Skip to main content

Thank you for visiting 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.

Membrane potential dynamics of grid cells

A Corrigendum to this article was published on 27 November 2013


During navigation, grid cells increase their spike rates in firing fields arranged on a markedly regular triangular lattice, whereas their spike timing is often modulated by theta oscillations. Oscillatory interference models of grid cells predict theta amplitude modulations of membrane potential during firing field traversals, whereas competing attractor network models predict slow depolarizing ramps. Here, using in vivo whole-cell recordings, we tested these models by directly measuring grid cell intracellular potentials in mice running along linear tracks in virtual reality. Grid cells had large and reproducible ramps of membrane potential depolarization that were the characteristic signature tightly correlated with firing fields. Grid cells also demonstrated intracellular theta oscillations that influenced their spike timing. However, the properties of theta amplitude modulations were not consistent with the view that they determine firing field locations. Our results support cellular and network mechanisms in which grid fields are produced by slow ramps, as in attractor models, whereas theta oscillations control spike timing.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type



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

Figure 1: Schematics of membrane potential predicted by different model families.
Figure 2: Tetrode recordings from grid cells in two-dimensional arenas and virtual linear tracks.
Figure 3: Whole-cell recordings from grid cells.
Figure 4: Grid cells exhibit slow intracellular ramps of depolarization and theta oscillations with variable amplitudes.
Figure 5: Ramps contain more information about position.
Figure 6: Ramps, not oscillations, are the primary drive of field formation.


  1. Hafting, T., Fyhn, M., Molden, S., Moser, M. B. & Moser, E. I. Microstructure of a spatial map in the entorhinal cortex. Nature 436, 801–806 (2005)

    Article  CAS  ADS  Google Scholar 

  2. Moser, E. I., Kropff, E. & Moser, M.-B. Place cells, grid cells, and the brain’s spatial representation system. Annu. Rev. Neurosci. 31, 69–89 (2008)

    Article  CAS  Google Scholar 

  3. McNaughton, B. L., Battaglia, F. P., Jensen, O., Moser, E. I. & Moser, M.-B. Path integration and the neural basis of the ‘cognitive map’. Nature Rev. Neurosci. 7, 663–678 (2006)

    Article  CAS  Google Scholar 

  4. Giocomo, L. M., Moser, M. B. & Moser, E. I. Computational models of grid cells. Neuron 71, 589–603 (2011)

    Article  CAS  Google Scholar 

  5. Zilli, E. A. Models of grid cell spatial firing published 2005–2011. Front. Neural Circ. 6, 16 (2012)

    Google Scholar 

  6. O’Keefe, J. & Burgess, N. Dual phase and rate coding in hippocampal place cells: theoretical significance and relationship to entorhinal grid cells. Hippocampus 15, 853–866 (2005)

    Article  Google Scholar 

  7. Burgess, N., Barry, C. & O’Keefe, J. An oscillatory interference model of grid cell firing. Hippocampus 17, 801–812 (2007)

    Article  Google Scholar 

  8. Hasselmo, M. E., Giocomo, L. M. & Zilli, E. A. Grid cell firing may arise from interference of theta frequency membrane potential oscillations in single neurons. Hippocampus 17, 1252–1271 (2007)

    Article  Google Scholar 

  9. Burgess, N. Grid cells and theta as oscillatory interference: theory and predictions. Hippocampus 18, 1157–1174 (2008)

    Article  Google Scholar 

  10. Giocomo, L. M. & Hasselmo, M. E. Computation by oscillations: Implications of experimental data for theoretical models of grid cells. Hippocampus 18, 1186–1199 (2008)

    Article  Google Scholar 

  11. Hasselmo, M. E. Grid cell mechanisms and function: contributions of entorhinal persistent spiking and phase resetting. Hippocampus 18, 1213–1229 (2008)

    Article  Google Scholar 

  12. Blair, H. T., Welday, A. C. & Zhang, K. Scale-invariant memory representations emerge from moiré interference between grid fields that produce theta oscillations: a computational model. J. Neurosci. 27, 3211–3229 (2007)

