Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Opinion
  • Published:

The new nanophysiology: regulation of ionic flow in neuronal subcompartments

A Publisher Correction to this article was published on 23 May 2019

An Author Correction to this article was published on 23 May 2019

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.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Geometric and morphological complexity of dendritic spines.
Figure 2: Imaging local membrane potential in a dendritic spine.
Figure 3: Comparison of simple diffusion and electrodiffusion theories.

Similar content being viewed by others

References

  1. Goldman, D. E. Potential, impedance, and rectification in membranes. J. Gen. Physiol. 27, 37–60 (1943).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  2. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  3. Bart, D. & Bart, J. Sir William Thomson, on the 150th Anniversary of the Atlantic Cable. Antique Wireless Association Rev. 21, 121–164 (2008).

    Google Scholar 

  4. Hille, B. Ionic Channels in Excitable Membranes 2nd edn (Sinauer, 1992).

    Google Scholar 

  5. Tuckwell, H. C. Introduction to Theoretical Neurobiology (Cambridge Univ. Press, 1988).

    Book  Google Scholar 

  6. Koch, C. Biophysics of Computation: Information Processing in Single Neurons (Oxford Univ. Press, 2004).

    Google Scholar 

  7. Stuart, G., Spruston, N. & Hausser, M. Dendrites (Oxford Univ. Press, 1999).

    Google Scholar 

  8. 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).

    Article  PubMed  Google Scholar 

  9. 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).

    Article  CAS  PubMed  Google Scholar 

  10. Malinow, R. & Malenka, R. C. AMPA receptor trafficking and synaptic plasticity. Annu. Rev. Neurosci. 25, 103–126 (2002).

    Article  CAS  PubMed  Google Scholar 

  11. Sabatini, B. L. & Svoboda, K. Analysis of calcium channels in single spines using optical fluctuation analysis. Nature 408, 589–593 (2000).

    Article  CAS  PubMed  Google Scholar 

  12. Fischer, M., Kaech, S., Knutti, D. & Matus, A. Rapid actin-based plasticity in dendritic spine. Neuron 20, 847–854 (1998).

    Article  CAS  PubMed  Google Scholar 

  13. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  14. 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).

    Article  CAS  PubMed  Google Scholar 

  15. Hoze, N. & Holcman, D. Residence times of receptors in dendritic spines analyzed by stochastic simulations in empirical domains. Biophys. J. 107, 3008–3017 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  16. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Araya, R., Jiang, J., Eisenthal, K. B. & Yuste, R. The spine neck filters membrane potentials. Proc. Natl Acad. Sci. USA 103, 17961–17966 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Tonnesen, J., Katona, G., Rozsa, B. & Nagerl, U. V. Spine neck plasticity regulates compartmentalization of synapses. Nat. Neurosci. 17, 678–685 (2014).

    Article  CAS  PubMed  Google Scholar 

  19. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  20. Rust, M. J., Bates, M. & Zhuang, X. Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM). Nat. Methods 3, 793–795 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  21. 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).

    Article  CAS  PubMed  Google Scholar 

  22. Svoboda, K., Tank, D. W. & Denk, W. Direct measurement of coupling between dendritic spines and shafts. Science 272, 716–719 (1996).

    Article  CAS  PubMed  Google Scholar 

  23. Holcman, D. & Schuss, Z. Diffusion laws in dendritic spines. J. Math. Neurosci. 1, 10 (2011).

    Article  PubMed  PubMed Central  Google Scholar 

  24. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Franks, K. M. & Sejnowski, T. J. Complexity of calcium signaling in synaptic spines. BioEssays 24, 1130–1144 (2002).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  26. Holcman, D., Schuss, Z. & Korkotian, E. Calcium dynamics in dendritic spines and spine motility. Biophys. J. 87, 81–91 (2004).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  27. Jackson, J. D. Classical Electrodynamics 3rd edn (Wiley, 1998).

    Google Scholar 

  28. 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).

    Article  CAS  PubMed  Google Scholar 

  29. Sylantyev, S. et al. Electric fields due to synaptic currents sharpen excitatory transmission. Science 319, 1845–1849 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  31. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  32. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  33. Eisenberg, R. S. From structure to function in open ionic channels. J. Membr. Biol. 171, 1–24 (1999).

    Article  CAS  PubMed  Google Scholar 

  34. Gillespie, D. et al. A physical mechanism for large-ion selectivity of ion channels. Phys. Chem. Chem. Phys. 4, 4763–4769 (2002).

    Article  CAS  Google Scholar 

  35. 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).

    Article  CAS  PubMed  Google Scholar 

  36. 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).

    Article  Google Scholar 

  37. 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).

    CAS  Google Scholar 

  38. Bloodgood, B. L. & Sabatini, B. L. Neuronal activity regulates diffusion across the neck of dendritic spines. Science 310, 866–869 (2005).

    Article  CAS  PubMed  Google Scholar 

  39. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Korkotian, E. & Segal, M. Synaptopodin regulates release of calcium from stores in dendritic spines of cultured hippocampal neurons. J. Physiol. 589, 5987–5995 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  41. Alivisatos, A. P. Less is more in medicine. Sci. Am. 285, 66–73 (2001).

    Article  CAS  PubMed  Google Scholar 

  42. Rall, W. Branching dendritic trees and motoneuron membrane resistivity. Exp. Neurol. 1, 491–527 (1959).

    Article  CAS  PubMed  Google Scholar 

  43. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  44. Schikorski, T. & Stevens, C. F. Morphological correlates of functionally defined synaptic vesicle populations. Nat. Neurosci. 4, 391–395 (2001).

    Article  CAS  PubMed  Google Scholar 

  45. Karube, F., Kubota, Y. & Kawaguchi, Y. Axon branching and synaptic bouton phenotypes in GABAergic nonpyramidal cell subtypes. J. Neurosci. 24, 2853–2865 (2004).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  46. Pannasch, U. et al. Connexin 30 sets synaptic strength by controlling astroglial synapse invasion. Nat. Neurosci. 17, 549–558 (2014).

    Article  CAS  PubMed  Google Scholar 

  47. Peters, A. & Paley, S. L. & Webster, H. D. Fine Structure of the Nervous System Saunders, 1976).

    Google Scholar 

  48. North, G. & Greenspan, R. J. Invertebrate Neurobiology (Cold Spring Harbor Press, 2008).

    Google Scholar 

  49. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  50. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  51. 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).

    Article  PubMed  PubMed 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

Authors

Corresponding author

Correspondence to David Holcman.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

PowerPoint slides

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

Check for updates. Verify currency and authenticity via CrossMark

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:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nrn4022

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing