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.

Entorhinal velocity signals reflect environmental geometry

This article has been updated


The entorhinal cortex contains neurons that represent self-location, including grid cells that fire in periodic locations and velocity signals that encode running speed and head direction. Although the size and shape of the environment influence grid patterns, whether entorhinal velocity signals are equally influenced or provide a universal metric for self-motion across environments remains unknown. Here we report that speed cells rescale after changes to the size and shape of the environment. Moreover, head direction cells reorganize in an experience-dependent manner to align with the axis of environmental change. A knockout mouse model allows dissociation of the coordination between cell types, with grid and speed cells, but not head direction cells, responding in concert to environmental change. These results point to malleability in the coding features of multiple entorhinal cell types and have implications for which cell types contribute to the velocity signal used by computational models of grid cells.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Environmental perturbation distorts grid spacing.
Fig. 2: S-encoding cells rescale in response to environmental perturbation.
Fig. 3: The gain (slope and intercept) of the theta frequency–speed relationship increases in compression and decreases in expansion conditions.
Fig. 4: A directionally specific asymmetric bias develops after multiple exposures to modified environments.
Fig. 5: TRIP8b KO grid spacing is less sensitive to environmental perturbation.
Fig. 6: TRIP8b KO speed signals are less sensitive to environmental perturbation while directional signals remain malleable.

Data availability

Data that support the findings of this study are available from the corresponding authors upon reasonable request.

Code availability

Code used in the analyses described in this manuscript can be accessed at: The code used in the LNP model can be accessed at

Change history

  • 21 February 2020

    The Supplementary Information originally published was missing and has been replaced on 21/02/2020.


  1. 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).

    CAS  PubMed  Google Scholar 

  2. 2.

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

    CAS  PubMed  Google Scholar 

  3. 3.

    Kropff, E., Carmichael, J. E., Moser, M. B. & Moser, E. I. Speed cells in the medial entorhinal cortex. Nature 523, 419–424 (2015).

    CAS  PubMed  Google Scholar 

  4. 4.

    Hinman, J. R., Brandon, M. P., Climer, J. R., Chapman, G. W. & Hasselmo, M. E. Multiple running speed signals in medial entorhinal cortex. Neuron 91, 666–679 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  5. 5.

    Hardcastle, K., Maheswaranathan, N., Ganguli, S. & Giocomo, L. M. A multiplexed, heterogeneous, and adaptive code for navigation in medial entorhinal cortex. Neuron 94, 375–387 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  6. 6.

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

    CAS  PubMed  Google Scholar 

  7. 7.

    Stensola, T., Stensola, H., Moser, M. B. & Moser, E. I. Shearing-induced asymmetry in entorhinal grid cells. Nature 518, 207–212 (2015).

    CAS  PubMed  Google Scholar 

  8. 8.

    Krupic, J., Bauza, M., Burton, S., Barry, C. & O’Keefe, J. Grid cell symmetry is shaped by environmental geometry. Nature 518, 232–235 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  9. 9.

    Barry, C., Hayman, R., Burgess, N. & Jeffery, K. J. Experience-dependent rescaling of entorhinal grids. Nat. Neurosci. 10, 682–684 (2007).

    CAS  PubMed  Google Scholar 

  10. 10.

    Stensola, H. et al. The entorhinal map is discretized. Nature 492, 72–78 (2012).

    CAS  PubMed  Google Scholar 

  11. 11.

    Keinath, A. T., Epstein, R. A. & Balasubramanian, V. Environmental deformations dynamically shift the grid cell spatial metric. eLife 7, e38169 (2018).

    PubMed  PubMed Central  Google Scholar 

  12. 12.

    Campbell, M. G. et al. Principles governing the integration of landmark and self-motion cues in entorhinal cortical codes for navigation. Nat. Neurosci. 21, 1096–1106 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  13. 13.

    Campbell, M. G. & Giocomo, L. M. Self-motion processing in visual and entorhinal cortices: inputs, integration and implications for position coding. J. Neurophysiol. 120, 2091–2106 (2018).

  14. 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).

    CAS  PubMed  PubMed Central  Google Scholar 

  15. 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).

    PubMed  Google Scholar 

  16. 16.

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

    PubMed  PubMed Central  Google Scholar 

  17. 17.

    Pastoll, H., Solanka, L., van Rossum, M. C. & Nolan, M. F. Feedback inhibition enables θ-nested γ oscillations and grid firing fields. Neuron 77, 141–154 (2013).

    CAS  PubMed  Google Scholar 

  18. 18.

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

    PubMed  PubMed Central  Google Scholar 

  19. 19.

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

    PubMed  PubMed Central  Google Scholar 

  20. 20.

    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).

    CAS  PubMed  PubMed Central  Google Scholar 

  21. 21.

    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).

    CAS  PubMed  PubMed Central  Google Scholar 

  22. 22.

