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.
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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.
The authors declare no competing financial interests.
- 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.
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.
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.
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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
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