The self-organization of grid cells in 3D

  1. Federico Stella  Is a corresponding author
  2. Alessandro Treves
  1. Scuola Internazionale Superiore di Studi Avanzati, Italy

Abstract

Do we expect periodic grid cells to emerge in bats, or perhaps dolphins, exploring a three-dimensional environment? How long will it take? Our self-organizing model, based on ring-rate adaptation, points at a complex answer. The mathematical analysis leads to asymptotic states resembling FCC and HCP crystal structures, which are calculated to be very close to each other in terms of cost function. The simulation of the full model, however, shows that the approach to such asymptotic states involves several sub-processes over distinct time scales. The smoothing of the initially irregular multiple fields of individual units and their arrangement into hexagonal grids over certain best planes are observed to occur relatively fast, even in large 3D volumes. The correct mutual orientation of the planes, though, and the coordinated arrangement of different units, take a longer time, with the network showing no sign of convergence towards either a pure FCC or HCP ordering.

Article and author information

Author details

  1. Federico Stella

    Cognitive Neuroscience, Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy
    For correspondence
    fstella@sissa.it
    Competing interests
    The authors declare that no competing interests exist.
  2. Alessandro Treves

    Cognitive Neuroscience, Scuola Internazionale Superiore di Studi Avanzati, Trieste, Italy
    Competing interests
    The authors declare that no competing interests exist.

Copyright

© 2015, Stella & Treves

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.

Metrics

  • 3,008
    views
  • 484
    downloads
  • 42
    citations

Views, downloads and citations are aggregated across all versions of this paper published by eLife.

Download links

A two-part list of links to download the article, or parts of the article, in various formats.

Downloads (link to download the article as PDF)

Open citations (links to open the citations from this article in various online reference manager services)

Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)

  1. Federico Stella
  2. Alessandro Treves
(2015)
The self-organization of grid cells in 3D
eLife 4:e05913.
https://doi.org/10.7554/eLife.05913

Share this article

https://doi.org/10.7554/eLife.05913

Further reading

    1. Neuroscience
    Sara Jamali, Sophie Bagur ... Brice Bathellier
    Research Article

    The brain predicts regularities in sensory inputs at multiple complexity levels, with neuronal mechanisms that remain elusive. Here, we monitored auditory cortex activity during the local-global paradigm, a protocol nesting different regularity levels in sound sequences. We observed that mice encode local predictions based on stimulus occurrence and stimulus transition probabilities, because auditory responses are boosted upon prediction violation. This boosting was due to both short-term adaptation and an adaptation-independent surprise mechanism resisting anesthesia. In parallel, and only in wakefulness, VIP interneurons responded to the omission of the locally expected sound repeat at the sequence ending, thus providing a chunking signal potentially useful for establishing global sequence structure. When this global structure was violated, by either shortening the sequence or ending it with a locally expected but globally unexpected sound transition, activity slightly increased in VIP and PV neurons, respectively. Hence, distinct cellular mechanisms predict different regularity levels in sound sequences.

    1. Neuroscience
    Emmanuel Ponsot
    Insight

    Damage to the synapses connecting hair cells to the auditory nerve leads to undetected hearing impairments.