1. Neuroscience
  2. Physics of Living Systems
Download icon

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
Research Article
  • Cited 5
  • Views 1,253
  • Annotations
Cite this article as: eLife 2019;8:e46687 doi: 10.7554/eLife.46687

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.

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

  • 1,253
    Page views
  • 202
    Downloads
  • 5
    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)

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

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

Further reading

    1. Cell Biology
    2. Neuroscience
    Antonietta Franco et al.
    Research Article

    Charcot-Marie-Tooth disease type 2A (CMT2A) is an untreatable childhood peripheral neuropathy caused by mutations of the mitochondrial fusion protein, mitofusin (MFN) 2. Here, pharmacological activation of endogenous normal mitofusins overcame dominant inhibitory effects of CMT2A mutants in reprogrammed human patient motor neurons, reversing hallmark mitochondrial stasis and fragmentation independent of causal MFN2 mutation. In mice expressing human MFN2 T105M, intermittent mitofusin activation with a small molecule, MiM111, normalized CMT2A neuromuscular dysfunction, reversed pre-treatment axon and skeletal myocyte atrophy, and enhanced axon regrowth by increasing mitochondrial transport within peripheral axons and promoting in vivo mitochondrial localization to neuromuscular junctional synapses. MiM111-treated MFN2 T105M mouse neurons exhibited accelerated primary outgrowth and greater post-axotomy regrowth, linked to enhanced mitochondrial motility. MiM111 is the first pre-clinical candidate for CMT2A.

    1. Neuroscience
    Chang-Hao Kao et al.
    Research Article

    Effective learning requires using errors in a task-dependent manner, for example adjusting to errors that result from unpredicted environmental changes but ignoring errors that result from environmental stochasticity. Where and how the brain represents errors in a task-dependent manner and uses them to guide behavior are not well understood. We imaged the brains of human participants performing a predictive-inference task with two conditions that had different sources of errors. Their performance was sensitive to this difference, including more choice switches after fundamental changes versus stochastic fluctuations in reward contingencies. Using multi-voxel pattern classification, we identified task-dependent representations of error magnitude and past errors in posterior parietal cortex. These representations were distinct from representations of the resulting behavioral adjustments in dorsomedial frontal, anterior cingulate, and orbitofrontal cortex. The results provide new insights into how the human brain represents errors in a task-dependent manner and guides subsequent adaptive behavior.