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ABSTRACT Cable theory and the Goldman–Hodgkin–Huxley–Katz models for the propagation of ions and voltage within a neuron have provided a theoretical foundation for electrophysiology and been

responsible for many cornerstone advances in neuroscience. However, these theories break down when they are applied to small neuronal compartments, such as dendritic spines, synaptic

terminals or small neuronal processes, because they assume spatial and ionic homogeneity. Here we discuss a broader theory that uses the Poisson–Nernst–Planck (PNP) approximation and

electrodiffusion to more accurately model the constraints that neuronal nanostructures place on electrical current flow. This extension of traditional cable theory could advance our

understanding of the physiology of neuronal nanocompartments. Access through your institution Buy or subscribe This is a preview of subscription content, access via your institution ACCESS

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institutional subscriptions * Read our FAQs * Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS A FIRST-PASSAGE APPROACH TO DIFFUSION-INFLUENCED REVERSIBLE BINDING AND ITS

INSIGHTS INTO NANOSCALE SIGNALING AT THE PRESYNAPSE Article Open access 08 March 2021 NEURAL SIGNAL PROPAGATION ATLAS OF _CAENORHABDITIS ELEGANS_ Article Open access 01 November 2023

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Central  Google Scholar  Download references ACKNOWLEDGEMENTS The authors thank A Fairhill and members of both laboratories for their comments, and R.Y. thanks the Holcman group and the

Ecole Normale Superieure for hosting him. R.Y. is supported by grants MH101218 and MH100561. This material is based upon work supported by, or in part by, the US Army Research Laboratory and

the US Army Research Office under contract number W911NF-12-1-0594 (MURI). Research in D.H.'s laboratory is supported by the generosity of N. Rouach. The authors also thank J.

Cartailler from the D.H. laboratory. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Computational Biology and Applied Mathematics (IBENS), Ecole Normale Superieure, Paris, 75005, France David

Holcman * Department of Biological Sciences and Neuroscience, Neurotechnology Center, Columbia University, New York, 10027, New York, USA Rafael Yuste Authors * David Holcman View author

publications You can also search for this author inPubMed Google Scholar * Rafael Yuste View author publications You can also search for this author inPubMed Google Scholar CORRESPONDING

AUTHOR Correspondence to David Holcman. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing financial interests. POWERPOINT SLIDES POWERPOINT SLIDE FOR FIG. 1 POWERPOINT

SLIDE FOR FIG. 2 POWERPOINT SLIDE FOR FIG. 3 GLOSSARY * Back-propagating action potential The wave propagation of an action potential that is due to the opening and closing of ion channels,

moving in the direction of the soma. * Debye length The length after which an electric charge is screened from the effects of an electric field by water or other polar molecules. *

Dielectric medium A media in which charged particles can become polarized, the properties of which are characterized by a dielectric constant (_ε_). The dielectric constant characterizes the

response of the medium to an electric field. * Diffusional coupling Coupling of two compartments that is due to the exchange of diffusing particles, such as ions or molecules. * Diffusional

flux The number of particles per unit of time entering through a surface. * Electrodiffusion The combination of diffusion and electrostatic forces that are applied to a charged particle.

The particle motion results from the sum of these two forces. * Ficks's diffusion law A macroscopic law that assumes that the diffusion flux is proportional to the gradient of

concentration. * Monte Carlo simulations Numerical simulations in which each particle (molecules or ions) is assumed to move through Brownian motion. This simulation allows all particle

trajectories to be monitored at any moment of time. * Nanostructures Complex geometrical domains with a clear identified electrophysiological function and with a characteristic length in a

range from tens to hundreds of nanometres. Examples include dendritic spines, cilia, synapses, parts of sensory cells, protrusions and the endoplasmic reticulum. * Neuronal ensembles Sets of

neurons connected by synapses. A neuronal ensemble can sustain a network activity such as synchronization, oscillation or rhythm. * Steady-state regime A system state described by

stationary parameters that are by definition independent of time. * Transient regime Period of time during which the parameters describing the state of a system vary and converge toward the

steady-state regime. RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Holcman, D., Yuste, R. The new nanophysiology: regulation of ionic flow in neuronal

subcompartments. _Nat Rev Neurosci_ 16, 685–692 (2015). https://doi.org/10.1038/nrn4022 Download citation * Published: 14 October 2015 * Issue Date: November 2015 * DOI:

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