Key Points
-
Cortical representations recreate features of the outside world in a language that is suitable for brain computation. Such representations exist at different levels of complexity, ranging from the relatively simple transformations of the spatial organization of peripheral sensory receptors found in primary sensory cortices to representations with no discernible relationship to properties of any sensory receptor population at higher hierarchical levels of the cortex. Grid cells in the medial entorhinal cortex (MEC) are examples of a high-level cortical representation.
-
Pattern formation and transformation processes in the well-studied primary visual cortex may provide clues as to how neural circuit computation occurs in the entorhinal cortex.
-
Grid cells are spatially modulated cells with periodic hexagonally spaced firing fields. They have been identified in and around the MEC in several mammalian species. Grid cells provide a window into neural circuit computation in higher-level association cortices, as they are many synapses away from both sensory receptors and motor output.
-
Grid cells provide the entorhinal–hippocampal spatial map with a metric. The regular structure of the grid pattern is likely to depend on path integration.
-
Grid cells simultaneously exhibit topographic and non-topographic organization. Firing location is non-topographic, whereas the grid scale changes in discrete but overlapping steps along the dorsoventral MEC axis. The entangled organization of grid modules differs from the continuous arrangement of many variables represented in sensory cortices.
-
Many properties of grid cells point to a continuous attractor network mechanism for the formation of hexagonal firing patterns. The exact implementation of such a mechanism remains elusive. Although continuous attractor networks rely on preferential and asymmetrical connections between grid cells with similar but not identical grid phases, such connections have yet to be demonstrated experimentally.
-
Grid cells provide a major spatial input to hippocampal place cells but border cells may also contribute. The mechanism for the transformation of the apparently universal entorhinal representation of space to environmentally- specific hippocampal spatial representations may involve local circuit mechanisms as well as plasticity. Teasing apart the relative contributions and dynamics of entorhinal inputs to hippocampal place cells remains one of the most intriguing challenges in the field.
Abstract
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.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$189.00 per year
only $15.75 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Felleman, D. J. & van Essen, D. C. Distributed hierarchical processing in the primate cerebral cortex. Cereb. Cortex 1, 1–47 (1991).
O'Keefe, J. & Nadel, L. The Hippocampus as a Cognitive Map (Clarendon, 1978). A seminal book proposing hippocampal place cells as the basis of a 'cognitive map' of the animal's external environment. The cognitive map is suggested to be critical for navigation and to provide a basis for memory more generally.
McNaughton, B. L., Battaglia, F. P., Jensen, O., Moser, E. I. & Moser, M. B. Path integration and the neural basis of the 'cognitive map'. Nature Rev. Neurosci. 7, 663–678 (2006). Along with Fuhs and Touretzky (reference 100), this paper is the first to propose that Turing pattern formation and continuous attractors informed by phase-dependent neural connectivity are the underlying mechanism of grid cells.
Moser, E. I., Kropff, E. & Moser, M.-B. Place cells, grid cells, and the brain's spatial representation system. Annu. Rev. Neurosci. 31, 69–89 (2008).
O'Keefe, J. & Dostrovsky, J. The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat. Brain Res. 34, 171–175 (1971). The paper that started it all: the first description (albeit mainly qualitative) of hippocampal place cells.
O'Keefe, J. Place units in the hippocampus of the freely moving rat. Exp. Neurol. 51, 78–109 (1976).
Fyhn, M., Molden, S., Witter, M. P., Moser, E. I. & Moser, M. B. Spatial representation in the entorhinal cortex. Science 305, 1258–1264 (2004).
Hafting, T., Fyhn, M., Molden, S., Moser, M.-B. & Moser, E. I. Microstructure of a spatial map in the entorhinal cortex. Nature 436, 801–806 (2005). The discovery of the second distinct kind of receptive field representing external space — the grid cells of the MEC. Grid cells are proposed as the basis for a path integration-dependent attractor network-dependent metric representation of the spatial environment.
Sargolini, F. et al. Conjunctive representation of position, direction, and velocity in entorhinal cortex. Science 312, 758–762 (2006).
Muller, R. U. & Kubie, J. L. The effects of changes in the environment on the spatial firing of hippocampal complex-spike cells. J. Neurosci. 7, 1951–1968 (1987).
Colgin, L. L., Moser, E. I. & Moser, M.-B. Understanding memory through hippocampal remapping. Trends Neurosci. 31, 469–477 (2008).
Fyhn, M., Hafting, T., Treves, A., Moser, M.-B. & Moser, E. I. Hippocampal remapping and grid realignment in entorhinal cortex. Nature 446, 190–194 (2007).
Rotenberg, A., Mayford, M., Hawkins, R. D., Kandel, E. R. & Muller, R. U. Mice expressing activated CaMKII lack low frequency LTP and do not form stable place cells in the CA1 region of the hippocampus. Cell 87, 1351–1361 (1996).
McHugh, T. J., Blum, K. I., Tsien, J. Z., Tonegawa, S. & Wilson, M. A. Impaired hippocampal representation of space in CA1-specific NMDAR1 knockout mice. Cell 87, 1339–1349 (1996).
Fyhn, M., Hafting, T., Witter, M. P., Moser, E. I. & Moser, M.-B. Grid cells in mice. Hippocampus 18, 1230–1238 (2008).
Ulanovsky, N. & Moss, C. F. Hippocampal cellular and network activity in freely moving echolocating bats. Nature Neurosci. 10, 224–233 (2007).
Yartsev, M. M., Witter, M. P. & Ulanovsky, N. Grid cells without theta oscillations in the entorhinal cortex of bats. Nature 479, 103–107 (2011).
Ono, T., Nakamura, K., Nishijo, H. & Eifuku, S. Monkey hippocampal neurons related to spatial and nonspatial functions. J. Neurophysiol. 70, 1516–1529 (1993).
Rolls, E. T. & O'Mara, S. M. View-responsive neurons in the primate hippocampal complex. Hippocampus 5, 409–424 (1995).