    Couey, J. J. et al. Recurrent inhibitory circuitry as a mechanism for grid formation. Nat. Neurosci. 16, 318–324 (2013).

    CAS  PubMed  Google Scholar 

  23. 23.

    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).

    PubMed  PubMed Central  Google Scholar 

  24. 24.

    Bush, D. & Burgess, N. A hybrid oscillatory interference/continuous attractor network model of grid cell firing. J. Neurosci. 34, 5065–5079 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  25. 25.

    Raudies, F. & Hasselmo, M. E. Differences in visual–spatial input may underlie different compression properties of firing fields for grid cell modules in medial entorhinal cortex. PLoS Comput. Biol. 11, e1004596 (2015).

    PubMed  PubMed Central  Google Scholar 

  26. 26.

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

    CAS  PubMed  Google Scholar 

  27. 27.

    Mallory, C. S., Hardcastle, K., Bant, J. S. & Giocomo, L. M. Grid scale drives the scale and long-term stability of place maps. Nat. Neurosci. 21, 270–282 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  28. 28.

    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).

    CAS  PubMed  PubMed Central  Google Scholar 

  29. 29.

    Xu, C., Datta, S., Wu, M. & Alreja, M. Hippocampal theta rhythm is reduced by suppression of the H-current in septohippocampal GABAergic neurons. Eur. J. Neurosci. 19, 2299–2309 (2004).

    PubMed  Google Scholar 

  30. 30.

    Kocsis, B. & Li, S. In vivo contribution of H channels in the septal pacemaker to theta rhythm generation. Eur. J. Neurosci. 20, 2149–2158 (2004).

    PubMed  Google Scholar 

  31. 31.

    Lewis, A. S. et al. Deletion of the hyperpolarization-activated cyclic nucleotide-gated channel auxiliary subunit TRIP8b impairs hippocampal I h localization and function and promotes antidepressant behavior in mice. J. Neurosci. 31, 7424–7440 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  32. 32.

    Mhatre, H., Gorchetchnikov, A. & Grossberg, S. Grid cell hexagonal patterns formed by fast self-organizing learning within entorhinal cortex. Hippocampus 22, 320–334 (2012).

    PubMed  Google Scholar 

  33. 33.

    Hasselmo, M. E. & Brandon, M. P. A model combining oscillations and attractor dynamics for generation of grid cell firing. Front. Neural Circuits 6, 30 (2012).

    PubMed  PubMed Central  Google Scholar 

  34. 34.

    Raudies, F., Brandon, M. P., Chapman, G. W. & Hasselmo, M. E. Head direction is coded more strongly than movement direction in a population of entorhinal neurons. Brain Res. 621, 355–367 (2015).

    Google Scholar 

  35. 35.

    Zutshi, I. et al. Recurrent circuits within medial entorhinal cortex superficial layer support grid cell firing. Nat. Commun. 9, 3701 (2018).

    PubMed  PubMed Central  Google Scholar 

  36. 36.

    Zutshi, I., Leutgeb, J. K. & Leutgeb, S. Theta sequences of grid cell populations can provide a movement-direction signal. Curr. Opn. Behav. Sci. 17, 147–154 (2017).

    Google Scholar 

  37. 37.

    Blair, H. T., Cho, J. & Sharp, P. E. Role of the lateral mammillary nucleus in the rat head direction circuit: a combined single unit recording and lesion study. Neuron 21, 1387–1397 (1998).

    CAS  PubMed  Google Scholar 

  38. 38.

    Blair, H. T. & Sharp, P. E. Anticipatory head direction signals in anterior thalamus: evidence for a thalamocortical circuit that integrates angular head motion to compute head direction. J. Neurosci. 9, 6260–6270 (1995).

    Google Scholar 

  39. 39.

    Krupic, J., Bauza, M., Burton, S., Lever, C. & O’Keefe, J. How environment geometry affects grid cell symmetry and what we can learn from it. Philos. Trans. R. Soc. B 369, 20130188 (2014).

    Google Scholar 

  40. 40.

    Ocko, S. A., Hardcastle, K., Giocomo, L. M. & Ganguli, S. Emergent elasticity in the neural code for space. Proc. Natl Acad. Sci. USA 115, E11798–E11806 (2018).

    CAS  PubMed  Google Scholar 

  41. 41.

    Park, E. H., Keeley, S., Ranck, J. B. Jr. & Fenton, A. A. How the internally-organized direction sense is used to navigate. Neuron 101, 1–9 (2018).

    Google Scholar 

  42. 42.

    Jacob, P.-Y. et al. An independent, landmark-dominated head-direction signal in dysgranular retrosplenial cortex. Nat. Neurosci. 20, 173–175 (2017).

    CAS  PubMed  Google Scholar 

  43. 43.

    Perez-Escobar, J. A., Kornienko, O., Latuske, P., Kohler, L. & Allen, K. Visual landmarks sharpen grid cell metric and confer context specificity to neurons of the medial entorhinal cortex. eLife 23, e16937 (2016).

