Grid cells and cortical representation

Journal name:
Nature Reviews Neuroscience
Year published:
Published online


One of the grand challenges in neuroscience is to comprehend neural computation in the association cortices, the parts of the cortex that have shown the largest expansion and differentiation during mammalian evolution and that are thought to contribute profoundly to the emergence of advanced cognition in humans. In this Review, we use grid cells in the medial entorhinal cortex as a gateway to understand network computation at a stage of cortical processing in which firing patterns are shaped not primarily by incoming sensory signals but to a large extent by the intrinsic properties of the local circuit.

At a glance


  1. Basic properties of grid cells.
    Figure 1: Basic properties of grid cells.

    a | Spatial firing pattern of a grid cell from layer II of the rat medial entorhinal cortex (MEC). The grey trace shows the trajectory of a foraging rat in a 2.2 m wide square enclosure. The locations at which the grid cell spikes are superimposed on the trajectory are shown in black. Each black dot corresponds to one spike. Note the periodic hexagonal pattern of the firing fields of the grid cell. b | Cartoons of firing patterns of pairs of grid cells (shown in blue and green), illustrating the differences between grid scale, grid orientation and grid phase. Lines in left and middle panels indicate two axes of the grid pattern (which define grid orientation); crosses in the panel on the right indicate grid phase (xy location of grid fields). c | Modular organization of the grid scale. Grid spacing is shown as a function of position along the recording track in the MEC, with cells (represented by grey circles) rank-ordered from dorsal to ventral and one panel per tetrode (TT). On each tetrode, grid spacing increases in discrete steps. d | A schematic showing that the increase in grid scale across modules follows a geometric progression rule. From one module to the next, average grid scale increases by a constant factor (1.4 in this case). Part a is reprinted from Moser, E. I. & Moser, M. B. Grid cells and neural coding in high-end cortices. Neuron 80, 765774 (2013)229. Copyright (2013), with permission from Elsevier. Part c from Ref. 24, Nature Publishing Group.

  2. Excitatory and inhibitory attractor models for grid cells.
    Figure 2: Excitatory and inhibitory attractor models for grid cells.

    ac | A variety of connectivity patterns have been used in attractor models of grid cells to generate hexagonal firing patterns. These include the Mexican hat connectivity used by Fuhs and Touretzky100 (part a), the Mexican hat-like connectivity of Burak and Fiete101 (part b) and the step-like inhibitory connectivity used by Couey et al.107 (part c). The connectivity patterns differ in the complexity of the phase dependence of the synaptic weights. In models with Mexican hat connectivity, cells have progressively decreasing excitatory connections combined with increasing inhibitory connections, whereas the Mexican hat-like connectivity model and the step-like connectivity model use purely inhibitory connections, although the inhibitory fields have different shapes. All three connectivity patterns produce a hexagonal grid pattern. d | The step-like connectivity model leads to the spontaneous formation of a hexagonal grid pattern. Successive sheets illustrate the network at different developmental stages (0 to 500 ms), with individual pixels corresponding to individual neurons and neurons arranged according to grid phase in each sheet. Activity of neurons is colour-coded, as indicated by the scale bar. Connection radii R of two example neurons are shown as white and green circles (diameter 2R). e | Single-neuron activity (red dots) in a circular arena from the simulation in part d. W0 is the strength of the inhibitory connectivity. It can be seen that W0 and R control the size of the grid fields and their spacing. f | External excitatory drive is necessary for grid formation. Spike distribution plots (on the left, as in part e) and directional tuning curves (firing rate as a function of direction, on the right) with strong excitatory output and weak excitatory output. When the external input drops below a critical amount, the activity on the neuronal sheet is vulnerable to distortions, and the hexagonal structure is not detectable in time-averaged plots. At the same time, head direction input becomes the dominant source of input and cells become directional. Parts d and e from Ref. 107, Nature Publishing Group. Part f from Ref. 109, Nature Publishing Group.


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  1. Kavli Institute for Systems Neuroscience and Centre for Neural Computation, Norwegian University of Science and Technology, 7491 Trondheim, Norway.

    • Edvard I. Moser,
    • Yasser Roudi,
    • Menno P. Witter,
    • Clifford Kentros,
    • Tobias Bonhoeffer &
    • May-Britt Moser
  2. Institute of Neuroscience, University of Oregon, Eugene, Oregon 97403-1254, USA.

    • Clifford Kentros
  3. Max Planck Institute of Neurobiology, Am Klopferspitz 18, 82152 Planegg-Martinsried, Germany.

    • Tobias Bonhoeffer

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The authors declare no competing interests.

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Author details

  • Edvard I. Moser

    Edvard I. Moser received his Ph.D. on the mechanisms of memory formation in the hippocampus in 1995 at the University of Oslo, Norway, under the supervision of Per Andersen. After short postdoctoral training with Richard Morris and John O'Keefe, he started his own laboratory, jointly with May-Britt Moser, at the Norwegian University of Science and Technology, Trondheim, in 1996. In 2002, he became the Founding Director of the Centre for the Biology of Memory and in 2007 the Founding Director of the Kavli Institute for Systems Neuroscience. He is interested in how spatial location and spatial memory are computed in the brain. His work, conducted mostly with May-Britt Moser, includes the discovery of grid cells in the entorhinal cortex. Subsequent to this discovery, the Mosers have identified additional space-representing cell types in the entorhinal cortex, and they are beginning to unravel how the neural microcircuit is organized. For more information, see the Kavli Institute for Systems Neuroscience Centre for Neural Computation website.

