IDEAS home Printed from https://ideas.repec.org/a/plo/pcbi00/1005922.html
   My bibliography  Save this article

Robust and efficient coding with grid cells

Author

Listed:
  • Lajos Vágó
  • Balázs B Ujfalussy

Abstract

The neuronal code arising from the coordinated activity of grid cells in the rodent entorhinal cortex can uniquely represent space across a large range of distances, but the precise conditions for optimal coding capacity are known only for environments with finite size. Here we consider a coding scheme that is suitable for unbounded environments, and present a novel, number theoretic approach to derive the grid parameters that maximise the coding range in the presence of noise. We derive an analytic upper bound on the coding range and provide examples for grid scales that achieve this bound and hence are optimal for encoding in unbounded environments. We show that in the absence of neuronal noise, the capacity of the system is extremely sensitive to the choice of the grid periods. However, when the accuracy of the representation is limited by neuronal noise, the capacity quickly becomes more robust against the choice of grid scales as the number of modules increases. Importantly, we found that the capacity of the system is near optimal even for random scale choices already for a realistic number of grid modules. Our study demonstrates that robust and efficient coding can be achieved without parameter tuning in the case of grid cell representation and provides a solid theoretical explanation for the large diversity of the grid scales observed in experimental studies. Moreover, we suggest that having multiple grid modules in the entorhinal cortex is not only required for the exponentially large coding capacity, but is also a prerequisite for the robustness of the system.Author summary: Navigation in natural, open environments poses serious challenges to animals as the distances to be represented may span several orders of magnitudes and are potentially unbounded. The recently discovered grid cells in the rodent brain are though to play a crucial role in generating unique representations for a large number of spatial locations. However, it is unknown how to choose the parameters of the grid cells to achieve maximal capacity, i.e., to uniquely encode the utmost locations in an open environment. In our manuscript, we demonstrate the surprising robustness of the grid cell coding system: The population code realised by grid cells is close to optimal for unique space representation irrespective of the choices of grid parameters. Thus, our study reveals a remarkable robustness of the grid cell coding scheme and provides a solid theoretical explanation for the large diversity of the grid scales observed in experimental studies.

Suggested Citation

  • Lajos Vágó & Balázs B Ujfalussy, 2018. "Robust and efficient coding with grid cells," PLOS Computational Biology, Public Library of Science, vol. 14(1), pages 1-28, January.
  • Handle: RePEc:plo:pcbi00:1005922
    DOI: 10.1371/journal.pcbi.1005922
    as

    Download full text from publisher

    File URL: https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1005922
    Download Restriction: no

