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.
This is a preview of subscription content, access via your institution
Subscribe to Journal
Get full journal access for 1 year
only $6.58 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Get time limited or full article access on ReadCube.
All prices are NET prices.
Goldman, D. E. Potential, impedance, and rectification in membranes. J. Gen. Physiol. 27, 37–60 (1943).
Hodgkin, A. L. & Huxley, A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500–544 (1952).
Bart, D. & Bart, J. Sir William Thomson, on the 150th Anniversary of the Atlantic Cable. Antique Wireless Association Rev. 21, 121–164 (2008).
Hille, B. Ionic Channels in Excitable Membranes 2nd edn (Sinauer, 1992).
Tuckwell, H. C. Introduction to Theoretical Neurobiology (Cambridge Univ. Press, 1988).
Koch, C. Biophysics of Computation: Information Processing in Single Neurons (Oxford Univ. Press, 2004).
Stuart, G., Spruston, N. & Hausser, M. Dendrites (Oxford Univ. Press, 1999).
Butera, R. J., Rinzel, J. & Smith, J. C. Models of respiratory rhythm generation in the pre-Bötzinger complex. I. Bursting pacemaker neurons. J. Neurophysiol. 82, 382–397 (1999).
Kennedy, M. B., Beale, H. C., Carlisle, H. J. & Washburn, L. R. Integration of biochemical signalling in spines. Nat. Rev. Neurosci. 6, 423–434 (2005).
Malinow, R. & Malenka, R. C. AMPA receptor trafficking and synaptic plasticity. Annu. Rev. Neurosci. 25, 103–126 (2002).
Sabatini, B. L. & Svoboda, K. Analysis of calcium channels in single spines using optical fluctuation analysis. Nature 408, 589–593 (2000).
Fischer, M., Kaech, S., Knutti, D. & Matus, A. Rapid actin-based plasticity in dendritic spine. Neuron 20, 847–854 (1998).
Dunaevsky, A., Tashiro, A., Majewska, A., Mason, C. A. & Yuste, R. Developmental regulation of spine motility in mammalian CNS. Proc. Natl Acad. Sci. USA 96, 13438–13443 (1999).
Lendvai, B., Stern, E., Chen, B. & Svoboda, K. Experience-dependent plasticity of dendritic spines in the developing rat barrel cortex in vivo. Nature 404, 876–881 (2000).
Hoze, N. & Holcman, D. Residence times of receptors in dendritic spines analyzed by stochastic simulations in empirical domains. Biophys. J. 107, 3008–3017 (2014).
Hoze, N. et al. Heterogeneity of AMPA receptor trafficking and molecular interactions revealed by superresolution analysis of live cell imaging. Proc. Natl Acad. Sci. USA 109, 17052–17057 (2012).
Araya, R., Jiang, J., Eisenthal, K. B. & Yuste, R. The spine neck filters membrane potentials. Proc. Natl Acad. Sci. USA 103, 17961–17966 (2006).
Tonnesen, J., Katona, G., Rozsa, B. & Nagerl, U. V. Spine neck plasticity regulates compartmentalization of synapses. Nat. Neurosci. 17, 678–685 (2014).
Araya, R., Vogels, T. P. & Yuste, R. Activity-dependent dendritic spine neck changes are correlated with synaptic strength. Proc. Natl Acad. Sci. USA 111, E2895–E2904 (2014).
Rust, M. J., Bates, M. & Zhuang, X. Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM). Nat. Methods 3, 793–795 (2006).
Biess, A., Korkotian, E. & Holcman, D. Diffusion in a dendritic spine: the role of geometry. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76, 021922 (2007).
Svoboda, K., Tank, D. W. & Denk, W. Direct measurement of coupling between dendritic spines and shafts. Science 272, 716–719 (1996).
Holcman, D. & Schuss, Z. Diffusion laws in dendritic spines. J. Math. Neurosci. 1, 10 (2011).
Franks, K. M., Bartol, T. M. Jr & Sejnowski, T. J. A Monte Carlo model reveals independent signaling at central glutamatergic synapses. Biophys. J. 83, 2333–2348 (2002).
Franks, K. M. & Sejnowski, T. J. Complexity of calcium signaling in synaptic spines. BioEssays 24, 1130–1144 (2002).
Holcman, D., Schuss, Z. & Korkotian, E. Calcium dynamics in dendritic spines and spine motility. Biophys. J. 87, 81–91 (2004).
Jackson, J. D. Classical Electrodynamics 3rd edn (Wiley, 1998).
Savtchenko, L. P., Kulahin, N., Korogod, S. M. & Rusakov, D. A. Electric fields of synaptic currents could influence diffusion of charged neurotransmitter molecules. Synapse 51, 270–278 (2004).