Rolls, E. T., Robertson, R. G. & Georges-François, P. Spatial view cells in the primate hippocampus. Eur. J. Neurosci. 9, 1789–1794 (1997).
Killian, N. J., Jutras, M. J. & Buffalo, E. A. A map of visual space in the primate entorhinal cortex. Nature 491, 761–764 (2012).
Ekstrom, A. D. et al. Cellular networks underlying human spatial navigation. Nature 425, 184–188 (2003).
Jacobs, J. et al. Direct recordings of grid-like neuronal activity in human spatial navigation. Nature Neurosci. 16, 1188–1190 (2013).
Stensola, H. et al. The entorhinal grid map is discretized. Nature 492, 72–78 (2012). This study shows that grid cells are arranged in discrete, relatively autonomous 'modules' rather than in a smooth topographic representation such as those found in sensory cortices.
Barry, C., Hayman, R., Burgess, N. & Jeffery, K. J. Experience-dependent rescaling of entorhinal grids. Nature Neurosci. 10, 682–684 (2007).
Krupic, J., Burgess, N. & O'Keefe, J. Neural representations of location composed of spatially periodic bands. Science 337, 853–857 (2012).
Mittelstaedt, M. L. & Mittelstaedt, H. Homing by path integration in a mammal. Naturwissenschaften 67, 566–567 (1980).
Müller, M. & Wehner, R. Path integration in desert ants, Cataglyphis fortis. Proc. Natl Acad. Sci. USA 85, 5287–5290 (1988).
Etienne, A. S. & Jeffery, K. J. Path integration in mammals. Hippocampus 14, 180–192 (2004).
Gothard, K. M., Skaggs, W. E. & McNaughton, B. L. Dynamics of mismatch correction in the hippocampal ensemble code for space: interaction between path integration and environmental cues. J. Neurosci. 16, 8027–8040 (1996).
McNaughton, B. L. et al. Deciphering the hippocampal polyglot: the hippocampus as a path integration system. J. Exp. Biol. 199, 173–185 (1996).
Derdikman, D. et al. Fragmentation of grid maps in a multicompartment environment. Nature Neurosci. 12, 1325–1332 (2009).
Chen, G., King, J. A., Burgess, N. & O'Keefe, J. How vision and movement combine in the hippocampal place code. Proc. Natl Acad. Sci. USA 110, 378–383 (2013).
Ravassard, P. et al. Multisensory control of hippocampal spatiotemporal selectivity. Science 340, 1342–1346 (2013).
Kropff Causa, E., Carmichael, J. E., Baldi, R., Moser, M.-B. & Moser, E. I. Modulation of hippocampal and entorhinal theta frequency by running speed and acceleration. Soc. Neurosci.Abstr. 39, 769.09 (2013).
Parron, C. & Save, E. Evidence for entorhinal and parietal cortices involvement in path integration in the rat. Exp. Brain Res. 159, 349–359 (2004).
Kim, S., Sapiurka, M., Clark, R. E. & Squire, L. R. Contrasting effects on path integration after hippocampal damage in humans and rats. Proc. Natl Acad. Sci. USA 110, 4732–4737 (2013).
Shrager, Y., Kirwan, C. B. & Squire, L. R. Neural basis of the cognitive map: path integration does not require hippocampus or entorhinal cortex. Proc. Natl Acad. Sci. USA 105, 12034–12038 (2008).
Biegler, R. Possible uses of path integration in animal navigation. Animal Learn. Behav. 28, 257–277 (2000).
Brun, V. H. et al. Progressive increase in grid scale from dorsal to ventral medial entorhinal cortex. Hippocampus 18, 1200–1212 (2008).
Illig, K. R. & Haberly, L. B. Odor-evoked activity is spatially distributed in piriform cortex. J. Comp. Neurol. 457, 361–373 (2003).
Stettler, D. D. & Axel, R. Representations of odor in the piriform cortex. Neuron 63, 854–864 (2009).
Ohki, K., Chung, S., Ch'ng, Y. H., Kara, P. & Reid, R. C. Functional imaging with cellular resolution reveals precise micro-architecture in visual cortex. Nature 433, 597–603 (2005).
Van Hooser, S. D., Heimel, J. A., Chung, S., Nelson, S. B. & Toth, L. J. Orientation selectivity without orientation maps in visual cortex of a highly visual mammal. J. Neurosci. 25, 19–28 (2005).
Bonin, V., Histed, M. H., Yurgenson, S. & Reid, R. C. Local diversity and fine-scale organization of receptive fields in mouse visual cortex. J. Neurosci. 31, 18506–18521 (2011).
Gray, C. M., Maldonado, P. E., Wilson, M. & McNaughton, B. Tetrodes markedly improve the reliability and yield of multiple single-unit isolation from multi-unit recordings in cat striate cortex. J. Neurosci. Methods 63, 43–54 (1995).
Dombeck, D. A., Harvey, C. D., Tian, L., Looger, L. L. & Tank, D. W. Functional imaging of hippocampal place cells at cellular resolution during virtual navigation. Nature Neurosci. 13, 1433–1440 (2010).
Ziv, L. et al. Long-term dynamics of CA1 hippocampal place codes. Nature Neurosci. 16, 264–266 (2013).
Mathis, A., Herz, A. V. & Stemmler, M. Optimal population codes for space: grid cells outperform place cells. Neural Comput. 24, 2280–2317 (2012).
Wei, X.-X., Prentice, J. & Balasubramanian, V. The sense of place: grid cells in the brain and the transcendental number e. [online], (2013).
Ratliff, C. P., Borghuis, B. G., Kao, Y. H., Sterling, P. & Balasubramanian, V. Retina is structured to process an excess of darkness in natural scenes. Proc. Natl Acad. Sci. USA 107, 17368–17373 (2010).
Chapman, B., Stryker, M. P. & Bonhoeffer, T. Development of orientation preference maps in ferret primary visual cortex. J. Neurosci. 16, 6443–6453 (1996).
Li, Y., Fitzpatrick, D. & White, L. E. The development of direction selectivity in ferret visual cortex requires early visual experience. Nature Neurosci. 9, 676–681 (2006).
