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Grid cells and cortical representation

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.

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Figure 1: Basic properties of grid cells.
Figure 2: Excitatory and inhibitory attractor models for grid cells.

References

  1. Felleman, D. J. & van Essen, D. C. Distributed hierarchical processing in the primate cerebral cortex. Cereb. Cortex 1, 1–47 (1991).

    Article  CAS  PubMed  Google Scholar 

  2. 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.

  3. 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.

    Article  CAS  Google Scholar 

  4. 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).

    Article  CAS  PubMed  Google Scholar 

  5. 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.

    Article  CAS  PubMed  Google Scholar 

  6. O'Keefe, J. Place units in the hippocampus of the freely moving rat. Exp. Neurol. 51, 78–109 (1976).

    Article  CAS  PubMed  Google Scholar 

  7. Fyhn, M., Molden, S., Witter, M. P., Moser, E. I. & Moser, M. B. Spatial representation in the entorhinal cortex. Science 305, 1258–1264 (2004).

    Article  CAS  PubMed  Google Scholar 

  8. 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.

    Article  CAS  PubMed  Google Scholar 

  9. Sargolini, F. et al. Conjunctive representation of position, direction, and velocity in entorhinal cortex. Science 312, 758–762 (2006).

    Article  CAS  PubMed  Google Scholar 

  10. 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).

    Article  CAS  PubMed  Google Scholar 

  11. Colgin, L. L., Moser, E. I. & Moser, M.-B. Understanding memory through hippocampal remapping. Trends Neurosci. 31, 469–477 (2008).

    Article  CAS  PubMed  Google Scholar 

  12. 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).

    Article  CAS  PubMed  Google Scholar 

  13. 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).

    Article  CAS  PubMed  Google Scholar 

  14. 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).

    Article  CAS  PubMed  Google Scholar 

  15. Fyhn, M., Hafting, T., Witter, M. P., Moser, E. I. & Moser, M.-B. Grid cells in mice. Hippocampus 18, 1230–1238 (2008).

    Article  PubMed  Google Scholar 

  16. Ulanovsky, N. & Moss, C. F. Hippocampal cellular and network activity in freely moving echolocating bats. Nature Neurosci. 10, 224–233 (2007).

    Article  CAS  PubMed  Google Scholar 

  17. Yartsev, M. M., Witter, M. P. & Ulanovsky, N. Grid cells without theta oscillations in the entorhinal cortex of bats. Nature 479, 103–107 (2011).

    Article  CAS  PubMed  Google Scholar 

  18. Ono, T., Nakamura, K., Nishijo, H. & Eifuku, S. Monkey hippocampal neurons related to spatial and nonspatial functions. J. Neurophysiol. 70, 1516–1529 (1993).

    Article  CAS  PubMed  Google Scholar 

  19. Rolls, E. T. & O'Mara, S. M. View-responsive neurons in the primate hippocampal complex. Hippocampus 5, 409–424 (1995).

    Article  CAS  PubMed  Google Scholar 

  20. Rolls, E. T., Robertson, R. G. & Georges-François, P. Spatial view cells in the primate hippocampus. Eur. J. Neurosci. 9, 1789–1794 (1997).

    Article  CAS  PubMed  Google Scholar 

  21. Killian, N. J., Jutras, M. J. & Buffalo, E. A. A map of visual space in the primate entorhinal cortex. Nature 491, 761–764 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  22. Ekstrom, A. D. et al. Cellular networks underlying human spatial navigation. Nature 425, 184–188 (2003).

    Article  CAS  PubMed  Google Scholar 

  23. Jacobs, J. et al. Direct recordings of grid-like neuronal activity in human spatial navigation. Nature Neurosci. 16, 1188–1190 (2013).

    Article  CAS  PubMed  Google Scholar 

  24. 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.

    Article  CAS  PubMed  Google Scholar 

  25. Barry, C., Hayman, R., Burgess, N. & Jeffery, K. J. Experience-dependent rescaling of entorhinal grids. Nature Neurosci. 10, 682–684 (2007).

    Article  CAS  PubMed  Google Scholar 

  26. Krupic, J., Burgess, N. & O'Keefe, J. Neural representations of location composed of spatially periodic bands. Science 337, 853–857 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  27. Mittelstaedt, M. L. & Mittelstaedt, H. Homing by path integration in a mammal. Naturwissenschaften 67, 566–567 (1980).

