A geometric attractor mechanism for self-organization of entorhinal grid modules

  1. Louis Kang  Is a corresponding author
  2. Vijay Balasubramanian
  1. University of Pennsylvania, United States

Abstract

Grid cells in the medial entorhinal cortex (MEC) respond when an animal occupies a periodic lattice of 'grid fields' in the environment. The grids are organized in modules with spatial periods, or scales, clustered around discrete values separated on average by ratios in the range 1.4-1.7. We propose a mechanism that produces this modular structure through dynamical self-organization in the MEC. In attractor network models of grid formation, the grid scale of a single module is set by the distance of recurrent inhibition between neurons. We show that the MEC forms a hierarchy of discrete modules if a smooth increase in inhibition distance along its dorso-ventral axis is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids and have values that fall within the observed range. We discuss how interactions required by our model might be tested experimentally.

Data availability

We have included the source code for our main simulation as a supporting file.

Article and author information

Author details

  1. Louis Kang

    David Rittenhouse Laboratories, University of Pennsylvania, Philadelphia, United States
    For correspondence
    louis.kang@berkeley.edu
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-5702-2740
  2. Vijay Balasubramanian

    Department of Physics, University of Pennsylvania, Philadelphia, United States
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-6497-3819

Funding

Honda Research Institute

  • Vijay Balasubramanian

National Science Foundation (PHY-1734030)

  • Vijay Balasubramanian

Adolph C. and Mary Sprague Miller Institute for Basic Research in Science, University of California Berkeley (Postdoctoral fellowship)

  • Louis Kang

National Institutes of Health (Medical Scientist Training Program)

  • Louis Kang

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Reviewing Editor

  1. Upinder Singh Bhalla, Tata Institute of Fundamental Research, India

Publication history

  1. Received: March 8, 2019
  2. Accepted: August 1, 2019
  3. Accepted Manuscript published: August 2, 2019 (version 1)
  4. Version of Record published: October 3, 2019 (version 2)

Copyright

© 2019, Kang & Balasubramanian

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

  • 1,779
    Page views
  • 274
    Downloads
  • 12
    Citations

Article citation count generated by polling the highest count across the following sources: Crossref, PubMed Central, Scopus.

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. Louis Kang
  2. Vijay Balasubramanian
(2019)
A geometric attractor mechanism for self-organization of entorhinal grid modules
eLife 8:e46687.
https://doi.org/10.7554/eLife.46687
  1. Further reading

Further reading

    1. Neuroscience
    Saloni Krishnan, Gabriel J Cler ... Kate E Watkins
    Research Article

    Developmental language disorder (DLD) is a common neurodevelopmental disorder characterised by receptive or expressive language difficulties or both. While theoretical frameworks and empirical studies support the idea that there may be neural correlates of DLD in frontostriatal loops, findings are inconsistent across studies. Here, we use a novel semiquantitative imaging protocol – multi-parameter mapping (MPM) – to investigate microstructural neural differences in children with DLD. The MPM protocol allows us to reproducibly map specific indices of tissue microstructure. In 56 typically developing children and 33 children with DLD, we derived maps of (1) longitudinal relaxation rate R1 (1/T1), (2) transverse relaxation rate R2* (1/T2*), and (3) Magnetization Transfer saturation (MTsat). R1 and MTsat predominantly index myelin, while R2* is sensitive to iron content. Children with DLD showed reductions in MTsat values in the caudate nucleus bilaterally, as well as in the left ventral sensorimotor cortex and Heschl’s gyrus. They also had globally lower R1 values. No group differences were noted in R2* maps. Differences in MTsat and R1 were coincident in the caudate nucleus bilaterally. These findings support our hypothesis of corticostriatal abnormalities in DLD and indicate abnormal levels of myelin in the dorsal striatum in children with DLD.

    1. Neuroscience
    Marie Chancel, H Henrik Ehrsson, Wei Ji Ma
    Research Article

    Many studies have investigated the contributions of vision, touch, and proprioception to body ownership, i.e., the multisensory perception of limbs and body parts as our own. However, the computational processes and principles that determine subjectively experienced body ownership remain unclear. To address this issue, we developed a detection-like psychophysics task based on the classic rubber hand illusion paradigm where participants were asked to report whether the rubber hand felt like their own (the illusion) or not. We manipulated the asynchrony of visual and tactile stimuli delivered to the rubber hand and the hidden real hand under different levels of visual noise. We found that (1) the probability of the emergence of the rubber hand illusion increased with visual noise and was well predicted by a causal inference model involving the observer computing the probability of the visual and tactile signals coming from a common source; (2) the causal inference model outperformed a non-Bayesian model involving the observer not taking into account sensory uncertainty; (3) by comparing body ownership and visuotactile synchrony detection, we found that the prior probability of inferring a common cause for the two types of multisensory percept was correlated but greater for ownership, which suggests that individual differences in rubber hand illusion can be explained at the computational level as differences in how priors are used in the multisensory integration process. These results imply that the same statistical principles determine the perception of the bodily self and the external world.