Ko, H. et al. The emergence of functional microcircuits in visual cortex. Nature 496, 96–100 (2013).
Meister, M., Wong, R. O., Baylor, D. A. & Shatz, C. J. Synchronous bursts of action potentials in ganglion cells of the developing mammalian retina. Science 252, 939–943 (1991).
Katz, L. C. & Shatz, C. J. Synaptic activity and the construction of cortical circuits. Science 274, 1133–1138 (1996).
Ackman, J. B., Burbridge, T. J. & Crair, M. C. Retinal waves coordinate patterned activity throughout the developing visual system. Nature 490, 219–225 (2012).
Kirkby, L. A., Sack, G. S., Firl, A. & Feller, M. B. A role for correlated spontaneous activity in the assembly of neural circuits. Neuron 80, 1129–1144 (2013).
Li, Y. et al. Clonally related visual cortical neurons show similar stimulus feature selectivity. Nature 486, 118–121 (2012).
Ohtsuki, G. et al. Similarity of visual selectivity among clonally related neurons in visual cortex. Neuron 75, 65–72 (2012).
Bonhoeffer, T. & Grinvald, A. Orientation columns in cat are organized in pin-wheel like patterns. Nature 353, 429–431 (1991).
Maldonado, P. E., Gödecke, I., Gray, C. M. & Bonhoeffer, T. Orientation selectivity in pinwheel centers in cat striate cortex. Science 276, 1551–1555 (1997).
Ohki, K. et al. Highly ordered arrangement of single neurons in orientation pinwheels. Nature 442, 925–928 (2006).
Hubel, D. H. & Wiesel, T. N. Receptive fields and functional architecture of monkey striate cortex. J. Physiol. 195, 215–243 (1968).
Hubel, D. H. & Wiesel, T. N. Receptive fields and functional architecture in two nonstriate visual areas (18 and 19) of the cat. J. Neurophysiol. 28, 229–289 (1965).
Tootell, R. B., Switkes, E., Silverman, M. S. & Hamilton, S. L. Retinotopic organization. J. Neurosci. 8, 1531–1568 (1988).
Ts'o, D. Y., Frostig, R. D., Lieke, E. E. & Grinvald, A. Functional organization of primate visual cortex revealed by high resolution optical imaging. Science 249, 417–420 (1990).
Shoham, D., Hübener, M., Schulze, S., Grinvald, A. & Bonhoeffer, T. Spatio-temporal frequency domains and their relation to cytochrome oxidase staining in cat visual cortex. Nature 385, 529–533 (1997).
Chen, G., Lu, H. D. & Roe, A. W. A map for horizontal disparity in monkey V2. Neuron 58, 442–450 (2008).
Kara, P. & Boyd, J. D. A micro-architecture for binocular disparity and ocular dominance in visual cortex. Nature 458, 627–631 (2009).
Ranck, J. B. Jr. in Electrical Activity of the Archicortex (eds Buzsáki, G. & Vanderwolf, C. H.) 217–220 (Akademiai Kiado, 1985).
Taube, J. S., Muller, R. U. & Ranck, J. B. Jr. Head-direction cells recorded from the postsubiculum in freely moving rats. I. Description and quantitative analysis. J. Neurosci. 10, 420–435 (1990).
Savelli, F., Yoganarasimha, D. & Knierim, J. J. Influence of boundary removal on the spatial representations of the medial entorhinal cortex. Hippocampus 18, 1270–1282 (2008).
Solstad, T., Boccara, C. N., Kropff, E., Moser, M.-B. & Moser, E. I. Representation of geometric borders in the entorhinal cortex. Science 322, 1865–1868 (2008).
Barry, C. et al. The boundary vector model of place cell firing and spatial memory. Rev. Neurosci. 17, 71–97 (2006).
Lever, C., Burton, S., Jeewajee, A., O'Keefe, J. & Burgess, N. Boundary vector cells in the subiculum of the hippocampal formation. J. Neurosci. 29, 9771–9777 (2009).
Hubel, D. H. & Livingstone, M. S. Segregation of form, color, and stereopsis in primate area 18. J. Neurosci. 7, 3378–3415 (1987).
Yoon, K. et al. Specific evidence of low-dimensional continuous attractor dynamics in grid cells. Nature Neurosci. 16, 1077–1084 (2013).
Barry, C., Ginzberg, L. L., O'Keefe, J. & Burgess, N. Grid cell firing patterns signal environmental novelty by expansion. Proc. Natl Acad. Sci. USA 109, 17687–17692 (2013).
Burgess, N., Barry, C. & O'Keefe, J. An oscillatory interference model of grid cell firing. Hippocampus 17, 801–812 (2007).
Hasselmo, M. E., Giocomo, L. M. & Zilli, E. A. Grid cell firing may arise from interference of theta frequency membrane potential oscillations in single neurons. Hippocampus 17, 1252–1271 (2007).
Blair, H. T., Welday, A. C. & Zhang, K. Scale-invariant memory representations emerge from moire interference between grid fields that produce theta oscillations: a computational model. J. Neurosci. 27, 3211–3229 (2007).
Giocomo, L. M., Moser, M.-B. & Moser, E. I. Computational models of grid cells. Neuron 71, 589–603 (2011).
Little, W. A. The existence of persistent states in the brain. Math. Biosci. 19, 101–120 (1971).
Hopfield, J. J. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl Acad. Sci. USA 79, 2554–2558 (1982).
Amit, D. J. Modelling Brain Function: The World of Attractor Networks (Cambridge Univ. Press, 1989).
Rolls, E. T. & Treves, A. Neural Networks and Brain Function (Oxford Univ. Press, 1998).
Hebb, D. O. The Organization of Behavior (Wiley, 1949).
Amari, S. Dynamics of pattern formation in lateral-inhibition type neural fields. Biol. Cybern. 27, 77–87 (1977).
Lushakin, A. V. & Georgopoulos, A. P. A dynamical neural network model for motor cortical activity during movement: population coding of movement trajectories. Biol. Cybern. 69, 517–524 (1993).