    Article  Google Scholar 

  28. Müller, M. & Wehner, R. Path integration in desert ants, Cataglyphis fortis. Proc. Natl Acad. Sci. USA 85, 5287–5290 (1988).

    Article  PubMed  Google Scholar 

  29. Etienne, A. S. & Jeffery, K. J. Path integration in mammals. Hippocampus 14, 180–192 (2004).

    Article  PubMed  Google Scholar 

  30. 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).

    Article  CAS  PubMed  Google Scholar 

  31. McNaughton, B. L. et al. Deciphering the hippocampal polyglot: the hippocampus as a path integration system. J. Exp. Biol. 199, 173–185 (1996).

    CAS  PubMed  Google Scholar 

  32. Derdikman, D. et al. Fragmentation of grid maps in a multicompartment environment. Nature Neurosci. 12, 1325–1332 (2009).

    Article  CAS  PubMed  Google Scholar 

  33. 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).

    Article  PubMed  Google Scholar 

  34. Ravassard, P. et al. Multisensory control of hippocampal spatiotemporal selectivity. Science 340, 1342–1346 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  35. 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).

    Google Scholar 

  36. Parron, C. & Save, E. Evidence for entorhinal and parietal cortices involvement in path integration in the rat. Exp. Brain Res. 159, 349–359 (2004).

    Article  PubMed  Google Scholar 

  37. 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).

    Article  PubMed  Google Scholar 

  38. 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).

    Article  PubMed  Google Scholar 

  39. Biegler, R. Possible uses of path integration in animal navigation. Animal Learn. Behav. 28, 257–277 (2000).

    Article  Google Scholar 

  40. Brun, V. H. et al. Progressive increase in grid scale from dorsal to ventral medial entorhinal cortex. Hippocampus 18, 1200–1212 (2008).

    Article  PubMed  Google Scholar 

  41. Illig, K. R. & Haberly, L. B. Odor-evoked activity is spatially distributed in piriform cortex. J. Comp. Neurol. 457, 361–373 (2003).

    Article  PubMed  Google Scholar 

  42. Stettler, D. D. & Axel, R. Representations of odor in the piriform cortex. Neuron 63, 854–864 (2009).

    Article  CAS  PubMed  Google Scholar 

  43. 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).

    Article  CAS  PubMed  Google Scholar 

  44. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  45. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  46. 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).

    Article  CAS  PubMed  Google Scholar 

  47. 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).

    Article  CAS  PubMed  Google Scholar 

  48. Ziv, L. et al. Long-term dynamics of CA1 hippocampal place codes. Nature Neurosci. 16, 264–266 (2013).

    Article  CAS  PubMed  Google Scholar 

  49. Mathis, A., Herz, A. V. & Stemmler, M. Optimal population codes for space: grid cells outperform place cells. Neural Comput. 24, 2280–2317 (2012).

    Article  PubMed  Google Scholar 

  50. Wei, X.-X., Prentice, J. & Balasubramanian, V. The sense of place: grid cells in the brain and the transcendental number e. [online], (2013).

  51. 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).

    Article  PubMed  Google Scholar 

  52. Chapman, B., Stryker, M. P. & Bonhoeffer, T. Development of orientation preference maps in ferret primary visual cortex. J. Neurosci. 16, 6443–6453 (1996).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  53. 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).

    Article  CAS  PubMed  Google Scholar 

  54. Ko, H. et al. The emergence of functional microcircuits in visual cortex. Nature 496, 96–100 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  55. 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).

    Article  CAS  PubMed  Google Scholar 

  56. Katz, L. C. & Shatz, C. J. Synaptic activity and the construction of cortical circuits. Science 274, 1133–1138 (1996).

    Article  CAS  PubMed  Google Scholar 

  57. Ackman, J. B., Burbridge, T. J. & Crair, M. C. Retinal waves coordinate patterned activity throughout the developing visual system. Nature 490, 219–225 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  58. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  59. Li, Y. et al. Clonally related visual cortical neurons show similar stimulus feature selectivity. Nature 486, 118–121 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  60. Ohtsuki, G. et al. Similarity of visual selectivity among clonally related neurons in visual cortex. Neuron 75, 65–72 (2012).

