Probable nature of higher-dimensional symmetries underlying mammalian grid-cell activity patterns

  1. Alexander Mathis  Is a corresponding author
  2. Martin B Stemmler
  3. Andreas V M Herz
  1. Harvard University, United States
  2. Ludwig-Maximilians-Universität München, Germany

Abstract

Lattices abound in nature - from the crystal structure of minerals to the honey-comb organization of ommatidia in the compound eye of insects. These arrangements provide solutions for optimal packings, efficient resource distribution and cryptographic protocols. Do lattices also play a role in how the brain represents information? We focus on higher-dimensional stimulus domains, with particular emphasis on neural representations of physical space, and derive which neuronal lattice codes maximize spatial resolution. For mammals navigating on a surface, we show that the hexagonal activity patterns of grid cells are optimal. For species that move freely in a 3D a face-centered cubic lattice is best. This prediction could be tested experimentally in flying bats, arboreal monkeys, or marine mammals. More generally, our theory suggests that the brain encodes higher-dimensional sensory or cognitive variables with populations of grid-cell-like neurons whose activity patterns exhibit lattice structures at multiple, nested scales.

Article and author information

Author details

  1. Alexander Mathis

    Department of Molecular and Cellular Biology, Harvard University, Cambridge, United States
    For correspondence
    amathis@fas.harvard.edu
    Competing interests
    The authors declare that no competing interests exist.
  2. Martin B Stemmler

    Bernstein Center for Computational Neuroscience, Ludwig-Maximilians-Universität München, München, Germany
    Competing interests
    The authors declare that no competing interests exist.
  3. Andreas V M Herz

    Bernstein Center for Computational Neuroscience Munich, Ludwig-Maximilians-Universität München, München, Germany
    Competing interests
    The authors declare that no competing interests exist.

Reviewing Editor

  1. Mark S. Goldman, University of California at Davis, United States

Version history

  1. Received: December 9, 2014
  2. Accepted: April 23, 2015
  3. Accepted Manuscript published: April 24, 2015 (version 1)
  4. Version of Record published: June 4, 2015 (version 2)

Copyright

© 2015, Mathis 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

  • 3,980
    Page views
  • 716
    Downloads
  • 28
    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. Alexander Mathis
  2. Martin B Stemmler
  3. Andreas V M Herz
(2015)
Probable nature of higher-dimensional symmetries underlying mammalian grid-cell activity patterns
eLife 4:e05979.
https://doi.org/10.7554/eLife.05979

Share this article

https://doi.org/10.7554/eLife.05979

Further reading

    1. Cancer Biology
    2. Computational and Systems Biology
    Bingrui Li, Fernanda G Kugeratski, Raghu Kalluri
    Research Article

    Non-invasive early cancer diagnosis remains challenging due to the low sensitivity and specificity of current diagnostic approaches. Exosomes are membrane-bound nanovesicles secreted by all cells that contain DNA, RNA, and proteins that are representative of the parent cells. This property, along with the abundance of exosomes in biological fluids makes them compelling candidates as biomarkers. However, a rapid and flexible exosome-based diagnostic method to distinguish human cancers across cancer types in diverse biological fluids is yet to be defined. Here, we describe a novel machine learning-based computational method to distinguish cancers using a panel of proteins associated with exosomes. Employing datasets of exosome proteins from human cell lines, tissue, plasma, serum, and urine samples from a variety of cancers, we identify Clathrin Heavy Chain (CLTC), Ezrin, (EZR), Talin-1 (TLN1), Adenylyl cyclase-associated protein 1 (CAP1), and Moesin (MSN) as highly abundant universal biomarkers for exosomes and define three panels of pan-cancer exosome proteins that distinguish cancer exosomes from other exosomes and aid in classifying cancer subtypes employing random forest models. All the models using proteins from plasma, serum, or urine-derived exosomes yield AUROC scores higher than 0.91 and demonstrate superior performance compared to Support Vector Machine, K Nearest Neighbor Classifier and Gaussian Naive Bayes. This study provides a reliable protein biomarker signature associated with cancer exosomes with scalable machine learning capability for a sensitive and specific non-invasive method of cancer diagnosis.

    1. Computational and Systems Biology
    2. Immunology and Inflammation
    Alain Pulfer, Diego Ulisse Pizzagalli ... Santiago Fernandez Gonzalez
    Tools and Resources

    Intravital microscopy has revolutionized live-cell imaging by allowing the study of spatial–temporal cell dynamics in living animals. However, the complexity of the data generated by this technology has limited the development of effective computational tools to identify and quantify cell processes. Amongst them, apoptosis is a crucial form of regulated cell death involved in tissue homeostasis and host defense. Live-cell imaging enabled the study of apoptosis at the cellular level, enhancing our understanding of its spatial–temporal regulation. However, at present, no computational method can deliver robust detection of apoptosis in microscopy timelapses. To overcome this limitation, we developed ADeS, a deep learning-based apoptosis detection system that employs the principle of activity recognition. We trained ADeS on extensive datasets containing more than 10,000 apoptotic instances collected both in vitro and in vivo, achieving a classification accuracy above 98% and outperforming state-of-the-art solutions. ADeS is the first method capable of detecting the location and duration of multiple apoptotic events in full microscopy timelapses, surpassing human performance in the same task. We demonstrated the effectiveness and robustness of ADeS across various imaging modalities, cell types, and staining techniques. Finally, we employed ADeS to quantify cell survival in vitro and tissue damage in mice, demonstrating its potential application in toxicity assays, treatment evaluation, and inflammatory dynamics. Our findings suggest that ADeS is a valuable tool for the accurate detection and quantification of apoptosis in live-cell imaging and, in particular, intravital microscopy data, providing insights into the complex spatial–temporal regulation of this process.