Ben-Yishai, R., Bar-Or, R. L. & Sompolinsky, H. Theory of orientation tuning in visual cortex. Proc. Natl Acad. Sci. USA 92, 3844–3848 (1995).
Sompolinsky, H. & Shapley, R. New perspectives on the mechanisms for orientation selectivity. Curr. Opin. Neurobiol. 7, 514–522 (1997).
Seung, H. S. How the brain keeps the eyes still. Proc. Natl Acad. Sci. USA 93, 13339–13344 (1996).
McNaughton, B. L., Chen, L. L. & Markus, E. J. “Dead reckoning”, landmark learning, and the sense of direction: a neurophysiological and computational hypothesis. J. Cogn. Neurosci. 3, 190–202 (1991).
Zhang, K. Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory. J. Neurosci. 16, 2112–2126 (1996).
Tsodyks, M. & Sejnowski, T. Associative memory and hippocampal place cells. Int. J. Neural Syst. 6 (Suppl.), 81–86 (1995).
Samsonovich, A. & McNaughton, B. L. Path integration and cognitive mapping in a continuous attractor neural network model. J. Neurosci. 17, 5900–5920 (1997).
Battaglia, F. P. & Treves, A. Attractor neural networks storing multiple space representations: a model for hippocampal place fields. Phys. Rev. E 58, 7738–7753 (1998).
Tsodyks, M. Attractor neural network models of spatial maps in hippocampus. Hippocampus 9, 481–489 (1999).
Fuhs, M. C. & Touretzky, D. S. A spin glass model of path integration in rat medial entorhinal cortex. J. Neurosci. 26, 4266–4276 (2006). Along with McNaughton et al . (reference 3), this paper is one of the first to propose attractor dynamics combined with directional translation of an activity pattern as the underlying mechanism of grid cell formation. As opposed to the toroidal Mexican hat-type connectivity of McNaughton et al . that leads to a single bump of activity, the model by Fuhs and Touretzky considered a connectivity that periodically became negative and positive at large-phase differences, leading to the formation of a grid-like pattern on the network.
Burak, Y. & Fiete, I. R. Accurate path integration in continuous attractor network models of grid cells. PLoS Comput. Biol. 5, e1000291 (2009). The authors report the first computer simulation of an attractor network in which grid cells are generated through a Mexican hat-like all-inhibitory connectivity pattern.
Guanella, A., Kiper, D. & Verschure, P. A model of grid cells based on a twisted torus topology. Int. J. Neural Syst. 17, 231–240 (2007).
Boccara, C. N. et al. Grid cells in pre- and parasubiculum. Nature Neurosci. 13, 987–994 (2010).
Domnisoru, C., Kinkhabwala, A. A. & Tank, D. W. Membrane potential dynamics of grid cells. Nature 495, 199–204 (2013).
Schmidt-Hieber, C. & Häusser, M. Cellular mechanisms of spatial navigation in the medial entorhinal cortex. Nature Neurosci. 16, 325–331 (2013). Domnisoru et al . (reference 104) and Schmidt-Hieber and Häusser carried out intracellular recordings from entorhinal stellate cells in rats navigating a virtual environment. The two papers demonstrate that fluctuations in membrane potential associated with grid fields are not primarily linked to local theta rhythm, arguing against oscillatory interference models.
Dhillon, A. & Jones, R. S. Laminar differences in recurrent excitatory transmission in the rat entorhinal cortex in vitro. Neuroscience 99, 413–422 (2000).
Couey, J. J. et al. Recurrent inhibitory circuitry as a mechanism for grid formation. Nature Neurosci. 16, 318–324 (2013). A combination of intracellularrecordings and optogenetics was used to show that the effective interaction between layer II stellate cells is purely inhibitory. It was also shown through simulations that a simple all-or-none inhibitory connectivity — in which cells with nearby phases inhibit each other to exactly the same extent, whereas those that are far apart are not coupled — is sufficient to generate grid cells.
Pastoll, H., Solanka, L., van Rossum, M. C. & Nolan, M. F. Feedback inhibition enables theta-nested gamma oscillations and grid firing fields. Neuron 77, 141–154 (2013).
Bonnevie, T. et al. Grid cells require excitatory drive from the hippocampus. Nature Neurosci. 16, 309–317 (2013).
Brandon, M. P. et al. Reduction of theta rhythm dissociates grid cell spatial periodicity from directional tuning. Science 332, 595–599 (2011).
Koenig, J., Linder, A. N., Leutgeb, J. K. & Leutgeb, S. The spatial periodicity of grid cells is not sustained during reduced theta oscillations. Science 332, 592–595 (2011).
Ts'o, D. Y., Gilbert, C. D. & Wiesel, T. N. Relationships between horizontal interactions and functional architecture in cat striate cortex as revealed by cross-correlation analysis. J. Neurosci. 6, 1160–1170 (1986).
Gilbert, C. D. & Wiesel, T. N. Columnar specificity of intrinsic horizontal and corticocortical connections in cat visual cortex. J. Neurosci. 9, 2432–2442 (1989).
Bosking, W. H., Zhang, Y., Schofield, B. & Fitzpatrick, D. Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. J. Neurosci. 17, 2112–2127 (1997).
Ko, H. et al. Functional specificity of local synaptic connections in neocortical networks. Nature 473, 87–91 (2011).
Mhatre, H., Gorchetchnikov, A. & Grossberg, S. Grid cell hexagonal patterns formed by fast self-organized learning within entorhinal cortex. Hippocampus 22, 320–334 (2012).
Grossberg, S. & Pilly, P. K. How entorhinal grid cells may learn multiple spatial scales from a dorsoventral gradient of cell response rates in a self-organizing map. PLoS Comput. Biol. 8, e1002648 (2012).
Buetfering, C., Allen, K. & Monyer, H. Parvalbumin interneurons provide grid cell-driven recurrent inhibition in the medial entorhinal cortex. Nature Neurosci. 17, 710–718 (2014).