    Article  CAS  PubMed  Google Scholar 

  61. Bonhoeffer, T. & Grinvald, A. Orientation columns in cat are organized in pin-wheel like patterns. Nature 353, 429–431 (1991).

    Article  CAS  PubMed  Google Scholar 

  62. Maldonado, P. E., Gödecke, I., Gray, C. M. & Bonhoeffer, T. Orientation selectivity in pinwheel centers in cat striate cortex. Science 276, 1551–1555 (1997).

    Article  CAS  PubMed  Google Scholar 

  63. Ohki, K. et al. Highly ordered arrangement of single neurons in orientation pinwheels. Nature 442, 925–928 (2006).

    Article  CAS  PubMed  Google Scholar 

  64. Hubel, D. H. & Wiesel, T. N. Receptive fields and functional architecture of monkey striate cortex. J. Physiol. 195, 215–243 (1968).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  65. 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).

    Article  CAS  PubMed  Google Scholar 

  66. Tootell, R. B., Switkes, E., Silverman, M. S. & Hamilton, S. L. Retinotopic organization. J. Neurosci. 8, 1531–1568 (1988).

    Article  CAS  PubMed  Google Scholar 

  67. 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).

    Article  CAS  PubMed  Google Scholar 

  68. 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).

    Article  CAS  PubMed  Google Scholar 

  69. Chen, G., Lu, H. D. & Roe, A. W. A map for horizontal disparity in monkey V2. Neuron 58, 442–450 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  70. Kara, P. & Boyd, J. D. A micro-architecture for binocular disparity and ocular dominance in visual cortex. Nature 458, 627–631 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  71. Ranck, J. B. Jr. in Electrical Activity of the Archicortex (eds Buzsáki, G. & Vanderwolf, C. H.) 217–220 (Akademiai Kiado, 1985).

    Google Scholar 

  72. 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).

    Article  CAS  PubMed  Google Scholar 

  73. 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).

    Article  PubMed  PubMed Central  Google Scholar 

  74. 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).

    Article  CAS  PubMed  Google Scholar 

  75. Barry, C. et al. The boundary vector model of place cell firing and spatial memory. Rev. Neurosci. 17, 71–97 (2006).

    Article  PubMed  PubMed Central  Google Scholar 

  76. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  77. Hubel, D. H. & Livingstone, M. S. Segregation of form, color, and stereopsis in primate area 18. J. Neurosci. 7, 3378–3415 (1987).

    Article  CAS  PubMed  Google Scholar 

  78. Yoon, K. et al. Specific evidence of low-dimensional continuous attractor dynamics in grid cells. Nature Neurosci. 16, 1077–1084 (2013).

    Article  CAS  PubMed  Google Scholar 

  79. 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).

    Article  Google Scholar 

  80. Burgess, N., Barry, C. & O'Keefe, J. An oscillatory interference model of grid cell firing. Hippocampus 17, 801–812 (2007).

    Article  PubMed  PubMed Central  Google Scholar 

  81. 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).

    Article  PubMed  PubMed Central  Google Scholar 

  82. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  83. Giocomo, L. M., Moser, M.-B. & Moser, E. I. Computational models of grid cells. Neuron 71, 589–603 (2011).

    Article  CAS  PubMed  Google Scholar 

  84. Little, W. A. The existence of persistent states in the brain. Math. Biosci. 19, 101–120 (1971).

    Article  Google Scholar 

  85. Hopfield, J. J. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl Acad. Sci. USA 79, 2554–2558 (1982).

    Article  CAS  PubMed  Google Scholar 

  86. Amit, D. J. Modelling Brain Function: The World of Attractor Networks (Cambridge Univ. Press, 1989).

    Book  Google Scholar 

  87. Rolls, E. T. & Treves, A. Neural Networks and Brain Function (Oxford Univ. Press, 1998).

    Google Scholar 

  88. Hebb, D. O. The Organization of Behavior (Wiley, 1949).

    Google Scholar 

  89. Amari, S. Dynamics of pattern formation in lateral-inhibition type neural fields. Biol. Cybern. 27, 77–87 (1977).

    Article  CAS  PubMed  Google Scholar 

  90. 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).

    Article  Google Scholar 

  91. 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).

    Article  CAS  PubMed  Google Scholar 

  92. Sompolinsky, H. & Shapley, R. New perspectives on the mechanisms for orientation selectivity. Curr. Opin. Neurobiol. 7, 514–522 (1997).