Sylantyev, S. et al. Electric fields due to synaptic currents sharpen excitatory transmission. Science 319, 1845–1849 (2008).
Sylantyev, S., Savtchenko, L. P., Ermolyuk, Y., Michaluk, P. & Rusakov, D. A. Spike-driven glutamate electrodiffusion triggers synaptic potentiation via a homer-dependent mGluR–NMDAR link. Neuron 77, 528–541 (2013).
Corry, B., Kuyucak, S. & Chung, S. H. Dielectric self-energy in Poisson–Boltzmann and Poisson–Nernst–Planck models of ion channels. Biophys. J. 84, 3594–3606 (2003).
Mamonov, A. B., Coalson, R. D., Nitzan, A. & Kurnikova, M. G. The role of the dielectric barrier in narrow biological channels: a novel composite approach to modeling single-channel currents. Biophys. J. 84, 3646–3661 (2003).
Eisenberg, R. S. From structure to function in open ionic channels. J. Membr. Biol. 171, 1–24 (1999).
Gillespie, D. et al. A physical mechanism for large-ion selectivity of ion channels. Phys. Chem. Chem. Phys. 4, 4763–4769 (2002).
Blunck, R., Chanda, B. & Bezanilla, F. Nano to micro — fluorescence measurements of electric fields in molecules and genetically specified neurons. J. Membr. Biol. 208, 91–102 (2005).
Qian, N. & Sejnowski, T. J. An electro-diffusion model for computing membrane potentials and ionic concentrations in branching dendrites, spines and axons. Biol. Cybern. 62, 1–15 (1989).
Holcman, D. & Schuss, Z. Control of flux by narrow passages and hidden targets in cellular biology. Reports on progress in physics. Phys. Soc. 76, 074601 (2013).
Bloodgood, B. L. & Sabatini, B. L. Neuronal activity regulates diffusion across the neck of dendritic spines. Science 310, 866–869 (2005).
McLaughlin, S. & Poo, M. M. The role of electro-osmosis in the electric-field-induced movement of charged macromolecules on the surfaces of cells. Biophys. J. 34, 85–93 (1981).
Korkotian, E. & Segal, M. Synaptopodin regulates release of calcium from stores in dendritic spines of cultured hippocampal neurons. J. Physiol. 589, 5987–5995 (2011).
Alivisatos, A. P. Less is more in medicine. Sci. Am. 285, 66–73 (2001).
Rall, W. Branching dendritic trees and motoneuron membrane resistivity. Exp. Neurol. 1, 491–527 (1959).
Harnett, M. T., Makara, J. K., Spruston, N., Kath, W. L. & Magee, J. C. Synaptic amplification by dendritic spines enhances input cooperativity. Nature 491, 599–602 (2012).
Schikorski, T. & Stevens, C. F. Morphological correlates of functionally defined synaptic vesicle populations. Nat. Neurosci. 4, 391–395 (2001).
Karube, F., Kubota, Y. & Kawaguchi, Y. Axon branching and synaptic bouton phenotypes in GABAergic nonpyramidal cell subtypes. J. Neurosci. 24, 2853–2865 (2004).
Pannasch, U. et al. Connexin 30 sets synaptic strength by controlling astroglial synapse invasion. Nat. Neurosci. 17, 549–558 (2014).
Peters, A. & Paley, S. L. & Webster, H. D. Fine Structure of the Nervous System Saunders, 1976).
North, G. & Greenspan, R. J. Invertebrate Neurobiology (Cold Spring Harbor Press, 2008).
Nagerl, U. V., Willig, K. I., Hein, B., Hell, S. W. & Bonhoeffer, T. Live-cell imaging of dendritic spines by STED microscopy. Proc. Natl Acad. Sci. USA 105, 18982–18987 (2008).
Ding, J. B., Takasaki, K. T. & Sabatini, B. L. Supraresolution imaging in brain slices using stimulated-emission depletion two-photon laser scanning microscopy. Neuron 63, 429–437 (2009).
Arellano, J. I., Benavides-Piccione, R., Defelipe, J. & Yuste, R. Ultrastructure of dendritic spines: correlation between synaptic and spine morphologies. Front. Neurosci. 1, 131–143 (2007).
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.
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
This article is cited by
An Algorithm Based on a Cable-Nernst Planck Model Predicting Synaptic Activity throughout the Dendritic Arbor with Micron Specificity
Nature Methods (2021)
Modeling the voltage distribution in a non-locally but globally electroneutral confined electrolyte medium: applications for nanophysiology
Journal of Mathematical Biology (2021)
Bulletin of Mathematical Biology (2021)
Nature Reviews Neuroscience (2020)