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Modeling grid fields instead of modeling grid cells

An effective model at the macroscopic level and its relationship with the underlying microscopic neural system

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Abstract

A neuron’s firing correlates are defined as the features of the external world to which its activity is correlated. In many parts of the brain, neurons have quite simple such firing correlates. A striking example are grid cells in the rodent medial entorhinal cortex: their activity correlates with the animal’s position in space, defining ‘grid fields’ arranged with a remarkable periodicity. Here, we show that the organization and evolution of grid fields relate very simply to physical space. To do so, we use an effective model and consider grid fields as point objects (particles) moving around in space under the influence of forces. We reproduce several observations on the geometry of grid patterns. This particle-like behavior is particularly salient in a recent experiment in which two separate grid patterns merge. We discuss pattern formation in the light of known results from physics of two-dimensional colloidal systems. Notably, we study the limitations of the widely used ‘gridness score’ and show how physics of 2d systems could be a source of inspiration, both for data analysis and computational modeling. Finally, we draw the relationship between our ‘macroscopic’ model for grid fields and existing ‘microscopic’ models of grid cell activity and discuss how a description at the level of grid fields allows to put constraints on the underlying grid cell network.

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Notes

  1. Grid patterns with non homogeneous orientation have been shown by Stensola et al. (2015) but, in the absence of a local measure, could not be quantified.

  2. Some slight differences, either of spacing or orientation, have been reported, but we neglect them for the present discussion.

  3. A question not answered by this experiment is whether this position is fixed with respect to the walls or with respect to something else, e.g., distal cues.

  4. Near the walls some grid distortion could come into play as we have shown, but let us assume here that the box is big enough so that we can neglect such edge effects.

  5. So this model differs from the place cell case only by its boundary conditions (Spalla et al. 2019)

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Acknowledgements

We are grateful to Alessandro Treves, Rémi Monasson, Giuseppe D’Adamo, Thomas Gueudré and Henning Sprekeler for their remarks on the model and its relationship with physics. We thank Tanja Wernle for extensive discussion on the merging experiment; Bailu Si and Eugenio Urdapilleta for their code of the adaptation model. Many thanks also to John Nicholls. The idea of grid alignment via recurrent inhibitory connections was developed in discussions between Henning Sprekeler and S.W.. S.R. would like to thank the GRIDMAP project for financial support and the Abdus Salam International Centre for Theoretical Physics in Trieste for hospitality in the conclusive phase of this work. S.W. was funded by the German Federal Ministry for Education and Research, FKZ 01GQ1201.

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  1. Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy

    Sophie Rosay

  2. Technische Universität, Berlin, Germany

    Simon Weber

  3. Technische Universität, Munich, Germany

    Marcello Mulas

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  1. Sophie Rosay
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Correspondence to Sophie Rosay.

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Rosay, S., Weber, S. & Mulas, M. Modeling grid fields instead of modeling grid cells. J Comput Neurosci 47, 43–60 (2019). https://doi.org/10.1007/s10827-019-00722-8

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