    Article  CAS  PubMed  Google Scholar 

  93. Seung, H. S. How the brain keeps the eyes still. Proc. Natl Acad. Sci. USA 93, 13339–13344 (1996).

    Article  CAS  PubMed  Google Scholar 

  94. 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).

    Article  CAS  PubMed  Google Scholar 

  95. Zhang, K. Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory. J. Neurosci. 16, 2112–2126 (1996).

    Article  CAS  PubMed  Google Scholar 

  96. Tsodyks, M. & Sejnowski, T. Associative memory and hippocampal place cells. Int. J. Neural Syst. 6 (Suppl.), 81–86 (1995).

    Google Scholar 

  97. Samsonovich, A. & McNaughton, B. L. Path integration and cognitive mapping in a continuous attractor neural network model. J. Neurosci. 17, 5900–5920 (1997).

    Article  CAS  PubMed  Google Scholar 

  98. 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).

    Article  CAS  Google Scholar 

  99. Tsodyks, M. Attractor neural network models of spatial maps in hippocampus. Hippocampus 9, 481–489 (1999).

    Article  CAS  PubMed  Google Scholar 

  100. 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.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  101. 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.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  102. 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).

    Article  PubMed  Google Scholar 

  103. Boccara, C. N. et al. Grid cells in pre- and parasubiculum. Nature Neurosci. 13, 987–994 (2010).

    Article  CAS  PubMed  Google Scholar 

  104. Domnisoru, C., Kinkhabwala, A. A. & Tank, D. W. Membrane potential dynamics of grid cells. Nature 495, 199–204 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  105. 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.

    Article  CAS  PubMed  Google Scholar 

  106. Dhillon, A. & Jones, R. S. Laminar differences in recurrent excitatory transmission in the rat entorhinal cortex in vitro. Neuroscience 99, 413–422 (2000).

    Article  CAS  PubMed  Google Scholar 

  107. 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.

    Article  CAS  PubMed  Google Scholar 

  108. 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).

    Article  CAS  PubMed  Google Scholar 

  109. Bonnevie, T. et al. Grid cells require excitatory drive from the hippocampus. Nature Neurosci. 16, 309–317 (2013).

    Article  CAS  PubMed  Google Scholar 

  110. Brandon, M. P. et al. Reduction of theta rhythm dissociates grid cell spatial periodicity from directional tuning. Science 332, 595–599 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  111. 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).

    Article  CAS  PubMed  Google Scholar 

  112. 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).

    Article  CAS  PubMed  Google Scholar 

  113. Gilbert, C. D. & Wiesel, T. N. Columnar specificity of intrinsic horizontal and corticocortical connections in cat visual cortex. J. Neurosci. 9, 2432–2442 (1989).

    Article  CAS  PubMed  Google Scholar 

  114. 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).

    Article  CAS  PubMed  Google Scholar 

  115. Ko, H. et al. Functional specificity of local synaptic connections in neocortical networks. Nature 473, 87–91 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  116. Mhatre, H., Gorchetchnikov, A. & Grossberg, S. Grid cell hexagonal patterns formed by fast self-organized learning within entorhinal cortex. Hippocampus 22, 320–334 (2012).

    Article  PubMed  Google Scholar 

  117. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  118. 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).

    Article  CAS  PubMed  Google Scholar 

  119. Roudi, Y. & Moser, E. I. Grid cells in an inhibitory network. Nature Neurosci. 17, 639–641 (2014).

    Article  CAS  PubMed  Google Scholar 

  120. 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).

    Article  CAS  PubMed  Google Scholar 

  121. Dunn, B., Mørreaunet, M. & Roudi, Y. Correlations and functional connections in a population of grid cells. [online], (2014).

  122. Roudi, Y. & Hertz, J. Mean field theory for nonequilibrium network reconstruction. Phys. Rev. Lett. 106, 048702 (2011).

    Article  CAS  PubMed  Google Scholar 

  123. Tocker, G. & Derdikman, D. Relation between spatial and temporal synchronization in MEC grid-cells. Soc. Neurosci. Abstr. 39, 769.27 (2013).

    Google Scholar 

  124. Langston, R. F. et al. Development of the spatial representation system in the rat. Science 328, 1576–1580 (2010).

    Article  CAS  PubMed  Google Scholar 

  125. Wills, T. J., Cacucci, F., Burgess, N. & O'Keefe, J. Development of the hippocampal cognitive map in preweanling rats. Science 328, 1573–1576 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  126. 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.