    Google Scholar 

  44. 44.

    Raudies, F., Mingolla, E. & Hasselmo, M. E. Modeling the influence of optic flow on grid cell firing in the absence of other cues. J. Comput. Neurosci. 33, 475–493 (2012).

    PubMed  PubMed Central  Google Scholar 

  45. 45.

    Garden, D. L., Dodson, P. D., O’Donnell, C., White, M. D. & Nolan, M. F. Tuning of synaptic integration in the medial entorhinal cortex to the organization of grid cell firing fields. Neuron 60, 875–889 (2008).

    CAS  PubMed  Google Scholar 

  46. 46.

    Justus, D. et al. Glutamatergic synaptic integration of locomotion speed via septoentorhinal projections. Nat. Neurosci. 20, 16–19 (2017).

    CAS  PubMed  Google Scholar 

  47. 47.

    Andermann, M. L., Kerlin, A. M., Roumis, D. K., Glickfeld, L. L. & Reid, R. C. Functional specialization of mouse higher visual cortical areas. Neuron 72, 1025–1039 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  48. 48.

    Wang, Q., Gao, E. & Burkhalter, A. Gateways of ventral and dorsal streams in mouse visual cortex. J. Neurosci. 31, 1905–1918 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  49. 49.

    Saleem, A. B., Ayaz, A., Jeffery, K. J., Harris, K. D. & Carandini, M. Integration of visual motion and locomotion in mouse visual cortex. Nat. Neurosci. 16, 1864–1869 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  50. 50.

    Pan, Y. et al. TRIP8b is required for maximal expression of HCN1 in the mouse retina. PLoS One 9, e85850 (2014).

    PubMed  PubMed Central  Google Scholar 

  51. 51.

    Schmitzer-Tobert, N., Jackson, J., Henze, D., Harris, K. & Redish, A. D. Quantitative measures of cluster quality for use in extracellular recordings. Neuroscience 131, 1–11 (2005).

    Google Scholar 

  52. 52.

    Skaggs, W. E., McNaughton, B. L., Wilson, M. A. & Barnes, C. A. Theta phase precession in hippocampal neuronal populations and the compression of temporal sequences. Hippocampus 6, 149–172 (1996).

    CAS  PubMed  Google Scholar 

  53. 53.

    Franklin, K. B. J. & Paxinos, G. The Mouse Brain in Stereotaxic Coordinates 3rd ed (Academic Press, 2007).

  54. 54.

    Langston, R. F. et al. Development of the spatial representation system in the rat. Science 328, 1576–1580 (2010).

    CAS  PubMed  Google Scholar 

  55. 55.

    Wills, T. J., Cacucci, F., Burgess, N. & O’Keefe, J. Development of the hippocampal cognitive map in preweanling rats. Science 328, 1573–1576 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  56. 56.

    Fitzgibbon, A., Pilu, M. & Fisher, R. B. Direct least square fitting of ellipses. IEEE Transactions on Pattern Analysis and Machine Intelligence 21, 476-480 (1999).

  57. 57.

    Berens, P. CircStat: a MATLAB toolbox for circular statistics. J. Stat. Softw. 31, 1–21 (2009).

    Google Scholar 

  58. 58.

    Zar, J. H. Biostatistical Analysis (Prentice Hall, 1999).

Download references


L.M.G. recieves funding as a New York Stem Cell Foundation–Robertson Investigator. This work was supported by funding from the New York Stem Cell Foundation, NIMH MH106475, the Office of Naval Research N000141812690, the Simons Foundation 542987SPI, the Whitehall Foundation, the James S. McDonnell Foundation and a Klingenstein–Simons award to L.M.G.; the Philip Wrightson Postdoctoral Fellowship from the Neurological Foundation of New Zealand awarded to R.G.M.; a National Science Foundation Graduate Research Fellowship awarded to C.S.M; a Stanford Interdiscplinary Graduate Fellowship awarded to K.H.; and NINDS NS059934 to D.M.C. We thank A. Borrayo and A. Diaz for histology assistance and M.E. Hasselmo for input on the oscillatory interference model.

Author information




L.M.G. and R.G.M. conceptualized experiments and analyses. C.S.M. and R.G.M. performed chronic implantations and collected and analyzed in vivo data. K.H. provided support on analyses and performed computational simulations. D.M.C. provided the TRIP8b KO mouse line. L.M.G. and R.G.M. wrote the paper with feedback from all authors.

Corresponding authors

Correspondence to Robert G. K. Munn or Lisa M. Giocomo.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Neuroscience thanks Dori Derdikman and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–14.

Reporting Summary

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Munn, R.G.K., Mallory, C.S., Hardcastle, K. et al. Entorhinal velocity signals reflect environmental geometry. Nat Neurosci 23, 239–251 (2020).

Download citation

Further reading


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