Roudi, Y. & Moser, E. I. Grid cells in an inhibitory network. Nature Neurosci. 17, 639–641 (2014).
Mathis, A., Herz, A. V. & Stemmler, M. B. Multiscale codes in the nervous system: the problem of noise correlations and the ambiguity of periodic scales. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 88, 022713 (2013).
Dunn, B., Mørreaunet, M. & Roudi, Y. Correlations and functional connections in a population of grid cells. [online], (2014).
Roudi, Y. & Hertz, J. Mean field theory for nonequilibrium network reconstruction. Phys. Rev. Lett. 106, 048702 (2011).
Tocker, G. & Derdikman, D. Relation between spatial and temporal synchronization in MEC grid-cells. Soc. Neurosci. Abstr. 39, 769.27 (2013).
Langston, R. F. et al. Development of the spatial representation system in the rat. Science 328, 1576–1580 (2010).
Wills, T. J., Cacucci, F., Burgess, N. & O'Keefe, J. Development of the hippocampal cognitive map in preweanling rats. Science 328, 1573–1576 (2010).
Kropff, E. & Treves, A. The emergence of grid cells: intelligent design or just adaptation? Hippocampus 18, 1256–1269 (2008). This paper proposes the only model for grid cells that is not primarily based on path integration. Grids are formed through a self-organizing mechanism that combines Hebbian plasticity, feedforward spatially selective input and neuronal adaptation.
Stensola, T., Stensola, H., Moser, M.-B. & Moser, E. I. Environmental constraints on grid cell orientation. Soc. Neurosci. Abstr. 39, 769.15 (2013).
Si, B., Kropff, E. & Treves, A. Grid alignment in entorhinal cortex. Biol. Cybern. 106, 483–506 (2012).
Stella, F., Si, B., Kropff, E. & Treves, A. Grid cells on the ball. J. Stat. Mech. P03013 (2013).
Stella, F., Si, B., Kropff, E. & Treves, A. Grid maps for spaceflight, anyone? They are for free! Behav. Brain Sci. 36, 566–567 (2013).
Kruge, I. U., Wernle, T., Moser, E. I. & Moser, M.-B. Grid cells of animals raised in spherical environments. Soc. Neurosci. Abstr. 39, 769.14 (2013).
Douglas, R. J. & Martin, K. A. Neuronal circuits of the neocortex. Annu. Rev. Neurosci. 27, 419–451 (2004).
Lefort, S., Tomm, C., Floyd Sarria, J. C. & Petersen, C. C. The excitatory neuronal network of the C2 barrel column in mouse primary somatosensory cortex. Neuron 61, 301–316 (2009).
McGuire, B. A., Gilbert, C. D., Rivlin, P. K. & Wiesel, T. N. Targets of horizontal connections in macaque primary visual cortex. J. Comp. Neurol. 305, 370–392 (1991).
Binzegger, T., Douglas, R. J. & Martin, K. A. A quantitative map of the circuit of cat primary visual cortex. J. Neurosci. 24, 8441–8453 (2004).
Haberly, L. B. & Presto, S. Ultrastructural analysis of synaptic relationships of intracellularly stained pyramidal cell axons in piriform cortex. J. Comp. Neurol. 248, 464–474 (1986).
Miles, R. & Wong, R. K. Excitatory synaptic interactions between CA3 neurones in the guinea-pig hippocampus. J. Physiol. 373, 397–418 (1986).
Ishizuka, N., Weber, J. & Amaral, D. G. Organization of intrahippocampal projections originating from CA3 pyramidal cells in the rat. J. Comp. Neurol. 295, 580–623 (1990).
Li, X. G., Somogyi, P., Ylinen, A. & Buzsáki, G. The hippocampal CA3 network: an in vivo intracellular labeling study. J. Comp. Neurol. 339, 181–208 (1994).
Harris, E., Witter, M. P., Weinstein, G. & Stewart, M. Intrinsic connectivity of the rat subiculum: I. dendritic morphology and patterns of axonal arborization by pyramidal neurons. J. Comp. Neurol. 435, 490–505 (2001).
Funahashi, M. & Stewart, M. Presubicular and parasubicular cortical neurons of the rat: functional separation of deep and superficial neurons in vitro. J. Physiol. 501, 387–403 (1997).
Wachowiak, M. & Shipley, M. T. Coding and synaptic processing of sensory information in the glomerular layer of the olfactory bulb. Semin. Cell Dev. Biol. 17, 411–423 (2006).
Scharfman, H. E., Kunkel, D. D. & Schwartzkroin, P. A. Synaptic connections of dentate granule cells and hilar neurons: results of paired intracellular recordings and intracellular horseradish peroxidase injections. Neuroscience 37, 693–707 (1990).
Acsády, L., Kamondi, A., Sik, A., Freund, T. & Buzsáki, G. GABAergic cells are the major postsynaptic targets of mossy fibers in the rat hippocampus. J. Neurosci. 18, 3386–3403 (1998).
Jung, M. W. & McNaughton, B. L. Spatial selectivity of unit activity in the hippocampal granular layer. Hippocampus 3, 165–182 (1993).
Leutgeb, J. K., Leutgeb, S., Moser, M.-B. & Moser, E. I. Pattern separation in the dentate gyrus and CA3 of the hippocampus. Science 315, 961–966 (2007).
Spruston, N. & Johnston, D. Perforated patch-clamp analysis of the passive membrane properties of three classes of hippocampal neurons. J. Neurophysiol. 67, 508–529 (1992).
Gatome, C. W., Slomianka, L., Lipp, H. P. & Amrein, I. Number estimates of neuronal phenotypes in layer II of the medial entorhinal cortex of rat and mouse. Neuroscience 170, 156–165 (2010).
Steward, O. & Scoville, S. A. Cells of origin of entorhinal cortical afferents to the hippocampus and fascia dentata of the rat. J. Comp. Neurol. 169, 347–370 (1976).
Tamamaki, N. & Nojyo, Y. Projection of the entorhinal layer II neurons in the rat as revealed by intracellular pressure-injection of neurobiotin. Hippocampus 3, 471–480 (1993).