    Article  PubMed  Google Scholar 

  127. Stensola, T., Stensola, H., Moser, M.-B. & Moser, E. I. Environmental constraints on grid cell orientation. Soc. Neurosci. Abstr. 39, 769.15 (2013).

    Google Scholar 

  128. Si, B., Kropff, E. & Treves, A. Grid alignment in entorhinal cortex. Biol. Cybern. 106, 483–506 (2012).

    Article  PubMed  Google Scholar 

  129. Stella, F., Si, B., Kropff, E. & Treves, A. Grid cells on the ball. J. Stat. Mech. P03013 (2013).

  130. Stella, F., Si, B., Kropff, E. & Treves, A. Grid maps for spaceflight, anyone? They are for free! Behav. Brain Sci. 36, 566–567 (2013).

    Article  PubMed  Google Scholar 

  131. 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).

    Google Scholar 

  132. Douglas, R. J. & Martin, K. A. Neuronal circuits of the neocortex. Annu. Rev. Neurosci. 27, 419–451 (2004).

    Article  CAS  PubMed  Google Scholar 

  133. 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).

    Article  CAS  PubMed  Google Scholar 

  134. 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).

    Article  CAS  PubMed  Google Scholar 

  135. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  136. 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).

    Article  CAS  PubMed  Google Scholar 

  137. Miles, R. & Wong, R. K. Excitatory synaptic interactions between CA3 neurones in the guinea-pig hippocampus. J. Physiol. 373, 397–418 (1986).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  138. 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).

    Article  CAS  PubMed  Google Scholar 

  139. 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).

    Article  CAS  PubMed  Google Scholar 

  140. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  141. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  142. 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).

    Article  PubMed  Google Scholar 

  143. 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).

    Article  CAS  PubMed  Google Scholar 

  144. 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).

    Article  PubMed  Google Scholar 

  145. Jung, M. W. & McNaughton, B. L. Spatial selectivity of unit activity in the hippocampal granular layer. Hippocampus 3, 165–182 (1993).

    Article  CAS  PubMed  Google Scholar 

  146. 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).

    Article  CAS  PubMed  Google Scholar 

  147. 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).

    Article  CAS  PubMed  Google Scholar 

  148. 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).

    Article  CAS  PubMed  Google Scholar 

  149. 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).

    Article  CAS  PubMed  Google Scholar 

  150. 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).

    Article  CAS  PubMed  Google Scholar 

  151. Zhang, S. J. et al. Optogenetic dissection of entorhinal-hippocampal functional connectivity. Science 340, 1232627 (2013).

    Article  CAS  PubMed  Google Scholar 

  152. Dickson, C. T., Mena, A. R. & Alonso, A. Electroresponsiveness of medial entorhinal cortex layer III neurons in vitro. Neuroscience 81, 937–950 (1997).

    Article  CAS  PubMed  Google Scholar 

  153. 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).

    Article  CAS  PubMed  Google Scholar 

  154. Leutgeb, S. et al. Independent codes for spatial and episodic memory in hippocampal neuronal ensembles. Science 309, 619–623 (2005).

    Article  CAS  PubMed  Google Scholar 

  155. 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).

    Article  CAS  PubMed  Google Scholar 

  156. 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.

    Article  CAS  Google Scholar 

  157. 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).

    Article  PubMed  PubMed Central  Google Scholar 

  158. Solstad, T., Moser, E. I. & Einevoll, G. T. From grid cells to place cells: a mathematical model. Hippocampus 16, 1026–1031 (2006).

    Article  PubMed  Google Scholar 

  159. 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).

    Article  PubMed  Google Scholar 

  160. 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).

    Article  PubMed  PubMed Central  Google Scholar 

  161. 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).

    Article  CAS  Google Scholar 

  162. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  163. O'Keefe, J. & Burgess, N. Geometric determinants of the place fields of hippocampal neurons. Nature 381, 425–428 (1996).

    Article  CAS  PubMed  Google Scholar 

  164. 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).

    Article  CAS  PubMed  Google Scholar 

  165. 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).