  • Yasser Roudi

    Yasser Roudi studied at Sharif University of Technology in Tehran, Iran, and SISSA (The International School for Advanced Studies) in Trieste, Italy, where he obtained his Ph.D. in 2005 with Alessandro Treves, working on statistical mechanics of neural networks. After postdoctoral training with Peter Latham at the Gatsby Computational Neuroscience Unit of University College London, UK, he accepted a fellowship at NORDITA, the Nordic Institute for Theoretical Physics, in Stockholm, Sweden, in 2008. During this period, together with John Hertz, he mainly worked on problems at the interface of statistical mechanics and inference. In 2010, he moved to the Kavli Institute for Systems Neuroscience at the Norwegian University of Science and Technology, Trondheim, where he established a new research group. His research has two main branches: the use of methods from statistical mechanics for modelling and inference in high-throughput biological data, and the development of network models to explain the properties of grid cells and other functional cell types. For more information, see the Kavli Institute for Systems Neuroscience Centre for Neural Computation website.

  • Menno P. Witter

    Menno P. Witter received his Ph.D. from the VU University in Amsterdam, the Netherlands, where he subsequently started his independent research, continuing to work on the anatomical organization of the hippocampal region. He trained with David Amaral at the Salk Institute for Biological Studies, San Diego, California, USA, and Gary Van Hoesen at the University of Iowa, Iowa City, USA. In his early work, he postulated the existence of functional differentiations within both the hippocampus and the entorhinal cortex. He joined May-Britt Moser and Edvard I. Moser as a visiting professor at the Kavli Institute for Systems Neuroscience at the Norwegian University of Science and Technology, Trondheim, in 2007, concluding a productive collaborative period that led to the discovery of grid cells. Recent research has resulted in the discovery of the inhibitory network between putative grid cells. His current research focuses on the functional architecture of the lateral and medial entorhinal cortex. He is currently Chair of the Norwegian Research School in Neuroscience. For more information, see the Kavli Institute for Systems Neuroscience Centre for Neural Computation website.

  • Clifford Kentros

    Clifford Kentros obtained his Ph.D. on potassium channels with Bernardo Rudy at New York University, USA. During his postdoctoral work with Robert Muller at the State University of New York Health Science Center, Brooklyn, USA, and Eric Kandel at Columbia University, New York, USA, he investigated the relationship between place cells and memory. His subsequent research has taken advantage of his dual molecular and neurophysiological background. He has combined the anatomical specificity of molecular genetics with in vivo electrophysiological recordings and anatomical analysis, first at the University of Oregon, Eugene, USA, and now at the Kavli Institute of Systems Neuroscience at the Norwegian University of Science and Technology, Trondheim. The laboratory uses mice that are capable of driving the expression of transgenes in particular subsets of neurons in brain areas involved in learning and memory to determine their precise connectivity and to modulate their neural activity while recording from other cell types. In this way, the laboratory investigates the anatomical and functional circuitry underlying learning and memory. For more information, see the Kavli Institute for Systems Neuroscience Centre for Neural Computation website.

  • Tobias Bonhoeffer

    Tobias Bonhoeffer received his Ph.D. in neuroscience for research that he did at the Max Planck Institute (MPI) for Biological Cybernetics in Tübingen, Germany. After 2 years of postdoctoral training with Amiram Grinvald and Torsten Wiesel at the Rockefeller University in New York, USA, he returned to Germany and worked in the laboratory of Wolf Singer at the MPI for Brain Research in Frankfurt, Germany. In 1993, he started his own laboratory at the MPI of Neurobiology in Munich, Germany. Five years later, he became Director at that institute and subsequently was made professor of the Ludwig Maximilians University in Munich. Throughout his career, Tobias Bonhoeffer has been interested in how information is represented and stored in the brain and how this representation is affected by experience in the sensory environment. Among other things, he is well known for his discovery of the pinwheel arrangement of orientation domains in the primary visual cortex of higher mammals and the demonstration that functional synaptic plasticity entails structural changes at the level of dendritic spines. Since 2014, he is a visiting professor at the Norwegian University of Science and Technology, Trondheim. Tobias Bonhoeffer's homepage.

  • May-Britt Moser

    May-Britt Moser received her Ph.D. on the structural basis of hippocampal memory in 1995 at the University of Oslo, Norway, under the supervision of Per Andersen. After short postdoctoral training with Richard Morris and John O'Keefe, she started her own laboratory, jointly with Edvard I. Moser, at the Norwegian University of Science and Technology, Trondheim in 1996. She has been the Vice Director of the Centre for the Biology of Memory (2002–2012) and the Kavli Institute for Systems Neuroscience (since 2007) and in 2013 became the Founding Director of the Centre for Neural Computation. Her research, conducted with Edvard I. Moser as a long-term collaborator, includes the discovery of grid cells as well as other functional cell types of the spatial representation system in the entorhinal cortex. Her current research includes studies of how grid cells develop and their relationship with memory. For more information, see the Kavli Institute for Systems Neuroscience Centre for Neural Computation website.

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