Journal of Computational Neuroscience

, Volume 47, Issue 1, pp 43–60 | Cite as

Modeling grid fields instead of modeling grid cells

An effective model at the macroscopic level and its relationship with the underlying microscopic neural system
  • Sophie RosayEmail author
  • Simon Weber
  • Marcello Mulas


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.


Hippocampus Grid cells Effective model Physics of 2d systems 



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.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.

Supplementary material

10827_2019_722_MOESM1_ESM.tex (22 kb)
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Authors and Affiliations

  1. 1.Scuola Internazionale Superiore di Studi AvanzatiTriesteItaly
  2. 2.Technische UniversitätBerlinGermany
  3. 3.Technische UniversitätMunichGermany

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