Zhang, S. J. et al. Optogenetic dissection of entorhinal-hippocampal functional connectivity. Science 340, 1232627 (2013).
Dickson, C. T., Mena, A. R. & Alonso, A. Electroresponsiveness of medial entorhinal cortex layer III neurons in vitro. Neuroscience 81, 937–950 (1997).
Hamam, B. N., Kennedy, T. E., Alonso, A. & Amaral, D. G. Morphological and electrophysiological characteristics of layer V neurons of the rat medial entorhinal cortex. J. Comp. Neurol. 418, 457–472 (2000).
Leutgeb, S. et al. Independent codes for spatial and episodic memory in hippocampal neuronal ensembles. Science 309, 619–623 (2005).
Jezek, K., Henriksen, E. J., Treves, A., Moser, E. I. & Moser, M.-B. Theta-paced flickering between place-cell maps in the hippocampus. Nature 478, 246–249 (2011).
Hubel, D. H. & Wiesel, T. Receptive fields, binocular interaction, and functional architecture of cat striate cortex. J. Physiol. (Lond.) 160, 106–154 (1962). An extensive description of the striate cortex, including its columnar organization and receptive field properties. The authors propose a model of how the concentric circular 'on or off' receptive fields of retinal ganglion cells and geniculate neurons could combine to form linear receptive fields in the primary visual cortex. This model still has merit half a century later.
O'Keefe, J. & Burgess, N. Dual phase and rate coding in hippocampal place cells: theoretical significance and relationship to entorhinal grid cells. Hippocampus 15, 853–866 (2005).
Solstad, T., Moser, E. I. & Einevoll, G. T. From grid cells to place cells: a mathematical model. Hippocampus 16, 1026–1031 (2006).
Rolls, E. T., Stringer, S. M. & Ellio, T. Entorhinal cortex grid cells can map to hippocampal place cells by competitive learning. Network 17, 447–465 (2006).
Savelli, F. & Knierim, J. J. Hebbian analysis of the transformation of medial entorhinal grid-cell inputs to hippocampal place fields. J. Neurophysiol. 103, 3167–3183 (2010).
de Almedia, L., Idiart, M. & Lisman, J. E. The input-output transformation of the hippocampal granule cells: from grid cells to place cells. J. Neurosci. 29, 7504–7512 (2009).
Monaco, J. D. & Abbott, L. F. Modular reealignment of entorhinal grid cell activity as a basis for hippocampal remapping. J. Neurosci. 31, 9414–9425 (2011).
O'Keefe, J. & Burgess, N. Geometric determinants of the place fields of hippocampal neurons. Nature 381, 425–428 (1996).
Hartley, T., Burgess, N., Lever, C., Cacucci, F. & O'Keefe, J. Modeling place fields in terms of the cortical inputs to the hippocampus. Hippocampus 10, 369–379 (2000).
O'Keefe, J. & Conway, D. H. Hippocampal place units in the freely moving rat: why they fire where they fire. Exp. Brain Res. 31, 573–590 (1978).
Wiener, S. I., Paul, C. A. & Eichenbaum, H. Spatial and behavioral correlates of hippocampal neuronal activity. J. Neurosci. 9, 2737–2763 (1989).
Hetherington, P. A. & Shapiro, M. L. Hippocampal place fields are altered by the removal of single visual cues in a distance-dependent manner. Behav. Neurosci. 111, 20–34 (1997).
Bjerknes, T. L., Moser, E. I. & Moser, M.-B. Representation of geometric borders in the developing rat. Neuron 82, 71–78 (2014).
Jia, H., Rochefort, N. L. & Konnerth, A. Dendritic organization of sensory input to cortical neurons in vivo. Nature 464, 1307–1312 (2010).
Chen, T. W. et al. Ultrasensitive fluorescent proteins for imaging neuronal activity. Nature 499, 295–300 (2013).
Singer, W. Synchronization of cortical activity and its putative role in information processing and learning. Annu. Rev. Physiol. 55, 349–374 (1993).
Fries, P. Neuronal gamma-band synchronization as a fundamental process in cortical computation. Annu. Rev. Neurosci. 32, 209–224 (2009).
Colgin, L. L. et al. Frequency of gamma oscillations routes flow of information in the hippocampus. Nature 462, 353–357 (2009).
Igarashi, K. M., Lu, L., Colgin, L. L., Moser, M.-B. & Moser, E. I. Coordination of entorhinal–hippocampal ensemble activity during associative learning. Nature http://dx.doi.org/10.1038/nature13162 (2014).
Ahmed, O. J. & Mehta, M. R. Running speed alters the frequency of hippocampal gamma oscillations. J. Neurosci. 32, 7373–7383 (2012).
Springer, M. S., Stanhope, M. J., Madsen, O. & de Jong, W. W. Molecules consolidate the placental mammal tree. Trends Ecol. Evol. 19, 430–438 (2004).
Rodríguez, F. et al. Spatial memory and hippocampal pallium through vertebrate evolution: insights from reptiles and teleost fish. Brain Res. Bull. 57, 499–503 (2002).
López, J. C., Vargas, J. P., Gómez, Y. & Salas, C. B. Spatial and non-spatial learning in turtles: the role of medial cortex. Behav. Brain Res. 143, 109–120 (2003).
Broglio, C., Rodríguez, F., Gómez, A., Arias, J. L. & Salas, C. Selective involvement of the goldfish lateral pallium in spatial memory. Behav. Brain Res. 210, 191–201 (2010).
Sperry, R. W. Chemoaffinity in the orderly growth of nerve fiber patterns and connections. Proc. Natl Acad. Sci. USA 50, 703–710 (1963).
Penfield, W. & Rasmussen, T. The Cerebral Cortex of Man. A Clinical Study of Localization of Function (Macmillan, 1950).
Woolsey, T. A. & van der Loos, H. The structural organization of layer IV in the somatosensory region (SI) of mouse cerebral cortex. The description of a cortical field composed of discrete cytoarchitectonic units. Brain Res. 17, 205–242 (1970).
