A principle of economy predicts the functional architecture of grid cells

  1. Xue-xin Wei
  2. Jason Prentice
  3. Vijay Balasubramanian  Is a corresponding author
  1. University of Pennsylvania, United States
  2. Princeton University, United States

Abstract

Grid cells in the brain respond when an animal occupies a periodic lattice of 'grid fields' during navigation. Grids are organized in modules with different periodicity. We propose that the grid system implements a hierarchical code for space that economizes the number of neurons required to encode location with a given resolution across a range equal to the largest period. This theory predicts: (i) grid fields should lie on a triangular lattice, (ii) grid scales should follow a geometric progression, (iii) the ratio between adjacent grid scales should be e^1/2 for idealized neurons, and lie between 1.4-1.7 for realistic neurons, (iv) the scale ratio should vary modestly within and between animals. These results explain the measured grid structure in rodents. We also predict optimal organization in one and three dimensions, the number of modules, and, with added assumptions, the ratio between grid periods and field widths.

Article and author information

Author details

  1. Xue-xin Wei

    Department of Psychology, University of Pennsylvania, Philadelphia, United States
    Competing interests
    The authors declare that no competing interests exist.
  2. Jason Prentice

    Princeton Neuroscience Institute, Princeton University, Princeton, United States
    Competing interests
    The authors declare that no competing interests exist.
  3. Vijay Balasubramanian

    Department of Physics, University of Pennsylvania, Philadelphia, United States
    For correspondence
    vijay@physics.upenn.edu
    Competing interests
    The authors declare that no competing interests exist.

Reviewing Editor

  1. Frances K Skinner, University Health Network, Canada

Version history

  1. Received: April 27, 2015
  2. Accepted: September 1, 2015
  3. Accepted Manuscript published: September 3, 2015 (version 1)
  4. Version of Record published: October 23, 2015 (version 2)

Copyright

© 2015, Wei et al.

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

  • 3,261
    views
  • 668
    downloads
  • 53
    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. Xue-xin Wei
  2. Jason Prentice
  3. Vijay Balasubramanian
(2015)
A principle of economy predicts the functional architecture of grid cells
eLife 4:e08362.
https://doi.org/10.7554/eLife.08362

Share this article

https://doi.org/10.7554/eLife.08362

Further reading

    1. Neuroscience
    Yu-Feng Xie, Jane Yang ... Steven A Prescott
    Research Article

    Nociceptive sensory neurons convey pain-related signals to the CNS using action potentials. Loss-of-function mutations in the voltage-gated sodium channel NaV1.7 cause insensitivity to pain (presumably by reducing nociceptor excitability) but clinical trials seeking to treat pain by inhibiting NaV1.7 pharmacologically have struggled. This may reflect the variable contribution of NaV1.7 to nociceptor excitability. Contrary to claims that NaV1.7 is necessary for nociceptors to initiate action potentials, we show that nociceptors can achieve similar excitability using different combinations of NaV1.3, NaV1.7, and NaV1.8. Selectively blocking one of those NaV subtypes reduces nociceptor excitability only if the other subtypes are weakly expressed. For example, excitability relies on NaV1.8 in acutely dissociated nociceptors but responsibility shifts to NaV1.7 and NaV1.3 by the fourth day in culture. A similar shift in NaV dependence occurs in vivo after inflammation, impacting ability of the NaV1.7-selective inhibitor PF-05089771 to reduce pain in behavioral tests. Flexible use of different NaV subtypes exemplifies degeneracy – achieving similar function using different components – and compromises reliable modulation of nociceptor excitability by subtype-selective inhibitors. Identifying the dominant NaV subtype to predict drug efficacy is not trivial. Degeneracy at the cellular level must be considered when choosing drug targets at the molecular level.

    1. Neuroscience
    Mischa Vance Bandet, Ian Robert Winship
    Research Article

    Despite substantial progress in mapping the trajectory of network plasticity resulting from focal ischemic stroke, the extent and nature of changes in neuronal excitability and activity within the peri-infarct cortex of mice remains poorly defined. Most of the available data have been acquired from anesthetized animals, acute tissue slices, or infer changes in excitability from immunoassays on extracted tissue, and thus may not reflect cortical activity dynamics in the intact cortex of an awake animal. Here, in vivo two-photon calcium imaging in awake, behaving mice was used to longitudinally track cortical activity, network functional connectivity, and neural assembly architecture for 2 months following photothrombotic stroke targeting the forelimb somatosensory cortex. Sensorimotor recovery was tracked over the weeks following stroke, allowing us to relate network changes to behavior. Our data revealed spatially restricted but long-lasting alterations in somatosensory neural network function and connectivity. Specifically, we demonstrate significant and long-lasting disruptions in neural assembly architecture concurrent with a deficit in functional connectivity between individual neurons. Reductions in neuronal spiking in peri-infarct cortex were transient but predictive of impairment in skilled locomotion measured in the tapered beam task. Notably, altered neural networks were highly localized, with assembly architecture and neural connectivity relatively unaltered a short distance from the peri-infarct cortex, even in regions within ‘remapped’ forelimb functional representations identified using mesoscale imaging with anaesthetized preparations 8 weeks after stroke. Thus, using longitudinal two-photon microscopy in awake animals, these data show a complex spatiotemporal relationship between peri-infarct neuronal network function and behavioral recovery. Moreover, the data highlight an apparent disconnect between dramatic functional remapping identified using strong sensory stimulation in anaesthetized mice compared to more subtle and spatially restricted changes in individual neuron and local network function in awake mice during stroke recovery.