    Article  CAS  Google Scholar 

  13. Samsonovich, A. & McNaughton, B. L. Path integration and cognitive mapping in a continuous attractor neural network model. J. Neurosci. 17, 5900–5920 (1997)

    Article  CAS  Google Scholar 

  14. Fuhs, M. C. & Touretzky, D. S. A spin glass model of path integration in rat medial entorhinal cortex. J. Neurosci. 26, 4266–4276 (2006)

    Article  CAS  Google Scholar 

  15. Guanella, A., Kiper, D. & Verschure, P. A model of grid cells based on a twisted torus topology. Int. J. Neural Syst. 17, 231–240 (2007)

    Article  Google Scholar 

  16. Burak, Y. & Fiete, I. R. Accurate path integration in continuous attractor network models of grid cells. PLOS Comput. Biol. 5, e1000291 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  17. Navratilova, Z., Giocomo, L. M., Fellous, J. M., Hasselmo, M. E. & McNaughton, B. L. Phase precession and variable spatial scaling in a periodic attractor map model of medial entorhinal grid cells with realistic after-spike dynamics. Hippocampus 22, 772–789 (2011)

    Article  Google Scholar 

  18. Alonso, A. & Llinas, R. R. Subthreshold Na+-dependent theta-like rhythmicity in stellate cells of entorhinal cortex layer II. Nature 342, 175–177 (1989)

    Article  CAS  ADS  Google Scholar 

  19. Giocomo, L. M., Zilli, E. A., Fransen, E. & Hasselmo, M. E. Temporal frequency of subthreshold oscillations scales with entorhinal grid cell field spacing. Science 315, 1719–1722 (2007)

    Article  CAS  ADS  Google Scholar 

  20. Hafting, T., Fyhn, M., Bonnevie, T., Moser, M. B. & Moser, E. I. Hippocampus-independent phase precession in entorhinal grid cells. Nature 453, 1248–1252 (2008)

    Article  CAS  ADS  Google Scholar 

  21. Brandon, M. P. et al. Reduction of theta rhythm dissociates grid cell spatial periodicity from directional tuning. Science 332, 595–599 (2011)

    Article  CAS  ADS  Google Scholar 

  22. Koenig, J., Linder, A. N., Leutgeb, J. K. & Leutgeb, S. The spatial periodicity of grid cells is not sustained during reduced theta oscillations. Science 332, 592–595 (2011)

    Article  CAS  ADS  Google Scholar 

  23. Welday, A. C., Shlifer, I. G., Bloom, M. L., Zhang, K. & Blair, H. T. Cosine directional tuning of theta cell burst frequencies: evidence for spatial coding by oscillatory interference. J. Neurosci. 31, 16157–16176 (2011)

    Article  CAS  Google Scholar 

  24. Yartsev, M. M., Witter, M. P. & Ulanovsky, N. Grid cells without theta oscillations in the entorhinal cortex of bats. Nature 479, 103–107 (2011)

    Article  CAS  ADS  Google Scholar 

  25. Welinder, P. E., Burak, Y. & Fiete, I. R. Grid cells: the position code, neural network models of activity, and the problem of learning. Hippocampus 18, 1283–1300 (2008)

    Article  Google Scholar 

  26. Giocomo, L. M. & Moser, E. I. Spatial representation: maps in a temporal void. Curr. Biol. 21, R962–R964 (2011)

    Article  CAS  Google Scholar 

  27. Barry, C., Bush, D., O’Keefe, J. & Burgess, N. Models of grid cells and theta oscillations. Nature 488, (2012); Reply 488, (2012)

  28. Holscher, C., Schnee, A., Dahmen, H., Setia, L. & Mallot, H. A. Rats are able to navigate in virtual environments. J. Exp. Biol. 208, 561–569 (2005)

    Article  CAS  Google Scholar 

  29. Harvey, C. D., Collman, F., Dombeck, D. A. & Tank, D. W. Intracellular dynamics of hippocampal place cells during virtual navigation. Nature 461, 941–946 (2009)

