from voltage-sensitive dyes and nanopipette recordings actually confirms our intuitions about significant concentration effects in dendritic spines4,5, demonstrating the need for electrodiffusional models.

Electrodiffusion is a theory that combines the Poisson (P) equation, which relates the local electrical field to the concentrations of ions, and the Nernst–Planck (NP) equation, which models the motion of ions with respect to the electrical field and concentration gradients. PNP equations thus form a coupled system of equations that can account for multiple ions, with different concentrations and motility, and can predict the local and transient changes in their concentrations. For simple geometries, the PNP model has been extensively used to model ionic fluxes inside channels, and the computation of their steady-state solution in reduced 1D geometries led to the well-known Goldman–Hodgkin–Katz formula of the reversal potential6. But for more complex neuronal morphologies, this coupled set of partial differential equations is unsolvable, and because of this, to untangle them, traditional cable theory assumes an infinite volume, with no changes in ionic concentration owing to electrical field changes.

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Authors and Affiliations

  1. Group of Data Modeling and Computational Biology, IBENS-PSL, École Normale Supérieure, Paris, France

    David Holcman

  2. Churchill College, DAMPT, University of Cambridge, Cambridge, UK

    David Holcman

  3. Neurotechnology Center, Department of Biological Sciences and Neuroscience, Columbia University, New York, New York, USA

    Rafael Yuste

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Holcman, D., Yuste, R. Reply to ‘Only negligible deviations from electroneutrality are expected in dendritic spines’. Nat Rev Neurosci 21, 54–55 (2020). https://doi.org/10.1038/s41583-019-0239-9

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