Katsuki, Y., Sumi, T., Uchiyama, H. & Watanabe, T. Electric responses of auditory neurons in cat to sound stimulation. J. Neurophysiol. 21, 569–588 (1958).
Evans, E. F., Ross, H. F. & Whitfield, I. C. The spatial distribution of unit characteristic frequency in the primary auditory cortex of the cat. J. Physiol. (Lond.) 179, 238–247 (1965).
Hubel, D. H. & Wiesel, T. Sequence regularity and geometry of orientation columns in the monkey striate cortex. J. Comp. Neurol. 158, 267–294 (1974).
Blasdel, G. G. & Salama, G. Voltage sensitive dyes reveal a modular organization in monkey striate cortex. Nature 321, 579–585 (1986).
Mooser, F., Bosking, W. H. & Fitzpatrick, D. A morphological basis for orientation tuning in primary visual cortex. Nature Neurosci. 7, 872–879 (2004).
Gross, C. G., Bender, D. B. & Rocha-Miranda, C. E. Visual receptive fields of neurons in inferotemporal cortex of the monkey. Science 166, 1303–1306 (1969).
Gross, C. G., Rocha-Miranda, C. E. & Bender, D. B. Visual properties of neurons in inferotemporal cortex of the macaque. J. Neurophysiol. 35, 96–111 (1972).
Tanaka, K., Saito, H., Fukada, Y. & Moriya, M. Coding visual images of objects in the inferotemporal cortex of the macaque monkey. J. Neurophysiol. 66, 170–189 (1991).
Bruce, C., Desimone, R. & Gross, C. G. Visual properties of neurons in a polysensory area in superior temporal sulculs in the macaque. J. Neurophysiol. 46, 369–384 (1981).
Perrett, D. I., Rolls, E. T. & Caan, W. Visual neurones responsive to faces in the monkey temporal cortex. Exp. Brain Res. 47, 329–342 (1982).
Rolls, E. Y. Neurons in the cortex of the temporal lobe and in the amygdala of the monkey with responses selective for faces. Hum. Neurobiol. 3, 209–222 (1984).
Fujita, I., Tanaka, K., Ito, M. & Cheng, K. Columns for visual features of objects in monkey inferotemporal cortex. Nature 360, 343–346 (1992).
Tsao, D. Y., Freiwald, W. A., Tootell, R. B. & Livingstone, M. S. A cortical region consisting entirely of face-selective cells. Science 311, 670–674 (2006).
Tsao, D. Y., Moeller, S. & Freiwald, W. A. Comparing face patch systems in macaques and humans. Proc. Natl Acad. Sci. USA 105, 19514–19519 (2008).
Moeller, S., Freiwald, W. A. & Tsao, D. Y. Patches with links: a unified system for processing faces in the macaque temporal lobe. Science 320, 1355–1359 (2008).
Knudsen, E. I. & Konishi, M. A neural map of auditory space in the owl. Science 200, 795–797 (1978).
Knudsen, E. I. & Konishi, M. Mechanisms of sound localization in the barn owl (Tyto alba). J. Comp. Physiol. 133, 13–21 (1979).
Papp, E. A., Leergaard, T. B., Calabrese, E., Johnson, G. A. & Bjaalie, J. G. Waxholm Space atlas of the Sprague Dawley rat brain. Neuroimage 97, 374–386 (2014).
Renart, A., Song, P. & Wang, X. J. Robust spatial working memory through homeostatic synaptic scaling in heterogeneous cortical networks. Neuron 38, 473–485 (2003).
Roudi, Y. & Treves, A. Representing where along with what information in a model of a cortical patch. PLoS Comput. Biol. 4, e1000012 (2007).
Itskov, V., Hansel, D. & Tsodyks, M. Short-term facilitation may stabilize parametric working memory trace. Front. Comput. Neurosci. 5, 40 (2011).
Remme, M. W., Lengyel, M. & Gutkin, B. S. Democracy-independence trade-off in oscillating dendrites and its implications for grid cells. Neuron 66, 429–437 (2010).
Burgess, N. Grid cells and theta as oscillatory interference: theory and predictions. Hippocampus 18, 1157–1174 (2008).
Zilli, E. A. & Hasselmo, M. E. Coupled noisy spiking neurons as velocity-controlled oscillators in a model of grid cell spatial firing. J. Neurosci. 30, 13850–13860 (2010).
Hafting, T., Fyhn, M., Bonnevie, T., Moser, M.-B. & Moser, E. I. Hippocampus-independent phase precession in entorhinal grid cells. Nature 453, 1248–1252 (2008).
Navratilova, Z., Giocomo, L. M., Fellous, J. M., Hasselmo, M. E. & McNaughton, B. L. Phase precession and variable spatial scaling in a periodic attractor map model of medial entorhinal grid cells with realistic after-spike dynamics. Hippocampus 22, 772–789 (2012).
Heys, J. G., MacLeod, K. M., Moss, C. F. & Hasselmo, M. E. Bat and rat neurons differ in theta-frequency resonance despite similar coding of space. Science 340, 363–367 (2013).
Giocomo, L. M. & Hasselmo, M. E. Knock-out of HCN1 subunit flattens dorsal-ventral frequency gradient of medial entorhinal neurons in adult mice. J. Neurosci. 29, 7625–7630 (2009).
Giocomo, L. M. et al. Grid cells use HCN1 channels for spatial scaling. Cell 147, 1159–1170 (2011).
Bush, D. & Burgess, N. A hybrid oscillatory interference/continuous attractor network model of grid cell firing. J. Neurosci. 34, 5065–5079 (2014).
Barry, C. & Doeller, C. F. 3D mapping in the brain. Science 340, 279–280 (2013).
Hasselmo, M. E. & Brandon, M. P. A model combining oscillations and attractor dynamics for generation of grid cell firing. Front. Neural Circuits 6, 30 (2012).
Yasuda, M. & Mayford, M. R. CaMKII activation in the entorhinal cortex disrupts previously encoded spatial memory. Neuron 50, 309–318 (2006).