    Article  CAS  PubMed  Google Scholar 

  166. Wiener, S. I., Paul, C. A. & Eichenbaum, H. Spatial and behavioral correlates of hippocampal neuronal activity. J. Neurosci. 9, 2737–2763 (1989).

    Article  CAS  PubMed  Google Scholar 

  167. 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).

    Article  CAS  PubMed  Google Scholar 

  168. Bjerknes, T. L., Moser, E. I. & Moser, M.-B. Representation of geometric borders in the developing rat. Neuron 82, 71–78 (2014).

    Article  CAS  PubMed  Google Scholar 

  169. Jia, H., Rochefort, N. L. & Konnerth, A. Dendritic organization of sensory input to cortical neurons in vivo. Nature 464, 1307–1312 (2010).

    Article  CAS  PubMed  Google Scholar 

  170. Chen, T. W. et al. Ultrasensitive fluorescent proteins for imaging neuronal activity. Nature 499, 295–300 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  171. Singer, W. Synchronization of cortical activity and its putative role in information processing and learning. Annu. Rev. Physiol. 55, 349–374 (1993).

    Article  CAS  PubMed  Google Scholar 

  172. Fries, P. Neuronal gamma-band synchronization as a fundamental process in cortical computation. Annu. Rev. Neurosci. 32, 209–224 (2009).

    Article  CAS  PubMed  Google Scholar 

  173. Colgin, L. L. et al. Frequency of gamma oscillations routes flow of information in the hippocampus. Nature 462, 353–357 (2009).

    Article  CAS  PubMed  Google Scholar 

  174. 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).

  175. Ahmed, O. J. & Mehta, M. R. Running speed alters the frequency of hippocampal gamma oscillations. J. Neurosci. 32, 7373–7383 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  176. 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).

    Article  PubMed  Google Scholar 

  177. 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).

    Article  PubMed  Google Scholar 

  178. 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).

    Article  PubMed  Google Scholar 

  179. 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).

    Article  CAS  PubMed  Google Scholar 

  180. Sperry, R. W. Chemoaffinity in the orderly growth of nerve fiber patterns and connections. Proc. Natl Acad. Sci. USA 50, 703–710 (1963).

    Article  CAS  PubMed  Google Scholar 

  181. Penfield, W. & Rasmussen, T. The Cerebral Cortex of Man. A Clinical Study of Localization of Function (Macmillan, 1950).

    Google Scholar 

  182. 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).

    Article  CAS  PubMed  Google Scholar 

  183. Katsuki, Y., Sumi, T., Uchiyama, H. & Watanabe, T. Electric responses of auditory neurons in cat to sound stimulation. J. Neurophysiol. 21, 569–588 (1958).

    Article  CAS  PubMed  Google Scholar 

  184. 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).

    Article  CAS  Google Scholar 

  185. Hubel, D. H. & Wiesel, T. Sequence regularity and geometry of orientation columns in the monkey striate cortex. J. Comp. Neurol. 158, 267–294 (1974).

    Article  CAS  PubMed  Google Scholar 

  186. Blasdel, G. G. & Salama, G. Voltage sensitive dyes reveal a modular organization in monkey striate cortex. Nature 321, 579–585 (1986).

    Article  CAS  PubMed  Google Scholar 

  187. Mooser, F., Bosking, W. H. & Fitzpatrick, D. A morphological basis for orientation tuning in primary visual cortex. Nature Neurosci. 7, 872–879 (2004).

    Article  CAS  PubMed  Google Scholar 

  188. 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).

    Article  CAS  PubMed  Google Scholar 

  189. 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).

    Article  CAS  PubMed  Google Scholar 

  190. 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).

    Article  CAS  PubMed  Google Scholar 

  191. 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).

    Article  CAS  PubMed  Google Scholar 

  192. 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).

    Article  CAS  PubMed  Google Scholar 

  193. 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).

    CAS  PubMed  Google Scholar 

  194. Fujita, I., Tanaka, K., Ito, M. & Cheng, K. Columns for visual features of objects in monkey inferotemporal cortex. Nature 360, 343–346 (1992).

    Article  CAS  PubMed  Google Scholar 

  195. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  196. 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).

    Article  PubMed  Google Scholar 

  197. 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).

    Article  CAS  PubMed  Google Scholar 

  198. Knudsen, E. I. & Konishi, M. A neural map of auditory space in the owl. Science 200, 795–797 (1978).

    Article  CAS  PubMed  Google Scholar 

  199. Knudsen, E. I. & Konishi, M. Mechanisms of sound localization in the barn owl (Tyto alba). J. Comp. Physiol. 133, 13–21 (1979).

