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Robust and efficient coding with grid cells

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
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