Fenno, L., Yizhar, O. & Deisseroth, K. The development and application of optogenetics. Annu. Rev. Neurosci. 34, 389–412 (2011).
Alexander, G. M. et al. Remote control of neuronal activity in transgenic mice expressing evolved G protein-coupled receptors. Neuron 63, 27–39 (2009).
Miyawaki, A. et al. Fluorescent indicators for Ca2+ based on green fluorescent proteins and calmodulin. Nature 388, 882–887 (1997).
Miyawaki, A., Griesbeck, O., Heim, R. & Tsien, R. Y. Dynamic and quantitative Ca2+ measurements using improved cameleons. Proc. Natl Acad. Sci. USA 96, 2135–2140 (1999).
Heim, N. et al. Improved calcium imaging in transgenic mice expressing a troponin C-based biosensor. Nature Methods 4, 127–129 (2007).
Mank, M. et al. A genetically encoded calcium indicator for chronic in vivo two-photon imaging. Nature Methods 5, 805–811 (2008).
Tian, L. et al. Imaging neural activity in worms, flies and mice with improved GCaMP calcium indicators. Nature Methods 6, 875–881 (2009).
Looger, L. L. & Griesbeck, O. Genetically encoded neural activity indicators. Curr. Opin. Neurobiol. 22, 18–23 (2012).
Harvey, C. D., Collman, F., Dombeck, D. A. & Tank, D. W. Intracellular dynamics of hippocampal place cells during virtual navigation. Nature 461, 941–946 (2009).
Taniguchi, H. et al. A resource of Cre driver lines for genetic targeting of GABAergic neurons in cerebral cortex. Neuron 71, 995–1013 (2011).
Girardeau, G., Benchenane, K., Wiener, S. I., Buzsáki, G. & Zugaro, M. B. Selective suppression of hippocampal ripples impairs spatial memory. Nature Neurosci. 12, 1222–1223 (2009).
Wickersham, I. R. et al. Monosynaptic restriction of transsynaptic tracing from single, genetically targeted neurons. Neuron 53, 639–647 (2007).
Wickersham, I. R., Finke, S., Conzelmann, K. K. & Callaway, E. M. Retrograde neuronal tracing with a deletion-mutant rabies virus. Nature Methods 4, 47–49 (2007).
Moser, E. I. & Moser, M.-B. Grid cells and neural coding in high-end cortices. Neuron 80, 765–774 (2013).
Acknowledgements
The authors are grateful to T. Mrsic-Flogel for comments on the manuscript. The authors thank the European Research Council ('CIRCUIT' Advanced Investigator Grant, grant agreement 232608; 'ENSEMBLE' Advanced Investigator Grant, grant agreement 268598), the European Commission's FP7 FET Proactive programme on Neuro-Bio-Inspired Systems (grant agreement 600725), an FP7 Marie Curie Training Network Grant (NETADIS; grant agreement 290038), the Louis-Jeantet Prize for Medicine, the Kavli Foundation and the Centre of Excellence scheme and the FRIPRO and NEVRONOR programmes of the Research Council of Norway for support. The authors thank T. Stensola for the design of figure 1 parts b and d. The authors are also grateful to F. Pinheiro for suggesting the Borges quote.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
PowerPoint slides
Glossary
- Entorhinal cortex
-
An interface between the three-layered hippocampal cortex and six-layered neocortex. It provides the main cortical input to the dentate gyrus.
- Place cell
-
A type of hippocampal neuron that typically has a single environmentally specific spatial receptive field. There is no discernible relationship between firing patterns in different environments.
- Grid cells
-
Parahippocampal neurons that have regularly repeating hexagonally spaced receptive fields. Co-activity patterns remain largely the same across different environments.
- Theta rhythm
-
Oscillatory activity in the range of 6–10 Hz in the local field potential of the hippocampus. It is produced by large and widespread ensembles of hippocampal neurons that oscillate in synchrony.
- Salt-and-pepper-like organization
-
Cortical architecture in which single cells are tuned for the orientation of a stimulus but show no particular order in their arrangement. This arrangement is seen in the rodent visual cortex.
- Head direction cells
-
Neurons found throughout parahippocampal areas and in other brain regions (for example, the anterior thalamus) for which the primary feature of the receptive field is the direction in which the animals head is pointing.
- Attractor network
-
A network with one or more stable firing-rate pattern that is stored in the structure of the synaptic connectivity.
- Continuous attractor
-
An attractor network in which the collection of attracting points form not a discrete set but a continuum (a ring or a sheet).
- Mexican hat connectivity
-
The connectivity of networks in which neurons are arranged on a ring or sheet such that the excitatory connections of each neuron decrease progressively with distance, whereas inhibitory connections increase in strength.
- Stellate cells
-
Morphologically defined as cells with a round soma and dendrites radiating from it in all directions. In the medial entorhinal cortex, stellate cells are the main origin of the projection to the dentate gyrus and CA3.
- Recurrent networks
-
Neural networks in which each neuronal element provides an input onto many of the other neurons in the network.
- Adaptation
-
Adaptation refers to the decrease in firing frequency that neurons exhibit following a period of repeated discharge.
Rights and permissions
About this article
Cite this article
Moser, E., Roudi, Y., Witter, M. et al. Grid cells and cortical representation. Nat Rev Neurosci 15, 466–481 (2014). https://doi.org/10.1038/nrn3766
Published:
Issue Date:
DOI: https://doi.org/10.1038/nrn3766
This article is cited by
-
Limbic progesterone receptors regulate spatial memory
Scientific Reports (2023)
-
The anterior thalamic nuclei: core components of a tripartite episodic memory system
Nature Reviews Neuroscience (2022)
-
Right entorhinal cortical thickness is associated with Mini-Mental State Examination scores from multi-country datasets using MRI
Neuroradiology (2022)
-
Dopamine facilitates associative memory encoding in the entorhinal cortex
Nature (2021)
-
Dentate granule cells encode auditory decisions after reinforcement learning in rats
Scientific Reports (2021)