    Article  CAS  ADS  Google Scholar 

  30. Dombeck, D. A., Harvey, C. D., Tian, L., Looger, L. L. & Tank, D. W. Functional imaging of hippocampal place cells at cellular resolution during virtual navigation. Nature Neurosci. 13, 1433–1440 (2010)

    Article  CAS  Google Scholar 

  31. Fyhn, M., Hafting, T., Witter, M. P., Moser, E. I. & Moser, M. B. Grid cells in mice. Hippocampus 18, 1230–1238 (2008)

    Article  Google Scholar 

  32. Brun, V. H. et al. Progressive increase in grid scale from dorsal to ventral medial entorhinal cortex. Hippocampus 18, 1200–1212 (2008)

    Article  MathSciNet  Google Scholar 

  33. Sargolini, F. et al. Conjunctive representation of position, direction, and velocity in entorhinal cortex. Science 312, 758–762 (2006)

    Article  CAS  ADS  Google Scholar 

  34. Witter, M. P. & Moser, E. I. Spatial representation and the architecture of the entorhinal cortex. Trends Neurosci. 29, 671–678 (2006)

    Article  CAS  Google Scholar 

  35. Burgalossi, A. et al. Microcircuits of functionally identified neurons in the rat medial entorhinal cortex. Neuron 70, 773–786 (2011)

    Article  CAS  Google Scholar 

  36. Quilichini, P., Sirota, A. & Buzsaki, G. Intrinsic circuit organization and theta-gamma oscillation dynamics in the entorhinal cortex of the rat. J. Neurosci. 30, 11128–11142 (2010)

    Article  CAS  Google Scholar 

  37. Barry, C., Heys, J. G. & Hasselmo, M. E. Possible role of acetylcholine in regulating spatial novelty effects on theta rhythm and grid cells. Front. Neural Circ. 6, 5 (2012)

    CAS  Google Scholar 

  38. Giocomo, L. M. et al. Grid cells use HCN1 channels for spatial scaling. Cell 147, 1159–1170 (2011)

    Article  CAS  Google Scholar 

  39. Jeewajee, A., Barry, C., O’Keefe, J. & Burgess, N. Grid cells and theta as oscillatory interference: electrophysiological data from freely moving rats. Hippocampus 18, 1175–1185 (2008)

    Article  CAS  Google Scholar 

  40. Tsodyks, M. V., Skaggs, W. E., Sejnowski, T. J. & McNaughton, B. L. Population dynamics and theta rhythm phase precession of hippocampal place cell firing: a spiking neuron model. Hippocampus 6, 271–280 (1996)

    Article  CAS  Google Scholar 

  41. Kinkhabwala, A. A. & Tank, D. W. Spatial Patterning of Grid Cell Firing in Virtual Reality Environments. Program No. 100.14/KKK30 (Society for Neuroscience, 2011)

    Google Scholar 

Download references


We thank C. Harvey, R. Low, A. Miri, S. Lewallen, J. Rickgauer, D. Little, D. Barson, D. Aronov, W. Bialek, I. Fiete and G. Buzsaki for helpful discussions. This work was supported by NINDS grant 5RC1NS068148-02 and 1R37NS081242-01, NIMH grant 5R01MH083686-04, NIH Postdoctoral Fellowship grant F32NS070514-01A1 (A.A.K.), and an NSF Graduate Research Fellowship (C.D.).

Author information

Authors and Affiliations



C.D. performed whole-cell recording experiments and histological identification. A.A.K. performed tetrode experiments; A.A.K. and D.W.T. designed the system for measuring grid cell activity in virtual reality; C.D. analysed the data with strategy and methods contributions from A.A.K. and D.W.T.; C.D. and D.W.T. wrote the paper.

Corresponding author

Correspondence to David W. Tank.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Figures 1

This file contains Supplementary Figures 1–9. This file was corrected on 27 November 2013. (PDF 22051 kb)

Supplementary Figures 2

This file contains Supplementary Figures 10–27. (PDF 21369 kb)

Supplementary Information

This file contains Supplementary Methods and Supplementary References. (PDF 1059 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Domnisoru, C., Kinkhabwala, A. & Tank, D. Membrane potential dynamics of grid cells. Nature 495, 199–204 (2013).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


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