    Article  Google Scholar 

  200. 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).

    Article  PubMed  PubMed Central  Google Scholar 

  201. Renart, A., Song, P. & Wang, X. J. Robust spatial working memory through homeostatic synaptic scaling in heterogeneous cortical networks. Neuron 38, 473–485 (2003).

    Article  CAS  PubMed  Google Scholar 

  202. Roudi, Y. & Treves, A. Representing where along with what information in a model of a cortical patch. PLoS Comput. Biol. 4, e1000012 (2007).

    Article  CAS  Google Scholar 

  203. Itskov, V., Hansel, D. & Tsodyks, M. Short-term facilitation may stabilize parametric working memory trace. Front. Comput. Neurosci. 5, 40 (2011).

    Article  PubMed  PubMed Central  Google Scholar 

  204. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  205. Burgess, N. Grid cells and theta as oscillatory interference: theory and predictions. Hippocampus 18, 1157–1174 (2008).

    Article  PubMed  PubMed Central  Google Scholar 

  206. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  207. 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).

    Article  CAS  PubMed  Google Scholar 

  208. 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).

    Article  PubMed  Google Scholar 

  209. 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).

    Article  CAS  PubMed  Google Scholar 

  210. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  211. Giocomo, L. M. et al. Grid cells use HCN1 channels for spatial scaling. Cell 147, 1159–1170 (2011).

    Article  CAS  PubMed  Google Scholar 

  212. Bush, D. & Burgess, N. A hybrid oscillatory interference/continuous attractor network model of grid cell firing. J. Neurosci. 34, 5065–5079 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  213. Barry, C. & Doeller, C. F. 3D mapping in the brain. Science 340, 279–280 (2013).

    Article  CAS  PubMed  Google Scholar 

  214. 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).

    Article  PubMed  PubMed Central  Google Scholar 

  215. Yasuda, M. & Mayford, M. R. CaMKII activation in the entorhinal cortex disrupts previously encoded spatial memory. Neuron 50, 309–318 (2006).

    Article  CAS  PubMed  Google Scholar 

  216. Fenno, L., Yizhar, O. & Deisseroth, K. The development and application of optogenetics. Annu. Rev. Neurosci. 34, 389–412 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  217. Alexander, G. M. et al. Remote control of neuronal activity in transgenic mice expressing evolved G protein-coupled receptors. Neuron 63, 27–39 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  218. Miyawaki, A. et al. Fluorescent indicators for Ca2+ based on green fluorescent proteins and calmodulin. Nature 388, 882–887 (1997).

    Article  CAS  PubMed  Google Scholar 

  219. 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).

    Article  CAS  PubMed  Google Scholar 

  220. Heim, N. et al. Improved calcium imaging in transgenic mice expressing a troponin C-based biosensor. Nature Methods 4, 127–129 (2007).

    Article  CAS  PubMed  Google Scholar 

  221. Mank, M. et al. A genetically encoded calcium indicator for chronic in vivo two-photon imaging. Nature Methods 5, 805–811 (2008).

    Article  CAS  PubMed  Google Scholar 

  222. Tian, L. et al. Imaging neural activity in worms, flies and mice with improved GCaMP calcium indicators. Nature Methods 6, 875–881 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  223. Looger, L. L. & Griesbeck, O. Genetically encoded neural activity indicators. Curr. Opin. Neurobiol. 22, 18–23 (2012).

    Article  CAS  PubMed  Google Scholar 

  224. 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).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  225. Taniguchi, H. et al. A resource of Cre driver lines for genetic targeting of GABAergic neurons in cerebral cortex. Neuron 71, 995–1013 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  226. 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).

    Article  CAS  PubMed  Google Scholar 

  227. Wickersham, I. R. et al. Monosynaptic restriction of transsynaptic tracing from single, genetically targeted neurons. Neuron 53, 639–647 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  228. 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).

    Article  CAS  PubMed  Google Scholar 

  229. Moser, E. I. & Moser, M.-B. Grid cells and neural coding in high-end cortices. Neuron 80, 765–774 (2013).

    Article  CAS  PubMed  Google Scholar 

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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.

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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.

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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

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