    File URL: https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1005922&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pcbi.1005922?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Hanne Stensola & Tor Stensola & Trygve Solstad & Kristian Frøland & May-Britt Moser & Edvard I. Moser, 2012. "The entorhinal grid map is discretized," Nature, Nature, vol. 492(7427), pages 72-78, December.
    2. Torkel Hafting & Marianne Fyhn & Sturla Molden & May-Britt Moser & Edvard I. Moser, 2005. "Microstructure of a spatial map in the entorhinal cortex," Nature, Nature, vol. 436(7052), pages 801-806, August.
    3. Noga Mosheiff & Haggai Agmon & Avraham Moriel & Yoram Burak, 2017. "An efficient coding theory for a dynamic trajectory predicts non-uniform allocation of entorhinal grid cells to modules," PLOS Computational Biology, Public Library of Science, vol. 13(6), pages 1-19, June.
    4. Marianne Fyhn & Torkel Hafting & Alessandro Treves & May-Britt Moser & Edvard I. Moser, 2007. "Hippocampal remapping and grid realignment in entorhinal cortex," Nature, Nature, vol. 446(7132), pages 190-194, March.
    5. Julija Krupic & Marius Bauza & Stephen Burton & Caswell Barry & John O’Keefe, 2015. "Grid cell symmetry is shaped by environmental geometry," Nature, Nature, vol. 518(7538), pages 232-235, February.
    6. Tor Stensola & Hanne Stensola & May-Britt Moser & Edvard I. Moser, 2015. "Shearing-induced asymmetry in entorhinal grid cells," Nature, Nature, vol. 518(7538), pages 207-212, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tiziano D’Albis & Richard Kempter, 2017. "A single-cell spiking model for the origin of grid-cell patterns," PLOS Computational Biology, Public Library of Science, vol. 13(10), pages 1-41, October.
    2. Taylor J. Malone & Nai-Wen Tien & Yan Ma & Lian Cui & Shangru Lyu & Garret Wang & Duc Nguyen & Kai Zhang & Maxym V. Myroshnychenko & Jean Tyan & Joshua A. Gordon & David A. Kupferschmidt & Yi Gu, 2024. "A consistent map in the medial entorhinal cortex supports spatial memory," Nature Communications, Nature, vol. 15(1), pages 1-22, December.
    3. Kyerl Park & Yoonsoo Yeo & Kisung Shin & Jeehyun Kwag, 2024. "Egocentric neural representation of geometric vertex in the retrosplenial cortex," Nature Communications, Nature, vol. 15(1), pages 1-14, December.
    4. Torsten Neher & Amir Hossein Azizi & Sen Cheng, 2017. "From grid cells to place cells with realistic field sizes," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-27, July.
    5. Axel Kammerer & Christian Leibold, 2014. "Hippocampal Remapping Is Constrained by Sparseness rather than Capacity," PLOS Computational Biology, Public Library of Science, vol. 10(12), pages 1-12, December.
    6. Simon N Weber & Henning Sprekeler, 2019. "A local measure of symmetry and orientation for individual spikes of grid cells," PLOS Computational Biology, Public Library of Science, vol. 15(2), pages 1-21, February.
    7. Laurenz Muessig & Fabio Ribeiro Rodrigues & Tale L. Bjerknes & Benjamin W. Towse & Caswell Barry & Neil Burgess & Edvard I. Moser & May-Britt Moser & Francesca Cacucci & Thomas J. Wills, 2024. "Environment geometry alters subiculum boundary vector cell receptive fields in adulthood and early development," Nature Communications, Nature, vol. 15(1), pages 1-17, December.
    8. Benjamin Dunn & Maria Mørreaunet & Yasser Roudi, 2015. "Correlations and Functional Connections in a Population of Grid Cells," PLOS Computational Biology, Public Library of Science, vol. 11(2), pages 1-21, February.
    9. Isabella C. Wagner & Luise P. Graichen & Boryana Todorova & Andre Lüttig & David B. Omer & Matthias Stangl & Claus Lamm, 2023. "Entorhinal grid-like codes and time-locked network dynamics track others navigating through space," Nature Communications, Nature, vol. 14(1), pages 1-18, December.
    10. Noga Mosheiff & Haggai Agmon & Avraham Moriel & Yoram Burak, 2017. "An efficient coding theory for a dynamic trajectory predicts non-uniform allocation of entorhinal grid cells to modules," PLOS Computational Biology, Public Library of Science, vol. 13(6), pages 1-19, June.
    11. Qiming Shao & Ligu Chen & Xiaowan Li & Miao Li & Hui Cui & Xiaoyue Li & Xinran Zhao & Yuying Shi & Qiang Sun & Kaiyue Yan & Guangfu Wang, 2024. "A non-canonical visual cortical-entorhinal pathway contributes to spatial navigation," Nature Communications, Nature, vol. 15(1), pages 1-18, December.
    12. Alexander Thomas Keinath, 2016. "The Preferred Directions of Conjunctive Grid X Head Direction Cells in the Medial Entorhinal Cortex Are Periodically Organized," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-11, March.
    13. Trygve Solstad & Hosam N Yousif & Terrence J Sejnowski, 2014. "Place Cell Rate Remapping by CA3 Recurrent Collaterals," PLOS Computational Biology, Public Library of Science, vol. 10(6), pages 1-10, June.
    14. Alexander Nitsch & Mona M. Garvert & Jacob L. S. Bellmund & Nicolas W. Schuck & Christian F. Doeller, 2024. "Grid-like entorhinal representation of an abstract value space during prospective decision making," Nature Communications, Nature, vol. 15(1), pages 1-20, December.
    15. Francis Kei Masuda & Emily A. Aery Jones & Yanjun Sun & Lisa M. Giocomo, 2023. "Ketamine evoked disruption of entorhinal and hippocampal spatial maps," Nature Communications, Nature, vol. 14(1), pages 1-19, December.
    16. Patrick A. LaChance & Michael E. Hasselmo, 2024. "Distinct codes for environment structure and symmetry in postrhinal and retrosplenial cortices," Nature Communications, Nature, vol. 15(1), pages 1-15, December.
    17. Florian Raudies & Michael E Hasselmo, 2015. "Differences in Visual-Spatial Input May Underlie Different Compression Properties of Firing Fields for Grid Cell Modules in Medial Entorhinal Cortex," PLOS Computational Biology, Public Library of Science, vol. 11(11), pages 1-27, November.
    18. Erik Hermansen & David A. Klindt & Benjamin A. Dunn, 2024. "Uncovering 2-D toroidal representations in grid cell ensemble activity during 1-D behavior," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    19. Balázs Ujfalussy & Tamás Kiss & Péter Érdi, 2009. "Parallel Computational Subunits in Dentate Granule Cells Generate Multiple Place Fields," PLOS Computational Biology, Public Library of Science, vol. 5(9), pages 1-16, September.
    20. Louis-Emmanuel Martinet & Denis Sheynikhovich & Karim Benchenane & Angelo Arleo, 2011. "Spatial Learning and Action Planning in a Prefrontal Cortical Network Model," PLOS Computational Biology, Public Library of Science, vol. 7(5), pages 1-21, May.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pcbi00:1005922. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ploscompbiol (email available below). General contact details of provider: https://journals.plos.org/ploscompbiol/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.